118
Surprises in the Magneto-resistance
measurements on Graphite
Sambuddha Sanyal
Physics Department
IISc
October 16, 2014
The Experiment
�Most of the experiments are very simple. Given a high magnetic�eld, typically from a commercial superconductive magnet, andgiven a temperature close to absolute zero, typically 1/100 to1/10 of a degree Kelvin from a commercially available heliumrefrigerator, only a battery, a resistor, and a voltmeter arerequired. In reality one employs somewhat more sophisticatedinstrumentation to increase the data accumulation rate� -H. L.Stormer (Nobel Lecture: The fractional quantum Hall e�ect)
System: Graphite, 3D semi metal ,stacked layers ofgraphene
Probe: A magnetic �eld (B) is applied along stackingdirection ( c-axis)
Response: Measure both in-plane(Ra) and out-of plane(Rc)resistance with B and T.
The Experiment
�Most of the experiments are very simple. Given a high magnetic�eld, typically from a commercial superconductive magnet, andgiven a temperature close to absolute zero, typically 1/100 to1/10 of a degree Kelvin from a commercially available heliumrefrigerator, only a battery, a resistor, and a voltmeter arerequired. In reality one employs somewhat more sophisticatedinstrumentation to increase the data accumulation rate� -H. L.Stormer (Nobel Lecture: The fractional quantum Hall e�ect)
System: Graphite, 3D semi metal ,stacked layers ofgraphene
Probe: A magnetic �eld (B) is applied along stackingdirection ( c-axis)
Response: Measure both in-plane(Ra) and out-of plane(Rc)resistance with B and T.
The Experiment
�Most of the experiments are very simple. Given a high magnetic�eld, typically from a commercial superconductive magnet, andgiven a temperature close to absolute zero, typically 1/100 to1/10 of a degree Kelvin from a commercially available heliumrefrigerator, only a battery, a resistor, and a voltmeter arerequired. In reality one employs somewhat more sophisticatedinstrumentation to increase the data accumulation rate� -H. L.Stormer (Nobel Lecture: The fractional quantum Hall e�ect)
System: Graphite, 3D semi metal ,stacked layers ofgraphene
Probe: A magnetic �eld (B) is applied along stackingdirection ( c-axis)
Response: Measure both in-plane(Ra) and out-of plane(Rc)resistance with B and T.
The Experiment
�Most of the experiments are very simple. Given a high magnetic�eld, typically from a commercial superconductive magnet, andgiven a temperature close to absolute zero, typically 1/100 to1/10 of a degree Kelvin from a commercially available heliumrefrigerator, only a battery, a resistor, and a voltmeter arerequired. In reality one employs somewhat more sophisticatedinstrumentation to increase the data accumulation rate� -H. L.Stormer (Nobel Lecture: The fractional quantum Hall e�ect)
System: Graphite, 3D semi metal ,stacked layers ofgraphene
Probe: A magnetic �eld (B) is applied along stackingdirection ( c-axis)
Response: Measure both in-plane(Ra) and out-of plane(Rc)resistance with B and T.
Goal of this talk
Temperature range0.4K < T < 7K
Magnetic �eld range0T < B < 80T
Pulsed Magnetic �eld
Measure Rc and Ra
Metallic Ra and insulatingRa
Suggesting Two phasetransition in Rc
PRL 110, 266601 (2013)
Goal of this talk
Temperature range0.4K < T < 7K
Magnetic �eld range0T < B < 80T
Pulsed Magnetic �eld
Measure Rc and Ra
Metallic Ra and insulatingRa
Suggesting Two phasetransition in Rc
PRL 110, 266601 (2013)
Goal of this talk
Temperature range0.4K < T < 7K
Magnetic �eld range0T < B < 80T
Pulsed Magnetic �eld
Measure Rc and Ra
Metallic Ra and insulatingRa
Suggesting Two phasetransition in Rc
PRL 110, 266601 (2013)
Goal of this talk
Temperature range0.4K < T < 7K
Magnetic �eld range0T < B < 80T
Pulsed Magnetic �eld
Measure Rc and Ra
Metallic Ra and insulatingRa
Suggesting Two phasetransition in Rc
PRL 110, 266601 (2013)
Goal of this talk
Temperature range0.4K < T < 7K
Magnetic �eld range0T < B < 80T
Pulsed Magnetic �eld
Measure Rc and Ra
Metallic Ra and insulatingRa
Suggesting Two phasetransition in Rc
PRL 110, 266601 (2013)
Goal of this talk
Temperature range0.4K < T < 7K
Magnetic �eld range0T < B < 80T
Pulsed Magnetic �eld
Measure Rc and Ra
Metallic Ra and insulatingRa
Suggesting Two phasetransition in Rc
PRL 110, 266601 (2013)
Goal of this talk
Temperature range0.4K < T < 7K
Magnetic �eld range0T < B < 80T
Pulsed Magnetic �eld
Measure Rc and Ra
Metallic Ra and insulatingRa
Suggesting Two phasetransition in Rc
PRL 110, 266601 (2013)
Goal of this talk
Temperature range0.4K < T < 7K
Magnetic �eld range0T < B < 80T
Pulsed Magnetic �eld
Measure Rc and Ra
Metallic Ra and insulatingRa
Suggesting Two phasetransition in Rc
PRL 110, 266601 (2013)
This talk
What happens when we apply a magnetic �eld on a 2Dmaterial ? 3D ? or stacked layers of 2D?
Why graphite? What is graphite?
What really happens to graphite in magnetic �eld?
What happens when that magnetic �eld is stronger?
What is the role of temperature?
Unexpected features
Overview and Comments
This talk
What happens when we apply a magnetic �eld on a 2Dmaterial ? 3D ? or stacked layers of 2D?
Why graphite? What is graphite?
What really happens to graphite in magnetic �eld?
What happens when that magnetic �eld is stronger?
What is the role of temperature?
Unexpected features
Overview and Comments
This talk
What happens when we apply a magnetic �eld on a 2Dmaterial ? 3D ? or stacked layers of 2D?
Why graphite? What is graphite?
What really happens to graphite in magnetic �eld?
What happens when that magnetic �eld is stronger?
What is the role of temperature?
Unexpected features
Overview and Comments
This talk
What happens when we apply a magnetic �eld on a 2Dmaterial ? 3D ? or stacked layers of 2D?
Why graphite? What is graphite?
What really happens to graphite in magnetic �eld?
What happens when that magnetic �eld is stronger?
What is the role of temperature?
Unexpected features
Overview and Comments
This talk
What happens when we apply a magnetic �eld on a 2Dmaterial ? 3D ? or stacked layers of 2D?
