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

∆∆