Interfaces with High Temperature Superconductors
Relevance of Interfacial Degrees of Freedom
Thilo Kopp, Universität Augsburg
(2) nanomagnetism at interfaces of HTSCs
(1) electrostatic interface tuning (SuFETs)
Why consider interfaces ? Why consider interfaces ?
• interfaces of correlated electronic systems may provide a new type of complexity;
»reconstruction« of electronic states (?)
• most devices are interface driven
• HTSC cables are not single crystals
─ grain boundaries may control the transport
Electrostatic interface tuning (SUFETs)Electrostatic interface tuning (SUFETs)
theory:
Natalia Pavlenko Verena KoertingQingshan YuanPeter Hirschfeld
experiment:
Jochen Mannhart Gennadij LogvenovChristof Schneider
field doping
? instead of ?
chemical doping
tune phase transitions electrostatically ?
Is electrostatic interface tuning feasible ?
DS-channel: 8 nm polycrystalline YBa2Cu3O7-d
gate barrier: 300 nm epitaxial Ba0.15Sr0.85TiO3
YBa2Cu3O7- , electric field across Kapton foils:
YBa2Cu3O7- , electric field across SrTiO3 barriers
fractional shifts in RN of O(10-5)
with 4 x106 V/cm: major Tc shift
(Fiory et al., 1990)
Tc shifts of 10 K YBCO film on SrTiO3
(J. Mannhart, 1991, `96)
35 40 45 500.010.020.050.10.20.5
125
T (K)
R DS (
)
VG = 34 V0 V
- 2.8 V
with 10 C/cm2 gate polarization
insulator-superconductortransition observed in aNd1.2Ba1.8Cu3O7 epitaxial film on SrTiO3 substrate(A. Cassinese et al., 2004)
(G. Logvenov, 2003)
●
●
●
interaction between charge excitations in L1 and L2:
,† †
,
†, ( )int i i
ii is iip c c p s sV pH
Theoretical design of the interface
accumulation of chargeat interface
polarization of dielectric
electric field energy:
sg zped E electrostatic gate field
single particle processes:
†, ,
, ,t i j
i j
H t c c
† †2
1 ( )2l sp i i i i
i
H p p s s
† †( )ext i ii
g i ip s s pH
two-level systems:levels , p s
2D band:bandwidth 8t
† †, , , , e e i i i i
i
H U c c c c interaction between charge carriers in L2:
2 t l ext in e etH H HH H
interaction between metallic charge carriers and (polarized) two-level systems
†,
†
,
2
, 2† ( ) i i i i
iiint
pp spi
ss c p sH
dV sc Vp
er
† †- ( +S )= x zzV Vc c cSc S
with
2 2
2 1 )
2
(
sp
spg
spx
VV
xV (virtual) transitions drivenby field of nearest charge carrier
induce pairingzV interaction of field induced dipoles
with the 2D charge carriers
repulsive term in pairing channel
2 2
2
2
1( )
g
g
z sp
sp
V V
Field dependence of TC (at U/4t = 0.1)
limited bycarrier dopingCT repulsive Vz
limits Tc
saturation ofdipole moment
maximum in Tc for intermediate fields
(V. Koerting, Q. Yuan, P. Hirschfeld, T.K., and J. Mannhart, PRB 71, 104510 (2005))
field energy / 4t
not strongly dependenton other parameters like
opt
2.54
sp
t
and spV
CT excitations in SrTiO3
Strong coupling: mapping onto a t-J model
eff/ 0.2 / 1.07U U J J
renormalization of nearest neighbor spin exchange through charge transfer excitons ( 8 , /́ 0.3, / 1) :sp spU t t t V
insignificant
band renormalization at CT
delocalization with increasing field
coupling to excitons:
field energy / 4t
eff eff/ 0.7 / 0.5t t J J major correction
Inclusion of phonon modes
(N. Pavlenko, T.K., cond-mat/0505714)
closer to realistic modelling, a further step in complexity:
' pol, 2 int t txt e eelHH H H H HH
coupling to polar phonons at the interface
SrTiO3 : soft TO1-mode at 50─80 cm-1TO
† †pol (1 () )TO i i i i
i iinH b b b b
TO pE where
is the hole-phonon coupling
pE is the polaron binding energy
0.01 0.1 eV
/ 0.1 5p TOE
Ep/t = 1.2
ω ω
Strong coupling: superconductor-insulator transition
localization with increasing doping
coupling to phonons :
similar evaluation for the CMR-manganitescompare: Röder, Zang, and Bishop (PRL 1996)
double exchange ↔ excitonic narrowing
JT phonon ↔ soft phonon mode
doping x
● slave-boson evaluation (with d-wave pairing):
Ep/t = 0Ep/t = 1.07
Strong coupling: superconductor-insulator transition
localization with increasing doping
coupling to phonons :
delocalization with increasing field
coupling to excitons:
transition not only depends on the overall doppingbut also on the details of chemical versus field doping
Strong coupling: reentrant behavior
field-induced reentrant behavior:
the phase diagram now depends on
doping at zero field x0
and the field doping x(εg)
●
x(εg)
observed (field-induced) Tc shift in HTSC cuprate films depends on doping:
in underdoped films sizable shift whereas in overdoped films (nearly) no shift
●
BKT transition
2D systems: Berezinskii-Kosterlitz-Thouless transition (BKT)
●
ε
always smaller than TBKT TBKT
● increases nonlinearly with doping, due to interface coupling (cf. with experiments by Walkenhorst et al., PRL,1992)
TBKT
[evaluation similar to Kim & Carbotte, 2002]
Nanomagnetism at Interfaces ?Nanomagnetism at Interfaces ?