Why graphite? What is graphite?
What really happens to graphite in magnetic �eld?
What happens when that magnetic �eld is stronger?
What is the role of temperature?
Unexpected features
Overview and Comments
This talk
What happens when we apply a magnetic �eld on a 2Dmaterial ? 3D ? or stacked layers of 2D?
Why graphite? What is graphite?
What really happens to graphite in magnetic �eld?
What happens when that magnetic �eld is stronger?
What is the role of temperature?
Unexpected features
Overview and Comments
This talk
What happens when we apply a magnetic �eld on a 2Dmaterial ? 3D ? or stacked layers of 2D?
Why graphite? What is graphite?
What really happens to graphite in magnetic �eld?
What happens when that magnetic �eld is stronger?
What is the role of temperature?
Unexpected features
Overview and Comments
This talk
What happens when we apply a magnetic �eld on a 2Dmaterial ? 3D ? or stacked layers of 2D?
Why graphite? What is graphite?
What really happens to graphite in magnetic �eld?
What happens when that magnetic �eld is stronger?
What is the role of temperature?
Unexpected features
Overview and Comments
Free electrons in 2D
∂2ψ
∂x2+
(∂
∂y+ ieBx
)2ψ + 2meEψ = 0
En = ωc(n + 12
), ωc = eBm
IQHE, FQHE
Free electrons in 2D
∂2ψ
∂x2+
(∂
∂y+ ieBx
)2ψ + 2meEψ = 0
En = ωc(n + 12
), ωc = eBm
IQHE, FQHE
Free electrons in 3D
∂2
∂x2ψ +
(∂
∂y+ ieBx
)2ψ +
∂2
∂z2ψ + 2meEψ = 0
En = ωc(n + 12
) + 12me
k2z , ωc = eBm
Free electrons in 3D
∂2
∂x2ψ +
(∂
∂y+ ieBx
)2ψ +
∂2
∂z2ψ + 2meEψ = 0
En = ωc(n + 12
) + 12me
k2z , ωc = eBm
Crystal electrons in 3D
Bohr-Sommer�eld∮pdr = 2π(N + 1
2)
EOMdr
dt= ∂E(k)
∂k ,dk
dt= e
dr
dt× B
SN = 2πeB(N + 12
)
∆S = 2πeB
SdH oscillation
Crystal electrons in 3D
Bohr-Sommer�eld∮pdr = 2π(N + 1
2)
EOMdr
dt= ∂E(k)
∂k ,dk
dt= e
dr
dt× B
SN = 2πeB(N + 12
)
∆S = 2πeB
SdH oscillation
Crystal electrons in 3D
Bohr-Sommer�eld∮pdr = 2π(N + 1
2)
EOMdr
dt= ∂E(k)
∂k ,dk
dt= e
dr
dt× B
SN = 2πeB(N + 12
)
∆S = 2πeB
SdH oscillation
Crystal electrons in 3D
Bohr-Sommer�eld∮pdr = 2π(N + 1
2)
EOMdr
dt= ∂E(k)
∂k ,dk
dt= e
dr
dt× B
SN = 2πeB(N + 12
)
∆S = 2πeB
SdH oscillation
Crystal electrons in 3D
Bohr-Sommer�eld∮pdr = 2π(N + 1
2)
EOMdr
dt= ∂E(k)
∂k ,dk
dt= e
dr
dt× B
SN = 2πeB(N + 12
)
∆S = 2πeB
SdH oscillation
Crystal electrons in 3D
Bohr-Sommer�eld∮pdr = 2π(N + 1
2)
EOMdr
dt= ∂E(k)
∂k ,dk
dt= e
dr
dt× B
SN = 2πeB(N + 12
)
∆S = 2πeB
SdH oscillation
Why Graphite?
Goal: explore 3D electronic system in the lowest landaulevels (quantum limit)
In the case of the copper, the magnetic �eld required toreach the quantum limit would be several 10kT!
Lower in the case of a semi-metal such as Bismuth andGraphite(7.5T) for which this limit is reached for a �eld offew Tesla.
Small carrier masses, high mobilities, and low carrierconcentrations
Bismuth Landau level , FS explored by thermoelectricmeasurements upto 28T
Why Graphite?
Goal: explore 3D electronic system in the lowest landaulevels (quantum limit)
In the case of the copper, the magnetic �eld required toreach the quantum limit would be several 10kT!
Lower in the case of a semi-metal such as Bismuth andGraphite(7.5T) for which this limit is reached for a �eld offew Tesla.
Small carrier masses, high mobilities, and low carrierconcentrations
Bismuth Landau level , FS explored by thermoelectricmeasurements upto 28T
Why Graphite?
Goal: explore 3D electronic system in the lowest landaulevels (quantum limit)
In the case of the copper, the magnetic �eld required toreach the quantum limit would be several 10kT!
Lower in the case of a semi-metal such as Bismuth andGraphite(7.5T) for which this limit is reached for a �eld offew Tesla.
Small carrier masses, high mobilities, and low carrierconcentrations
Bismuth Landau level , FS explored by thermoelectricmeasurements upto 28T
Why Graphite?
Goal: explore 3D electronic system in the lowest landaulevels (quantum limit)
In the case of the copper, the magnetic �eld required toreach the quantum limit would be several 10kT!
Lower in the case of a semi-metal such as Bismuth andGraphite(7.5T) for which this limit is reached for a �eld offew Tesla.
Small carrier masses, high mobilities, and low carrierconcentrations
Bismuth Landau level , FS explored by thermoelectricmeasurements upto 28T
Why Graphite?
Goal: explore 3D electronic system in the lowest landaulevels (quantum limit)
In the case of the copper, the magnetic �eld required toreach the quantum limit would be several 10kT!
Lower in the case of a semi-metal such as Bismuth andGraphite(7.5T) for which this limit is reached for a �eld offew Tesla.
Small carrier masses, high mobilities, and low carrierconcentrations
Bismuth Landau level , FS explored by thermoelectricmeasurements upto 28T
Why Graphite?
Goal: explore 3D electronic system in the lowest landaulevels (quantum limit)
In the case of the copper, the magnetic �eld required toreach the quantum limit would be several 10kT!
Lower in the case of a semi-metal such as Bismuth andGraphite(7.5T) for which this limit is reached for a �eld offew Tesla.
Small carrier masses, high mobilities, and low carrierconcentrations
Bismuth Landau level , FS explored by thermoelectricmeasurements upto 28T
What is Graphite?
Stacked layer of graphene
Bound by weak Van dar waal force
Stacking can be di�erent: Kish and HOPG
Described by SWM Hamiltonian (Slonczewski, Weiss,McClure-1957,58)
What is Graphite?
