1. 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)

2. 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

3. Electrostatic interface tuning (SUFETs) theory: Natalia Pavlenko Verena Koerting Qingshan Yuan Peter Hirschfeld experiment: Jochen Mannhart Gennadij Logvenov Christof Schneider field doping ? instead of ? chemical doping tune phase transitions electrostatically ?

4. Is electrostatic interface tuning feasible ? DS-channel: 8 nm polycrystalline YBa 2 Cu 3 O 7-d gate barrier: 300 nm epitaxial Ba 0.15 Sr 0.85 TiO 3 YBa 2 Cu 3 O 7- , electric field across Kapton foils: YBa 2 Cu 3 O 7- , electric field across SrTiO 3 barriers fractional shifts in R N of O(10 -5 ) with 4 x10 6 V/cm: major T c shift (Fiory et al., 1990) T c shifts of 10 K YBCO film on SrTiO 3 (J. Mannhart, 1991, `96) 35404550 0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 T (K) R DS (  ) V G = 34 V 0 V - 2.8 V with 10  C/cm 2 gate polarization insulator-superconductor transition observed in a Nd 1.2 Ba 1.8 Cu 3 O 7 epitaxial film on SrTiO 3 substrate (A. Cassinese et al., 2004) (G. Logvenov, 2003) ● ● ●

5. interaction between charge excitations in L1 and L2: Theoretical design of the interface accumulation of charge at interface polarization of dielectric electric field energy: electrostatic gate field single particle processes: two-level systems: 2D band: interaction between charge carriers in L2:

6. interaction between metallic charge carriers and (polarized) two-level systems with (virtual) transitions driven by field of nearest charge carrier induce pairing interaction of field induced dipoles with the 2D charge carriers repulsive term in pairing channel

7. Field dependence of T C (at U/4t = 0.1) limited by carrier doping repulsive V z limits T c saturation of dipole moment maximum in T c for intermediate fields (V. Koerting, Q. Yuan, P. Hirschfeld, T.K., and J. Mannhart, PRB 71, 104510 (2005)) field energy / 4t not strongly dependent on other parameters like CT excitations in SrTiO 3

8. Strong coupling: mapping onto a t-J model renormalization of nearest neighbor spin exchange through charge transfer excitons insignificant band renormalization at delocalization with increasing field coupling to excitons: field energy / 4t major correction

9. Inclusion of phonon modes (N. Pavlenko, T.K., cond-mat/0505714) closer to realistic modelling, a further step in complexity: coupling to polar phonons at the interface SrTiO 3 : soft TO 1 -mode at 50─80 cm -1 where is the hole-phonon coupling is the polaron binding energy

10. E p /t = 1.2 ω ω Strong coupling: superconductor-insulator transition localization with increasing doping coupling to phonons : similar evaluation for the CMR-manganites compare: Röder, Zang, and Bishop (PRL 1996) double exchange ↔ excitonic narrowing JT phonon ↔ soft phonon mode doping x ● slave-boson evaluation (with d-wave pairing): E p /t = 0 E p /t = 1.07

11. 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 dopping but also on the details of chemical versus field doping

12. Strong coupling: reentrant behavior field-induced reentrant behavior: the phase diagram now depends on doping at zero field x 0 and the field doping x(ε g ) ● x(ε g ) observed (field-induced) T c shift in HTSC cuprate films depends on doping: in underdoped films sizable shift whereas in overdoped films (nearly) no shift ●

13. BKT transition 2D systems: Berezinskii-Kosterlitz-Thouless transition (BKT) ● ε always smaller than T BKT ● increases nonlinearly with doping, due to interface coupling (cf. with experiments by Walkenhorst et al., PRL,1992) T BKT [evaluation similar to Kim & Carbotte, 2002]

14. Nanomagnetism at Interfaces ? Jochen Mannhart Christian Laschinger (theory) Christof Schneider (exp) Alexander Weber (exp)

15. Measured R(T)-Characteristics R gb (Ω) R gb A (Ωcm 2 ) T (K) C.W. Schneider et al., Phys. Rev. Lett. 92, 257003 (2004) 0 5 10 15 0100200300 0 5×10 -9 (001)/(110)-tilt Grain Boundary ? ? YBa 2 Cu 3 O 7-d 0100200300 T (K) R g (Ω) 0 150 300 Epitaxial Film YBa 2 Cu 3 O 7-d

16. Y 0.8 Ca 0.2 Ba 2 Cu 3 O 7-δ

17. Grain Boundary Mechanism Tunneling Resonant Tunneling T R EbEb exponential Nanobridges T R dR/dT > 0 T R Glazman-Matveev power-law tunnel barrier EbEb

18. 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

19. 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 (1) (2) then with a pronounced increase for

20. Grain Boundary Mechanism potential 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

21. Magnetic States at Grain Boundaries Tunneling magnetic states assist tunneling T < T K : pronounced Kondo- resonance Kondo-assisted tunneling tunnel barrier Kondo- resonance Nanobridges R decreases with T, how? insulating barrier magnetic states scatter charges T < T K : strong Kondo- scattering Kondo-resonance

22. Magnetic Scattering Centers at Grain Boundaries? localized Cu spins at interface Kondo resonance ? strong potential fluctuations local moment formation varying coupling

23. Kondo Disorder at Grain Boundaries 1) Single Kondo impurity: 2) Kondo impurities with distribution P(T K ) (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 T K distribution

24. Summary Challenge: Interfaces in Correlated Electron Systems new states at the interface anomalous transport through interface example: grain boundaries in HTSC R gb (Ω) 5 10 15 T (K) 0 0100200300 example: SuFET with HTSC

25. 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) YBa 2 Cu 3 O 7- δ, 5 K 25° [001]-tilt 100 μ m wide

26. 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 K 115 K 207 K

27. 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 SrTiO 3 films: ε ~ 100 and breakdown ~ 10 8 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 feasible no fundamental objection to higher charge densities

28. Theoretical design of the interface

29. 1. bosonization (Holstein-Primakoff) not exact but correct for negligible inversion: 2. generalized Lang-Firsov transformation purpose of unitary transformation: Steps towards an approximate solution

30. Induced pairing (at U=0) second order perturbation theory for zero field: positive: attractive interaction exciton 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 V spine-sc side-chains (sc)

31. Including a repulsive interaction in the metallic layer (V. Koerting, Q. Yuan, P. Hirschfeld, T.K., and J. Mannhart, PRB 71, 104510 (2005)) field energy / 4t

32. Strong coupling: reentrant behavior field-induced reentrant behavior: the phase diagram now depends on doping at zero field x 0 and the field doping x(ε g ) ● x(ε g ) observed (field-induced) T c shift in HTSC cuprate films depends on doping: in underdoped films sizable shift whereas in overdoped films (nearly) no shift ● E p (exp) /t ∆ ∆