Jochen MannhartChristian Laschinger (theory)Christof Schneider (exp)Alexander Weber (exp)
Measured R(T)-CharacteristicsR
gb (Ω
)
Rgb
A (Ω
cm2 )
T (K)
C.W. Schneider et al., Phys. Rev. Lett. 92, 257003 (2004)
0
5
10
15
0 100 200 3000
5×10-9
(001)/(110)-tilt Grain Boundary
?
YBa2Cu3O7-d
0 100 200 300T (K)
Rg (
Ω)
0
150
300
Epitaxial Film
YBa2Cu3O7-d
Y0.8Ca0.2Ba2Cu3O7-δ
Grain Boundary Mechanism
Tunneling Resonant Tunneling
T
R
Eb
exponential
Nanobridges
T
R
dR/dT > 0
T
R
Glazman-Matveev
power-law
tunnel barrier
Eb
TEM image of a 30º [001] YBCO tilt grain boundary
N.D. Browning et al., Physica C 294, 183 (1998)
Cu/O partially occpuied
atomic reconstruction at a large angle grain boundary
if is randomly distributed with
assuming that is wide and has no structure up to
Grain Boundary Mechanism
R(T) decreases linearly with T,^
range of linearity given by width of T٭ distribution
Phenomenology
if transport scattering rate depends, besides , on a single energy scale
tr /( )T T T (1)
T (2) ( )P T
( )P T max 300 KT
tr tr tr*ˆ ( ) ( ) ( / ) (0) ( ) T T TT T dP x dxT P then
T
with a pronounced increase for T T
Grain Boundary Mechanismpotential fluctuations and distribution of bonds in a nanobridge
→ formation of local moments
compare: formation of localized moments in Si:P Lakner, von Löhneysen, Langenfeld, and Wölfle (1994)
→ distribution of Kondo temperatures
Magnetic States at Grain BoundariesTunneling
magnetic states assist tunnelingT < TK: pronounced Kondo-resonance Kondo-assisted tunneling
tunnel barrier
Kondo- resonance
Nanobridges
R decreases with T, how?
insulating barrier
magnetic states scatter chargesT < TK: strong Kondo-scattering
Kondo-resonance
Magnetic Scattering Centers at Grain Boundaries?
localized Cu spins at interface
Kondo resonance ?
strong potential fluctuations local moment formation varying coupling
T TK R(T TK ) 1 c (T TK )2
T TK R(T TK ) 1 ln2 (T TK )
Kondo Disorder at Grain Boundaries1) Single Kondo impurity:
2) Kondo impurities with distribution P(TK) (disordered interface):
compare with R(T) of certain Kondo alloys:
Miranda, Dobrosavljević, and Kotliar
PRL 78, 290 (1997)
R(T) decreases linearly with T^
range of linearity is given by width of
TK distribution
scales with /KR x T T
ˆ( ) (0) (1/ ) R T const P T R x dx
SummaryChallenge: Interfaces in Correlated Electron Systems
new states at the interface
anomalous transport through interface
example: grain boundaries in
HTSC
Rgb
(Ω)
5
10
15
T (K)
00 100 200 300
example: SuFET with HTSC
Nanobridges across Grain Boundaries?
M. Däumling et al., Appl. Phys. Lett. 61, 1355 (1992)B.H. Moeckly et al., Phys. Rev. B 47, 400 (1993)
YBa2Cu3O7-δ, 5 K
25° [001]-tilt 100 μm wide
Measured I (V)-Characteristic (23 Junctions in Series)
(001)/(110) tilt boundary
C.W. Schneider et al., Phys. Rev. Lett. 92, 257003 (2004)
4.2 K115 K207 K
Is electrostatic interface tuning feasible ?
achieved areal carrier densities: 0.01 ─ 0.05 carriers per unit cell
limited by dielectric constant ε and breakdown field
for SrTiO3 films: ε ~ 100 and breakdown ~ 108 V/m
●
charge profile studied by Wehrli, Poilblanc & Rice (2001) and Pavlenko (unpublished)●
charge confined to surface layer when field doping the insulating state~ underdoped ~ 80 % , overdoping ~ 100 % in surface layer
electrostrostatic interface tuning is feasibleno fundamental objection to higher charge densities
Theoretical design of the interface
1. bosonization (Holstein-Primakoff)
† †1 , , 2
zj j j j j j jS b S b S b b
not exact but correct for negligible inversion:
† 1j jb b
2. generalized Lang-Firsov transformation
†LF LFH U HU
purpose of unitary transformation:
† † †† ( )x effb bV Vc c cc c c
Steps towards an approximate solution
Induced pairing (at U=0)
second order perturbation theory for zero field:
zero fiel
2
d| 2 speff
sp
VV
positive: attractive interaction
exciton
spV
spV
Possibility of Synthesizing an Organic Superconductor(W. A. Little, 1964)
spine
spine: metallic half-filled band k
(polyene chain)
side-chains: charge oscillation with low-lying excited state sc
Vspine-sc
side-chains (sc)
Including a repulsive interaction in the metallic layer
(V. Koerting, Q. Yuan, P. Hirschfeld, T.K., and J. Mannhart, PRB 71, 104510 (2005))
† †, , , , e e i i i i
i
H U c c c c
field energy / 4t
Strong coupling: reentrant behavior
field-induced reentrant behavior:
the phase diagram now depends on
doping at zero field x0
and the field doping x(εg)
●
x(εg)
observed (field-induced) Tc shift in HTSC cuprate films depends on doping:
in underdoped films sizable shift whereas in overdoped films (nearly) no shift
●
Ep(exp)/t
∆∆