Stacked layer of graphene
Bound by weak Van dar waal force
Stacking can be di�erent: Kish and HOPG
Described by SWM Hamiltonian (Slonczewski, Weiss,McClure-1957,58)
Quantum oscillation in Graphite
Soule, McClure, Smith,
1964
0 < B < 7.3T, SdH
oscillations with
frequencies 6.6 T
(electron pocket) and
4.8 T (majority hole
pocket)
Quantum oscillation in Graphite
Soule, McClure, Smith,
1964
0 < B < 7.3T, SdH
oscillations with
frequencies 6.6 T
(electron pocket) and
4.8 T (majority hole
pocket)
Quantum oscillation in Graphite
Soule, McClure, Smith,
1964
0 < B < 7.3T, SdH
oscillations with
frequencies 6.6 T
(electron pocket) and
4.8 T (majority hole
pocket)
History of magneto-resistance measurements on graphite
B > 7.3T, quantum limit, a linear �eld dependence of themagneto resistance (McClure and Spry, 1968 ) is observed.
Explained as a magnetic-�eld dependent scattering rangefor the ionized impurity scattering mechanism, thedominant scattering mechanism at low temperatures.
B > 12T, the magneto resistance starts to saturate (Brandtet al. and Woollam et al., 1975)
Saturation of the magneto resistance: magnetic freeze-oute�ect of the ionized impurity scattering centers.
Measurements up to 40 T using a pulsed magnet and foundabrupt increase in magneto resistance, later done understatic �eld(Tanuma et al, 1981).
Out of plane measurement and two phase transition(Yaguchi and Singleton ,1998)
History of magneto-resistance measurements on graphite
B > 7.3T, quantum limit, a linear �eld dependence of themagneto resistance (McClure and Spry, 1968 ) is observed.
Explained as a magnetic-�eld dependent scattering rangefor the ionized impurity scattering mechanism, thedominant scattering mechanism at low temperatures.
B > 12T, the magneto resistance starts to saturate (Brandtet al. and Woollam et al., 1975)
Saturation of the magneto resistance: magnetic freeze-oute�ect of the ionized impurity scattering centers.
Measurements up to 40 T using a pulsed magnet and foundabrupt increase in magneto resistance, later done understatic �eld(Tanuma et al, 1981).
Out of plane measurement and two phase transition(Yaguchi and Singleton ,1998)
History of magneto-resistance measurements on graphite
B > 7.3T, quantum limit, a linear �eld dependence of themagneto resistance (McClure and Spry, 1968 ) is observed.
Explained as a magnetic-�eld dependent scattering rangefor the ionized impurity scattering mechanism, thedominant scattering mechanism at low temperatures.
B > 12T, the magneto resistance starts to saturate (Brandtet al. and Woollam et al., 1975)
Saturation of the magneto resistance: magnetic freeze-oute�ect of the ionized impurity scattering centers.
Measurements up to 40 T using a pulsed magnet and foundabrupt increase in magneto resistance, later done understatic �eld(Tanuma et al, 1981).
Out of plane measurement and two phase transition(Yaguchi and Singleton ,1998)
History of magneto-resistance measurements on graphite
B > 7.3T, quantum limit, a linear �eld dependence of themagneto resistance (McClure and Spry, 1968 ) is observed.
Explained as a magnetic-�eld dependent scattering rangefor the ionized impurity scattering mechanism, thedominant scattering mechanism at low temperatures.
B > 12T, the magneto resistance starts to saturate (Brandtet al. and Woollam et al., 1975)
Saturation of the magneto resistance: magnetic freeze-oute�ect of the ionized impurity scattering centers.
Measurements up to 40 T using a pulsed magnet and foundabrupt increase in magneto resistance, later done understatic �eld(Tanuma et al, 1981).
Out of plane measurement and two phase transition(Yaguchi and Singleton ,1998)
History of magneto-resistance measurements on graphite
B > 7.3T, quantum limit, a linear �eld dependence of themagneto resistance (McClure and Spry, 1968 ) is observed.
Explained as a magnetic-�eld dependent scattering rangefor the ionized impurity scattering mechanism, thedominant scattering mechanism at low temperatures.
B > 12T, the magneto resistance starts to saturate (Brandtet al. and Woollam et al., 1975)
Saturation of the magneto resistance: magnetic freeze-oute�ect of the ionized impurity scattering centers.
Measurements up to 40 T using a pulsed magnet and foundabrupt increase in magneto resistance, later done understatic �eld(Tanuma et al, 1981).
Out of plane measurement and two phase transition(Yaguchi and Singleton ,1998)
Indications of electronic phase transitions
Tanuma et al, 1981
Yaguchi and Singleton,1998
Understanding Magneto-resistance measurement in 3D
Su�ciently strong B: strong enough to such that only thelowest landau levels are important.
Celli and Mermin(1965), Yoshioka, Fukuyama (1978, 1981),Halperin(1981), McDonald and Brant(1975), Biagini et. al.(2001) etc.
Understanding Magneto-resistance measurement in 3D
Su�ciently strong B: strong enough to such that only thelowest landau levels are important.
Celli and Mermin(1965), Yoshioka, Fukuyama (1978, 1981),Halperin(1981), McDonald and Brant(1975), Biagini et. al.(2001) etc.
Understanding Magneto-resistance measurement in 3D
Su�ciently strong B: strong enough to such that only thelowest landau levels are important.
Celli and Mermin(1965), Yoshioka, Fukuyama (1978, 1981),Halperin(1981), McDonald and Brant(1975), Biagini et. al.(2001) etc.
FS Nesting in 3DRecap 1D CDW
En =ωc(n + 1
2) + 1
2me
k2z :E�ectively 1D.
2kF nesting
CDW ⇒ gap
FS Nesting in 3DRecap 1D CDW
En =ωc(n + 1
2) + 1
2me
k2z :E�ectively 1D.
2kF nesting
CDW ⇒ gap
FS Nesting in 3DRecap 1D CDW
En =ωc(n + 1
2) + 1
2me
k2z :E�ectively 1D.
2kF nesting
CDW ⇒ gap
FS Nesting in 3DRecap 1D CDW
En =ωc(n + 1
2) + 1
2me
k2z :E�ectively 1D.
