Magnetic field effects on the CDW and SC states in -(BEDT-TTF)2KHg(SCN)4

Dieter Andres, Sebastian Jakob, Werner Biberacher, Karl Neumaier and Mark Kartsovnik

Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Garching, Germany

Ilya SheikinLaboratoire National des Champs Magnétiques Intenses, Grenoble, France

Harald MüllerEuropean Synchrotron Radiation Facility, Grenoble, France

Natalia KushchInstitute of Problems of Chemical Physics, Chernogolovka, Russia

c

a

-(BEDT-TTF)2KHg(SCN)4: basic featuresS

CHBEDT-TTF molecule:bis(ethylenedithio)-tetrathiafulvalene

a

b

r||(300K) 10 - 20 mW•cm r/r|| ~ 104 - 105 ra/rc 2

r (300K) / r (1.4K) ~ 102 t ||/t 670 ,coh/|| 2.210-6

T. Mori et al., Bull. Chem. Soc. Jpn. 1990;R. Rousseau et al., J. Phys. I (France) 1996;P. Foury-Leylekian et al., PRB 2010

-(BEDT-TTF)2KHg(SCN)4: basic features

2D Fermi surface

CDW formation at 8 K

Nesting instability of the Fermi surface

Q

very low!!

small DCDW kBTCDW high sensitivity to external conditions: pressure, magnetic field

[P. Foury-Leylekian et al., PRB 2010]

Q+

Q-

CDW in a magnetic field

Pauli paramagnetic effect: suppresses CDW [W. Dieterich & P. Fulde, 1973]

2mBB/hvF

B

Q- < Q+

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.5

1.0

1.5

2.0

TCDW/TCDW(0), exp

Phase diagram of -(BEDT-TTF)2KHg(SCN)4

P. Christ, W. Biberacher, M.K., et al., JETP Lett. 2000

~ 23 T

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

TCDW/TCDW(0)

Theory: A. Buzdin & V. Tugushev, JETP 1983 D. Zanchi et al., PRB 1996; P. Grigoriev & D. Lyubshin , PRB 2005

CDWx

CDW0

NM

CDW in a magnetic field

Orbital effect (requires an imperfectly nested FS): stimulates CDW );2cos(2)cos(2)( yyyyFxF katkatkkv ---k Ftt

4( vt + t ’ ) / F

k y

c

k x

~ t’/ v F

-c

)0'(DWDW tTT

CDW in a magnetic field

Orbital effect (requires an imperfectly nested FS): stimulates CDW );2cos(2)cos(2)( yyyyFxF katkatkkv ---k Ftt

4( vt + t ’ ) / F

k y

c

k x

~ t’/ v F

-c

I n a magnetic field:

zFy Bve

dtdk

;

zFyc Bvae

Dy ~ 1/Bz

electrons become effectively more 1D

lB = 2vF/c

Dy =

ay(4

t /

c )

Real space orbit:

)0'(DWDW tTT

0 2 4 6 8 100

5

10

15

20

25

30

2.3 kbar

3.6 kbar

1.8 kbar

0 kbar

B [T

]T [K]

D. Andres, M.K., et al., PRB 2001

-(BEDT-TTF)2KHg(SCN)4

CDW in a magnetic field

Orbital effect (requires an imperfectly nested FS): stimulates CDW

Theory:

D. Zanchi et al., PRB 1996

0 2 4 6 8 100

5

10

15

20

25

30

2.3 kbar

3.6 kbar

1.8 kbar

0 kbar

B [T

]T [K]

D. Andres, M.K., et al., PRB 2001

-(BEDT-TTF)2KHg(SCN)4

CDW in a magnetic field

Orbital effect (requires an imperfectly nested FS): stimulates CDW

Theory:

D. Zanchi et al., PRB 1996

FICDW at t’ > t’ * ???L. Gor’kov & A. Lebed, J. Phys. Lett. (Paris) 1984

CDW in a magnetic field

Field-induced CDW (FICDW) transitions

The “slow oscillations”

appear at P Pc 2.5 kbar

approximately periodic with 1/B

SdHo

display a weak hysteresis

P = 3 kbar

Positions of the FICDW transitions can be fitted with t 0.5 meV

[A. Lebed, PRL 2010]

CDW in a magnetic field

Field-induced CDW (FICDW) transitions

A. Kornilov et al., PRB 2002

FICDW in -(BEDT-TTF)2KHg(SCN)4

FISDW in (TMTSF)2PF6

A. Lebed, JETP Lett. 2003

FICDW is weaker than FISDW due to the paramagnetic effect!

Superconductivity vs. CDW

0.05 0.10 0.150.0

0.5

1.0

3.03.5 4.0

R(

T )/R

(16

0mK

)

T (K)

P [kbar] =

0.05 0.10 0.150.0

0.5

1.0

2 kbar1.5 kbar

0 kbar

R(

T )/R

(30

0mK

)

T (K)

0.05 0.10 0.15

60.0

63.3

66.7

R (

Ohm

)

T (K)

P = 0 kbar; sample #1

Sample #2:zero resistancebut no Meissner!