2kF nesting
CDW ⇒ gap
Theoretical Model
One type of spinful carrier, isotropic e�ective mass, in anuniform positive background, in a magnetic �eld less thanthe critical values needed to completely polarize
Hartree-Fock calculation with screened coulomb interaction
At su�ciently low temperature the gas is unstable to SDWwith wavevector chosen to span the FS in the direction of B
Attributed to 1D nature of dispersion
No matter how small is the SDW, it will open a gap over a�nite region of FS
Theoretical Model
One type of spinful carrier, isotropic e�ective mass, in anuniform positive background, in a magnetic �eld less thanthe critical values needed to completely polarize
Hartree-Fock calculation with screened coulomb interaction
At su�ciently low temperature the gas is unstable to SDWwith wavevector chosen to span the FS in the direction of B
Attributed to 1D nature of dispersion
No matter how small is the SDW, it will open a gap over a�nite region of FS
Theoretical Model
One type of spinful carrier, isotropic e�ective mass, in anuniform positive background, in a magnetic �eld less thanthe critical values needed to completely polarize
Hartree-Fock calculation with screened coulomb interaction
At su�ciently low temperature the gas is unstable to SDWwith wavevector chosen to span the FS in the direction of B
Attributed to 1D nature of dispersion
No matter how small is the SDW, it will open a gap over a�nite region of FS
Theoretical Model
One type of spinful carrier, isotropic e�ective mass, in anuniform positive background, in a magnetic �eld less thanthe critical values needed to completely polarize
Hartree-Fock calculation with screened coulomb interaction
At su�ciently low temperature the gas is unstable to SDWwith wavevector chosen to span the FS in the direction of B
Attributed to 1D nature of dispersion
No matter how small is the SDW, it will open a gap over a�nite region of FS
Theoretical Model
One type of spinful carrier, isotropic e�ective mass, in anuniform positive background, in a magnetic �eld less thanthe critical values needed to completely polarize
Hartree-Fock calculation with screened coulomb interaction
At su�ciently low temperature the gas is unstable to SDWwith wavevector chosen to span the FS in the direction of B
Attributed to 1D nature of dispersion
No matter how small is the SDW, it will open a gap over a�nite region of FS
Theoretical Model
One type of spinful carrier, isotropic e�ective mass, in anuniform positive background, in a magnetic �eld less thanthe critical values needed to completely polarize
Hartree-Fock calculation with screened coulomb interaction
At su�ciently low temperature the gas is unstable to SDWwith wavevector chosen to span the FS in the direction of B
Attributed to 1D nature of dispersion
No matter how small is the SDW, it will open a gap over a�nite region of FS
Theoretical Model
What if the magnetic �eld is stronger such that theelectrons are completely spin polarized → no SDW
Depending on the parameters CDW can occur, predictedsimultaneous occurrence of CDW with wave vectors inseveral directions: ground state winger crystal
In a model with equivalent electron valleys, one can have aVDW: two CDW with 180 degree phase di�erence formedby electrons of di�erent valleys.
In all above the ground state has lower translationalsymmetry than original crystal
The broken symmetry is manifested in one or morefollowing quantities: e-density, spin-density, orbital electroncurrent, spin current.
Theoretical Model
What if the magnetic �eld is stronger such that theelectrons are completely spin polarized → no SDW
Depending on the parameters CDW can occur, predictedsimultaneous occurrence of CDW with wave vectors inseveral directions: ground state winger crystal
In a model with equivalent electron valleys, one can have aVDW: two CDW with 180 degree phase di�erence formedby electrons of di�erent valleys.
In all above the ground state has lower translationalsymmetry than original crystal
The broken symmetry is manifested in one or morefollowing quantities: e-density, spin-density, orbital electroncurrent, spin current.
Theoretical Model
What if the magnetic �eld is stronger such that theelectrons are completely spin polarized → no SDW
Depending on the parameters CDW can occur, predictedsimultaneous occurrence of CDW with wave vectors inseveral directions: ground state winger crystal
In a model with equivalent electron valleys, one can have aVDW: two CDW with 180 degree phase di�erence formedby electrons of di�erent valleys.
In all above the ground state has lower translationalsymmetry than original crystal
The broken symmetry is manifested in one or morefollowing quantities: e-density, spin-density, orbital electroncurrent, spin current.
Theoretical Model
What if the magnetic �eld is stronger such that theelectrons are completely spin polarized → no SDW
Depending on the parameters CDW can occur, predictedsimultaneous occurrence of CDW with wave vectors inseveral directions: ground state winger crystal
In a model with equivalent electron valleys, one can have aVDW: two CDW with 180 degree phase di�erence formedby electrons of di�erent valleys.
In all above the ground state has lower translationalsymmetry than original crystal
The broken symmetry is manifested in one or morefollowing quantities: e-density, spin-density, orbital electroncurrent, spin current.
Theoretical Model
What if the magnetic �eld is stronger such that theelectrons are completely spin polarized → no SDW
Depending on the parameters CDW can occur, predictedsimultaneous occurrence of CDW with wave vectors inseveral directions: ground state winger crystal
In a model with equivalent electron valleys, one can have aVDW: two CDW with 180 degree phase di�erence formedby electrons of di�erent valleys.
In all above the ground state has lower translationalsymmetry than original crystal
The broken symmetry is manifested in one or morefollowing quantities: e-density, spin-density, orbital electroncurrent, spin current.
Theoretical Model
What if the magnetic �eld is stronger such that theelectrons are completely spin polarized → no SDW
Depending on the parameters CDW can occur, predictedsimultaneous occurrence of CDW with wave vectors inseveral directions: ground state winger crystal
In a model with equivalent electron valleys, one can have aVDW: two CDW with 180 degree phase di�erence formedby electrons of di�erent valleys.
In all above the ground state has lower translationalsymmetry than original crystal
The broken symmetry is manifested in one or morefollowing quantities: e-density, spin-density, orbital electroncurrent, spin current.
Signature of instability
CDW /SDW/ VDW?
If SDW is pinned in crystal, because of interaction with thecrystal or with an arbitrarily small density of impurities ,electrical resistance will be in�nite for an wave vectorparallel to SDW.
This direction is parallel to the magnetic �eld if carriershave isotropic mass tensor. Q = n/eB
Current �ow perpendicular to B will remain una�ected anddissipation less. ρxy = B/ne
σxy = Qe2
Signature of instability
CDW /SDW/ VDW?
If SDW is pinned in crystal, because of interaction with thecrystal or with an arbitrarily small density of impurities ,electrical resistance will be in�nite for an wave vectorparallel to SDW.
This direction is parallel to the magnetic �eld if carriershave isotropic mass tensor. Q = n/eB
Current �ow perpendicular to B will remain una�ected anddissipation less. ρxy = B/ne
σxy = Qe2
Signature of instability
CDW /SDW/ VDW?
If SDW is pinned in crystal, because of interaction with thecrystal or with an arbitrarily small density of impurities ,electrical resistance will be in�nite for an wave vectorparallel to SDW.
This direction is parallel to the magnetic �eld if carriershave isotropic mass tensor. Q = n/eB
Current �ow perpendicular to B will remain una�ected anddissipation less. ρxy = B/ne
σxy = Qe2
Signature of instability
CDW /SDW/ VDW?
If SDW is pinned in crystal, because of interaction with thecrystal or with an arbitrarily small density of impurities ,electrical resistance will be in�nite for an wave vectorparallel to SDW.
This direction is parallel to the magnetic �eld if carriershave isotropic mass tensor. Q = n/eB
Current �ow perpendicular to B will remain una�ected anddissipation less. ρxy = B/ne
σxy = Qe2
Result -1Rc vs Ra
Below transition: Rc << Ra ⇒ Lorentzforce.
Sensitivity if c-axis transport: Ra lessthan factor of 2, Rc it is 3 orders ofmagnitude.
Above 53T: Rc increases , Ra decreases;temperature dependence.
Only known 1D system: activatedconductivity along one axis coexistswith metallic conductivityperpendicular to it.
Result -1Rc vs Ra
Below transition: Rc << Ra ⇒ Lorentzforce.
Sensitivity if c-axis transport: Ra lessthan factor of 2, Rc it is 3 orders ofmagnitude.
Above 53T: Rc increases , Ra decreases;temperature dependence.
Only known 1D system: activatedconductivity along one axis coexistswith metallic conductivityperpendicular to it.
Result -1Rc vs Ra
Below transition: Rc << Ra ⇒ Lorentzforce.
Sensitivity if c-axis transport: Ra lessthan factor of 2, Rc it is 3 orders ofmagnitude.
Above 53T: Rc increases , Ra decreases;temperature dependence.
Only known 1D system: activatedconductivity along one axis coexistswith metallic conductivityperpendicular to it.
Result -1Rc vs Ra
Below transition: Rc << Ra ⇒ Lorentzforce.
Sensitivity if c-axis transport: Ra lessthan factor of 2, Rc it is 3 orders ofmagnitude.
Above 53T: Rc increases , Ra decreases;temperature dependence.
Only known 1D system: activatedconductivity along one axis coexistswith metallic conductivityperpendicular to it.
Result -1Rc vs Ra
Below transition: Rc << Ra ⇒ Lorentzforce.
Sensitivity if c-axis transport: Ra lessthan factor of 2, Rc it is 3 orders ofmagnitude.
Above 53T: Rc increases , Ra decreases;temperature dependence.
Only known 1D system: activatedconductivity along one axis coexistswith metallic conductivityperpendicular to it.
Result -2First time identi�cation of two phase transitions
Before this work, the system wasbelieved to reenter its low-�eld stateabove 53T
Motivation to measure Rc at higher�elds (80 T) and lower temperatures(0.44 K).
Rc is enhanced by several orders ofmagnitude in two adjacent yet distinct�eld windows.
Result -2First time identi�cation of two phase transitions
Before this work, the system wasbelieved to reenter its low-�eld stateabove 53T
Motivation to measure Rc at higher�elds (80 T) and lower temperatures(0.44 K).
Rc is enhanced by several orders ofmagnitude in two adjacent yet distinct�eld windows.
Result -2First time identi�cation of two phase transitions
Before this work, the system wasbelieved to reenter its low-�eld stateabove 53T
Motivation to measure Rc at higher�elds (80 T) and lower temperatures(0.44 K).
Rc is enhanced by several orders ofmagnitude in two adjacent yet distinct�eld windows.
Result -2First time identi�cation of two phase transitions
Before this work, the system wasbelieved to reenter its low-�eld stateabove 53T
Motivation to measure Rc at higher�elds (80 T) and lower temperatures(0.44 K).
Rc is enhanced by several orders ofmagnitude in two adjacent yet distinct�eld windows.
Results -3Further probe in nature of Rc and Ra
Cooling leads to activated region
No insulating behavior in Ra at theordered state.
Rc as a function of T, reveals anArrhenius behavior upon the entry tothe ordered state.
2∆[47T] = 2.4 meV and 2∆[64T] = 1.1meV.
Tc[47T] = 7± 0 : 5K andTc[64T] = 3.5± 0.5 K.
2∆/kTc[47T] = 3.9,2∆/kTc[64T] = 3.6
Edge states?
Results -3Further probe in nature of Rc and Ra
Cooling leads to activated region
No insulating behavior in Ra at theordered state.
Rc as a function of T, reveals anArrhenius behavior upon the entry tothe ordered state.
2∆[47T] = 2.4 meV and 2∆[64T] = 1.1meV.
Tc[47T] = 7± 0 : 5K andTc[64T] = 3.5± 0.5 K.
2∆/kTc[47T] = 3.9,2∆/kTc[64T] = 3.6
Edge states?
Results -3Further probe in nature of Rc and Ra
Cooling leads to activated region
No insulating behavior in Ra at theordered state.
Rc as a function of T, reveals anArrhenius behavior upon the entry tothe ordered state.
2∆[47T] = 2.4 meV and 2∆[64T] = 1.1meV.
Tc[47T] = 7± 0 : 5K andTc[64T] = 3.5± 0.5 K.
2∆/kTc[47T] = 3.9,2∆/kTc[64T] = 3.6
Edge states?
Results -3Further probe in nature of Rc and Ra
Cooling leads to activated region
No insulating behavior in Ra at theordered state.
Rc as a function of T, reveals anArrhenius behavior upon the entry tothe ordered state.
2∆[47T] = 2.4 meV and 2∆[64T] = 1.1meV.
Tc[47T] = 7± 0 : 5K andTc[64T] = 3.5± 0.5 K.
2∆/kTc[47T] = 3.9,2∆/kTc[64T] = 3.6
Edge states?
Results -3Further probe in nature of Rc and Ra
Cooling leads to activated region
No insulating behavior in Ra at theordered state.
Rc as a function of T, reveals anArrhenius behavior upon the entry tothe ordered state.
2∆[47T] = 2.4 meV and 2∆[64T] = 1.1meV.
Tc[47T] = 7± 0 : 5K andTc[64T] = 3.5± 0.5 K.
2∆/kTc[47T] = 3.9,2∆/kTc[64T] = 3.6
Edge states?
Results -3Further probe in nature of Rc and Ra
Cooling leads to activated region
No insulating behavior in Ra at theordered state.
Rc as a function of T, reveals anArrhenius behavior upon the entry tothe ordered state.
2∆[47T] = 2.4 meV and 2∆[64T] = 1.1meV.
Tc[47T] = 7± 0 : 5K andTc[64T] = 3.5± 0.5 K.