0.05 0.10 0.150

1

2

3

R (

Ohm

)T (K)

P = 0 kbar sample #2R

(O

hm)

0 1 2 3 4

0.01

0.1

1

10

SC

Normal metalCDW

T ( K

)P ( kbar )

R 0 R = 0

Resistance at zero field

See also: H. Ito et al., SSC 85 1005 (1993) – inhomogeneous superconductivity at P = 0

Superconductivity vs. CDW

0.1 0.2 0.3 0.435

40

45

50

0.1 0.2 0.3 0.445

50

55

60

65

P = 2 kbar0.5 mA

2 mA

0.05 mA

3.0 kbar

R (W)

T (K)

3.5 kbar

R (W)

T (K)

P =

0 2 445

50

55

60

0 2 435

40

45

50

P = 2 kbar

R (W)

B (mT)

180 mK 160 mK 140 mK 120 mK 100 mK

110 mK 100 mK 95 mK

B (mT)

P = 3.5 kbar

R (W)

Onset of superconductivity

The SC onset temperature is 3 times higher in the SC/CDW coexistence region!

Superconductivity vs. CDW

Onset of superconductivity

0 2 40.0

0.2

0.4

T (K

)

P (kbar)

CDWNormal metal

SC

CDW+SC

R = 0R 0

Superconductivity in a magnetic field; P > Pc

Critical field layers

0 20 40 60 80 1000

1

2

3

4

5

6

B (m

T)

T (mK)

3.0 kbar 3.5 kbar 4.0 kbar

at P = 3 kbar: x||(0) 250 nm

cf. mean free path 1mm

Superconductivity in a magnetic field; P > Pc

Critical field // layers

0 20 40 60 80 100 1200

100

200

300

400

Mag

netic

fiel

d (m

T)

Temperature (mK)

R(T)R(H)

GL: Hc2 (Tc-T )

Hp0: Chandrasekhar-Clogston paramagnetic limit

dHc2/dT 12 T/K

x(0) = 1.0 nm d/2;

x||(0)/ x(0) 250!

1.6Hp0

Superconductivity in a magnetic field; P > Pc

-4 -2 0 2 4

10

100

102 mK 90 mK 40 mK

Hc2

(,T

)/H

c2(0

,T )

90o -

Direct manifestation of the paramagnetic pair-breaking!

Summary

0 2 40.0

0.2

0.4

T (K

)

P (kbar)

CDWNormal metal

SC

-4 -2 0 2 4

10

100

102 mK 90 mK 40 mK

Hc2

(,T

)/H

c2(0

,T )

90o -

CDW state:

• rich phase diagram due to the interplay of

competing Pauli paramagnetic and orbital

effects of magnetic field

SC state:

• at P < Pc: coexists with the CDW state; the

SC onset temperature is drastically increased

in the coexistence region;

• at P > Pc: bulk SC state with a highly

anisotropic Hc2 near Tc(0) and a clear

manifestation of paramagnetic pair-breaking

at H // layers.

CDW in a magnetic field

Field-induced density wave transitions, t’>t’*:

B

ky

a y

kx

Q

-a y

kF-kF

N=

0

1

234567

B

Q x

2k F

Q k NG

G ea B

x F = 2 + ,

= /y z

Qx = 2kF + NG,

G = eayBz/

CDW in a magnetic field

Field-induced CDW (FICDW) transitions

2QP = MG

N = 3,4 2,3

1,2

0,1

0

Commensurate splitting (A. Bjelis et al., 1999; A. Lebed, 2003) “Spin-zero”

2QP = (M + 1/2)G

with M - integer

CDW in a magnetic field

Field-induced CDW (FICDW) transitions

N = 5 4 3 2

1

0

4N = 332

1

2

1

0

0

no Pauli effect (FISDW) Pauli effect on (FICDW)

Qx = 2kF + NG Qx = 2kF QP + NG

G = 2eayBz/QP = 2mBB/vF

CDW in a magnetic field

Field-induced CDW (FICDW) transitions

4N = 332

1

2

1

0

0

no Pauli effect (FISDW) Pauli effect on (FICDW)

Qx = 2kF + NG Qx = 2kF QP + NG

A. Lebed, JETP Lett. 78, 138 (2003)

G = 2eayBz/QP = 2mBB/vF

CDW in a magnetic field

Field-induced CDW (FICDW) transitions

m

cos1222/1

F

BP

veaG

QMy

Spin-zero condition:

vF 1.2105 m/s

The SC onset temperature is 3 times higher in the SC/CDW coexistence region!

Superconductivity vs. CDW

Onset of superconductivity

0 2 40.0

0.2

0.4

T (K

)

P (kbar)

CDWNormal metal

SC

CDW+SC

R = 0R 0 Ginzburg-Levanyuk

parameter:

Gi(2) ~ 10-5

Low Tc weak fluctuations!

Superconductivity in a magnetic field; P > Pc

0

20

40

60

0.05 0.10 0.15 0.20

P = 2 kbar

B:

2.9 mT

0 mT

1.5 mT

15.2 mT

4.4 mT

T (K)

R (W

)

0

20

40

60

0 5 10 15

112 mK80 mK60.8 mK44 mK27 mK23 mK

Bk

P = 2 kbar

B (T)

R

(W)

B (mT)

Critical field layers

Superconductivity in a magnetic field; P > Pc

Critical field // layers

0.04 0.06 0.08 0.10 0.120

5

10

15

20

R (

Ohm

)

T (K)

m0H (mT):

270150210

60

0

Tc