2∆/kTc[47T] = 3.9,2∆/kTc[64T] = 3.6
Edge states?
Results -3Further probe in nature of Rc and Ra
Cooling leads to activated region
No insulating behavior in Ra at theordered state.
Rc as a function of T, reveals anArrhenius behavior upon the entry tothe ordered state.
2∆[47T] = 2.4 meV and 2∆[64T] = 1.1meV.
Tc[47T] = 7± 0 : 5K andTc[64T] = 3.5± 0.5 K.
2∆/kTc[47T] = 3.9,2∆/kTc[64T] = 3.6
Edge states?
Results -3Further probe in nature of Rc and Ra
Cooling leads to activated region
No insulating behavior in Ra at theordered state.
Rc as a function of T, reveals anArrhenius behavior upon the entry tothe ordered state.
2∆[47T] = 2.4 meV and 2∆[64T] = 1.1meV.
Tc[47T] = 7± 0 : 5K andTc[64T] = 3.5± 0.5 K.
2∆/kTc[47T] = 3.9,2∆/kTc[64T] = 3.6
Edge states?
Results -3Probing the nature of the two phase transitions: Possible scenarios
Two CDWs (per valley) formed in both (n = 0/− 1, ↑) and(n = 0/− 1, ↓).One SDW (per valley) in each electron and hole pocket.
Yaguchi and Singleton: (n = 0, ↑ )and (n = −1, ↓) aredepopulated at 53 T and this destroys the CDW state.
Available LLs would be (n = 0, ↓ ) and (n = 1, ↑): Seconddensity-wave instability along the c axis at 53T.
When B > 53 T, only the two last spin-polarized Landausublevels would remain occupied, reducing the number ofpossible con�gurations for any nesting scenario.
But persistence of a sizable conductivity above 75 T is notcompatible with a total depopulation of all Landausublevels above this �eld.
Results -3Probing the nature of the two phase transitions: Possible scenarios
Two CDWs (per valley) formed in both (n = 0/− 1, ↑) and(n = 0/− 1, ↓).One SDW (per valley) in each electron and hole pocket.
Yaguchi and Singleton: (n = 0, ↑ )and (n = −1, ↓) aredepopulated at 53 T and this destroys the CDW state.
Available LLs would be (n = 0, ↓ ) and (n = 1, ↑): Seconddensity-wave instability along the c axis at 53T.
When B > 53 T, only the two last spin-polarized Landausublevels would remain occupied, reducing the number ofpossible con�gurations for any nesting scenario.
But persistence of a sizable conductivity above 75 T is notcompatible with a total depopulation of all Landausublevels above this �eld.
Results -3Probing the nature of the two phase transitions: Possible scenarios
Two CDWs (per valley) formed in both (n = 0/− 1, ↑) and(n = 0/− 1, ↓).One SDW (per valley) in each electron and hole pocket.
Yaguchi and Singleton: (n = 0, ↑ )and (n = −1, ↓) aredepopulated at 53 T and this destroys the CDW state.
Available LLs would be (n = 0, ↓ ) and (n = 1, ↑): Seconddensity-wave instability along the c axis at 53T.
When B > 53 T, only the two last spin-polarized Landausublevels would remain occupied, reducing the number ofpossible con�gurations for any nesting scenario.
But persistence of a sizable conductivity above 75 T is notcompatible with a total depopulation of all Landausublevels above this �eld.
Results -3Probing the nature of the two phase transitions: Possible scenarios
Two CDWs (per valley) formed in both (n = 0/− 1, ↑) and(n = 0/− 1, ↓).One SDW (per valley) in each electron and hole pocket.
Yaguchi and Singleton: (n = 0, ↑ )and (n = −1, ↓) aredepopulated at 53 T and this destroys the CDW state.
Available LLs would be (n = 0, ↓ ) and (n = 1, ↑): Seconddensity-wave instability along the c axis at 53T.
When B > 53 T, only the two last spin-polarized Landausublevels would remain occupied, reducing the number ofpossible con�gurations for any nesting scenario.
But persistence of a sizable conductivity above 75 T is notcompatible with a total depopulation of all Landausublevels above this �eld.
Results -3Probing the nature of the two phase transitions: Possible scenarios
Two CDWs (per valley) formed in both (n = 0/− 1, ↑) and(n = 0/− 1, ↓).One SDW (per valley) in each electron and hole pocket.
Yaguchi and Singleton: (n = 0, ↑ )and (n = −1, ↓) aredepopulated at 53 T and this destroys the CDW state.
Available LLs would be (n = 0, ↓ ) and (n = 1, ↑): Seconddensity-wave instability along the c axis at 53T.
When B > 53 T, only the two last spin-polarized Landausublevels would remain occupied, reducing the number ofpossible con�gurations for any nesting scenario.
But persistence of a sizable conductivity above 75 T is notcompatible with a total depopulation of all Landausublevels above this �eld.
Results -3Probing the nature of the two phase transitions: Possible scenarios
Two CDWs (per valley) formed in both (n = 0/− 1, ↑) and(n = 0/− 1, ↓).One SDW (per valley) in each electron and hole pocket.
Yaguchi and Singleton: (n = 0, ↑ )and (n = −1, ↓) aredepopulated at 53 T and this destroys the CDW state.
Available LLs would be (n = 0, ↓ ) and (n = 1, ↑): Seconddensity-wave instability along the c axis at 53T.
When B > 53 T, only the two last spin-polarized Landausublevels would remain occupied, reducing the number ofpossible con�gurations for any nesting scenario.
But persistence of a sizable conductivity above 75 T is notcompatible with a total depopulation of all Landausublevels above this �eld.
Results -3Probing the nature of the two phase transitions: Possible scenarios
Two CDWs (per valley) formed in both (n = 0/− 1, ↑) and(n = 0/− 1, ↓).One SDW (per valley) in each electron and hole pocket.
Yaguchi and Singleton: (n = 0, ↑ )and (n = −1, ↓) aredepopulated at 53 T and this destroys the CDW state.
Available LLs would be (n = 0, ↓ ) and (n = 1, ↑): Seconddensity-wave instability along the c axis at 53T.
When B > 53 T, only the two last spin-polarized Landausublevels would remain occupied, reducing the number ofpossible con�gurations for any nesting scenario.
But persistence of a sizable conductivity above 75 T is notcompatible with a total depopulation of all Landausublevels above this �eld.
Proposed scenario
Revise this scenario and assume that atB = 53T only one sub level (instead oftwo) depopulates.
In this case, for B > 53 T, there arethree occupied sublevels and a secondgapped state.
At B = 75 T, the other sub level is depopulated and theordered state is destroyed:The holelike Fermi surface has aslightly smaller cross section than the electronlike one.
In this case, beyond 75 T, the ultimate electron and holeLandau sublevels will remain full, in agreement with the�nite conductivity observed.
Electron correlations modify the SWM spectrum at a highmagnetic �eld!
Proposed scenario
Revise this scenario and assume that atB = 53T only one sub level (instead oftwo) depopulates.
In this case, for B > 53 T, there arethree occupied sublevels and a secondgapped state.
At B = 75 T, the other sub level is depopulated and theordered state is destroyed:The holelike Fermi surface has aslightly smaller cross section than the electronlike one.
In this case, beyond 75 T, the ultimate electron and holeLandau sublevels will remain full, in agreement with the�nite conductivity observed.
Electron correlations modify the SWM spectrum at a highmagnetic �eld!
Proposed scenario
Revise this scenario and assume that atB = 53T only one sub level (instead oftwo) depopulates.
In this case, for B > 53 T, there arethree occupied sublevels and a secondgapped state.
At B = 75 T, the other sub level is depopulated and theordered state is destroyed:The holelike Fermi surface has aslightly smaller cross section than the electronlike one.
In this case, beyond 75 T, the ultimate electron and holeLandau sublevels will remain full, in agreement with the�nite conductivity observed.
Electron correlations modify the SWM spectrum at a highmagnetic �eld!
Proposed scenario
Revise this scenario and assume that atB = 53T only one sub level (instead oftwo) depopulates.
In this case, for B > 53 T, there arethree occupied sublevels and a secondgapped state.
At B = 75 T, the other sub level is depopulated and theordered state is destroyed:The holelike Fermi surface has aslightly smaller cross section than the electronlike one.
In this case, beyond 75 T, the ultimate electron and holeLandau sublevels will remain full, in agreement with the�nite conductivity observed.
Electron correlations modify the SWM spectrum at a highmagnetic �eld!
Proposed scenario
Revise this scenario and assume that atB = 53T only one sub level (instead oftwo) depopulates.
In this case, for B > 53 T, there arethree occupied sublevels and a secondgapped state.
At B = 75 T, the other sub level is depopulated and theordered state is destroyed:The holelike Fermi surface has aslightly smaller cross section than the electronlike one.
In this case, beyond 75 T, the ultimate electron and holeLandau sublevels will remain full, in agreement with the�nite conductivity observed.
Electron correlations modify the SWM spectrum at a highmagnetic �eld!
Proposed scenario
Revise this scenario and assume that atB = 53T only one sub level (instead oftwo) depopulates.
In this case, for B > 53 T, there arethree occupied sublevels and a secondgapped state.
At B = 75 T, the other sub level is depopulated and theordered state is destroyed:The holelike Fermi surface has aslightly smaller cross section than the electronlike one.
In this case, beyond 75 T, the ultimate electron and holeLandau sublevels will remain full, in agreement with the�nite conductivity observed.
Electron correlations modify the SWM spectrum at a highmagnetic �eld!
Note: Sample properties
Results are sample dependent
Kish is expected to have more stacking defect.
Di�erence ρc in the two systems has been a subject ofdebate
Comments
The conduction is metallic within the layers and insulatingperpendicular to the layers.Weak temperature dependence of Ra.The resistivity perpendicular to the layers becomesactivated, below about 6 K, with an energy gap of about2.4 meV=25 K.But charge gap (like in a quasi-one-dimensional CDW) willproduce activated transport in all directions.The results are sample dependent, although qualitativelyconsistent (kish and HOPG).In layered metals it is di�cult to measure the interlayerand intra layer resistivity. Due to impurities, stackingdefects, and contact mis-alignment.Edge states: this paper → interlayer resistivity saturates atlow temperatures (i.e. is no longer activated) is evidence foredge states.Why there is no evidence of the gap in the interlayerresistance. Mixing of interlayer and intra layer currents dueto stacking defects?
Comments
The conduction is metallic within the layers and insulatingperpendicular to the layers.Weak temperature dependence of Ra.The resistivity perpendicular to the layers becomesactivated, below about 6 K, with an energy gap of about2.4 meV=25 K.But charge gap (like in a quasi-one-dimensional CDW) willproduce activated transport in all directions.The results are sample dependent, although qualitativelyconsistent (kish and HOPG).In layered metals it is di�cult to measure the interlayerand intra layer resistivity. Due to impurities, stackingdefects, and contact mis-alignment.Edge states: this paper → interlayer resistivity saturates atlow temperatures (i.e. is no longer activated) is evidence foredge states.Why there is no evidence of the gap in the interlayerresistance. Mixing of interlayer and intra layer currents dueto stacking defects?
Comments
The conduction is metallic within the layers and insulatingperpendicular to the layers.Weak temperature dependence of Ra.The resistivity perpendicular to the layers becomesactivated, below about 6 K, with an energy gap of about2.4 meV=25 K.But charge gap (like in a quasi-one-dimensional CDW) willproduce activated transport in all directions.The results are sample dependent, although qualitativelyconsistent (kish and HOPG).In layered metals it is di�cult to measure the interlayerand intra layer resistivity. Due to impurities, stackingdefects, and contact mis-alignment.Edge states: this paper → interlayer resistivity saturates atlow temperatures (i.e. is no longer activated) is evidence foredge states.Why there is no evidence of the gap in the interlayerresistance. Mixing of interlayer and intra layer currents dueto stacking defects?
Comments
The conduction is metallic within the layers and insulatingperpendicular to the layers.Weak temperature dependence of Ra.The resistivity perpendicular to the layers becomesactivated, below about 6 K, with an energy gap of about2.4 meV=25 K.But charge gap (like in a quasi-one-dimensional CDW) willproduce activated transport in all directions.The results are sample dependent, although qualitativelyconsistent (kish and HOPG).In layered metals it is di�cult to measure the interlayerand intra layer resistivity. Due to impurities, stackingdefects, and contact mis-alignment.Edge states: this paper → interlayer resistivity saturates atlow temperatures (i.e. is no longer activated) is evidence foredge states.Why there is no evidence of the gap in the interlayerresistance. Mixing of interlayer and intra layer currents dueto stacking defects?
Comments
The conduction is metallic within the layers and insulatingperpendicular to the layers.Weak temperature dependence of Ra.The resistivity perpendicular to the layers becomesactivated, below about 6 K, with an energy gap of about2.4 meV=25 K.But charge gap (like in a quasi-one-dimensional CDW) willproduce activated transport in all directions.The results are sample dependent, although qualitativelyconsistent (kish and HOPG).In layered metals it is di�cult to measure the interlayerand intra layer resistivity. Due to impurities, stackingdefects, and contact mis-alignment.Edge states: this paper → interlayer resistivity saturates atlow temperatures (i.e. is no longer activated) is evidence foredge states.Why there is no evidence of the gap in the interlayerresistance. Mixing of interlayer and intra layer currents dueto stacking defects?
Comments
The conduction is metallic within the layers and insulatingperpendicular to the layers.Weak temperature dependence of Ra.The resistivity perpendicular to the layers becomesactivated, below about 6 K, with an energy gap of about2.4 meV=25 K.But charge gap (like in a quasi-one-dimensional CDW) willproduce activated transport in all directions.The results are sample dependent, although qualitativelyconsistent (kish and HOPG).In layered metals it is di�cult to measure the interlayerand intra layer resistivity. Due to impurities, stackingdefects, and contact mis-alignment.Edge states: this paper → interlayer resistivity saturates atlow temperatures (i.e. is no longer activated) is evidence foredge states.Why there is no evidence of the gap in the interlayerresistance. Mixing of interlayer and intra layer currents dueto stacking defects?
Comments
The conduction is metallic within the layers and insulatingperpendicular to the layers.Weak temperature dependence of Ra.The resistivity perpendicular to the layers becomesactivated, below about 6 K, with an energy gap of about2.4 meV=25 K.But charge gap (like in a quasi-one-dimensional CDW) willproduce activated transport in all directions.The results are sample dependent, although qualitativelyconsistent (kish and HOPG).In layered metals it is di�cult to measure the interlayerand intra layer resistivity. Due to impurities, stackingdefects, and contact mis-alignment.Edge states: this paper → interlayer resistivity saturates atlow temperatures (i.e. is no longer activated) is evidence foredge states.Why there is no evidence of the gap in the interlayerresistance. Mixing of interlayer and intra layer currents dueto stacking defects?
Comments
The conduction is metallic within the layers and insulatingperpendicular to the layers.Weak temperature dependence of Ra.The resistivity perpendicular to the layers becomesactivated, below about 6 K, with an energy gap of about2.4 meV=25 K.But charge gap (like in a quasi-one-dimensional CDW) willproduce activated transport in all directions.The results are sample dependent, although qualitativelyconsistent (kish and HOPG).In layered metals it is di�cult to measure the interlayerand intra layer resistivity. Due to impurities, stackingdefects, and contact mis-alignment.Edge states: this paper → interlayer resistivity saturates atlow temperatures (i.e. is no longer activated) is evidence foredge states.Why there is no evidence of the gap in the interlayerresistance. Mixing of interlayer and intra layer currents dueto stacking defects?
Comments
The conduction is metallic within the layers and insulatingperpendicular to the layers.Weak temperature dependence of Ra.The resistivity perpendicular to the layers becomesactivated, below about 6 K, with an energy gap of about2.4 meV=25 K.But charge gap (like in a quasi-one-dimensional CDW) willproduce activated transport in all directions.The results are sample dependent, although qualitativelyconsistent (kish and HOPG).In layered metals it is di�cult to measure the interlayerand intra layer resistivity. Due to impurities, stackingdefects, and contact mis-alignment.Edge states: this paper → interlayer resistivity saturates atlow temperatures (i.e. is no longer activated) is evidence foredge states.Why there is no evidence of the gap in the interlayerresistance. Mixing of interlayer and intra layer currents dueto stacking defects?
Review and Future direction
�So what is the most likely explanation? I am not sure.Perhaps, there are no phase transitions. The role of the�eld may be to somehow decouple the layers. There areseveral comparable energy scales involved, particularly dueto the semi-metal character of graphite. Thermodynamicexperiments are desirable. Calculations of the interlayerand interlayer resistance within CDW models need to bedone too�- Ross H. Mckenzie
Chiral surface transport : Corbino geometry (JasonAlicea-CMJC)
Sort out the competition among various candidateinstabilities
The origin of the wildly anisotropic resistance behavior
Review and Future direction
�So what is the most likely explanation? I am not sure.Perhaps, there are no phase transitions. The role of the�eld may be to somehow decouple the layers. There areseveral comparable energy scales involved, particularly dueto the semi-metal character of graphite. Thermodynamicexperiments are desirable. Calculations of the interlayerand interlayer resistance within CDW models need to bedone too�- Ross H. Mckenzie
Chiral surface transport : Corbino geometry (JasonAlicea-CMJC)
Sort out the competition among various candidateinstabilities
The origin of the wildly anisotropic resistance behavior
Review and Future direction
�So what is the most likely explanation? I am not sure.Perhaps, there are no phase transitions. The role of the�eld may be to somehow decouple the layers. There areseveral comparable energy scales involved, particularly dueto the semi-metal character of graphite. Thermodynamicexperiments are desirable. Calculations of the interlayerand interlayer resistance within CDW models need to bedone too�- Ross H. Mckenzie
Chiral surface transport : Corbino geometry (JasonAlicea-CMJC)
Sort out the competition among various candidateinstabilities
The origin of the wildly anisotropic resistance behavior
Review and Future direction
�So what is the most likely explanation? I am not sure.Perhaps, there are no phase transitions. The role of the�eld may be to somehow decouple the layers. There areseveral comparable energy scales involved, particularly dueto the semi-metal character of graphite. Thermodynamicexperiments are desirable. Calculations of the interlayerand interlayer resistance within CDW models need to bedone too�- Ross H. Mckenzie
Chiral surface transport : Corbino geometry (JasonAlicea-CMJC)
Sort out the competition among various candidateinstabilities
The origin of the wildly anisotropic resistance behavior
Review and Future direction
�So what is the most likely explanation? I am not sure.Perhaps, there are no phase transitions. The role of the�eld may be to somehow decouple the layers. There areseveral comparable energy scales involved, particularly dueto the semi-metal character of graphite. Thermodynamicexperiments are desirable. Calculations of the interlayerand interlayer resistance within CDW models need to bedone too�- Ross H. Mckenzie
Chiral surface transport : Corbino geometry (JasonAlicea-CMJC)
Sort out the competition among various candidateinstabilities
The origin of the wildly anisotropic resistance behavior
PunchlinesSuggests two phasetransitions as a function ofmagnetic �eld with variouspossible scenarios.
Possibility of edge states indirections perpendicular tothe layers, vanishinginterlayer resistance at highmagnetic �eld.
Di�erent behavior betweenRc and Ra
Only known 1D systemwith activated conductivityalong one axis coexistswith metallic conductivityperpendicular to it.
Acknowledgement
Thanks to Adhip and Aabhas.
Thank You for your attention.
