SOCIETA ITALIANA DI FISICA

RENDICONTI DELLA

SCUOLA INTERNAZIONALE DI FISICA

«ENRICO FERMI»

CXXXVI CORSO a cura di G. IADONISI, ]. R. SCHRIEFFER e M. 1. CHIOFALO

Direttori del Corso

V ARENNA SUL LAGO DI COMO

VILLA MONASTERO

24 Giugno - 4 Luglio 1997

Modelli e fenomenologia della Superconduttivita convenzionale e ad alta

• • temperatura crtttca

1998

SOCIETA ITALIANA DI FISICA BOLOGNA-ITALY

ITALIAN PHYSICAL SOCIETY

PROCEEDINGS

OF THE

INTERNATIONAL SCHOOL OF PHYSICS

«ENRICO FERMI»

COURSE CXXXVI edited by G. IADONISI, ]. R. SCHRIEFFER and M. 1. CHIOFALO

Directors of the Course

V ARENNA ON LAKE COMO

VILLA MONASTERO

24 June - 4 July 1997

Models and Phenomenology for Conventional

and High-temperature Superconductivity

1998

lOS Press

Ohmsha

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Copyright © 1998, by Societa Italiana di Fisica

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INDICE

G. IADONISI, J. R. SCHRIEFFER and M. L. CHIOFALO - Foreword................. pag. XI

Gruppo fotografico dei partecipanti al Corso fuori testo

A. S. ALEXANDROV - Sir Nevill Mott-70 years in physics ............................... . pag. 1

G. C. STRINATI - BCS and Eliashberg theories ..................................................... . » 7

1. Introduction .................................................................................................................. . » 7 2. Model Hamiltonian with an effective electron attraction ................................. .. » 8 3. Instability of the normal state and emergence of the order parameter ....... . » 9 4. BCS wave function and its properties ................................................................... . » 15 5. Low-lying excited states and Landau criterion for superfluidity .................... . » 23 6. Finite-temperature properties and Ginzburg criterion ....................................... . » 27 7. Meissner effect and conserving approximations .................................................. . » 31 8. Eliashberg theory ........................................................................................................ . » 38

M. RANDERIA - Precursor pairing correlations and pseudogaps ..................... . » 53

1. Introduction .................................................................................................................. . » 53 2. Pseudogap exper,iments ............................................................................................. . » 54 3. Survey of scenarios .................................................................................................... . » 56 4. Pairing correlations above Tc ................................................................................... . » 57 5. Pseudogap in s-wave models ............................................................ : ....................... . » 59 6. Commonly asked questions ................................................................ , ...................... . » 64 7. Phase fluctuations and Tc ......................................................................................... . » 66 8. Pseudogaps in d-wave models .................................................................................. . » 67 9. Open questions ............................................................................................................ . » 72 10. Conclusions ................................................................................................................... . » 73

H. B. BROM - NMR in high-temperature superconductors ............................... . » 77

1. Introduction .................................................................................................................. . » 77 2. Spin-lattice and spin-spin relaxation, linewidths and lineshlfts ........................ . » 78

V

VI

3. NMR/NQR in the normal state of high-Tc superconductors ............................ . 4. NQR/NMR in the superconducting state .............................................................. .

4·1. NQR and low-field NMR-spin pairing mechanism .................................... . 4·2. NMR and vortices ............................................................................................ .

5. NMR evidence for phase separation and stripe phases .................................... . 6. Concluding remarks .................................................................................................... .

A. BARONE - The Josephson effect: What it is-What it allows ..................... .

1. Introduction .................................................................................................................. . 2. A Josephson effect primer ........................................................................................ . 3. High-Tc superconductor junctions counterpart .................................................... . 4. Symmetry of the order parameter and half-flux quantization in unconventional

superconductors ........................................................................................................... . 4.1. Heavy fermions ................................................................................................. . 4·2. High-Tc cuprate superconductors .................................................................. .

5. Conclusions ................................................................................................................... .

M. RANDERIA and J.-C. CAMPUZANO - High-Tc superconductors: Insights from angle-resolved photoemission ......................................................................... .

1. Introduction .................................................................................................................. . 2. What does ARPES measure? ................................................................................... . 3. Spectral functions and sum rules ............................................................................ . 4. Experimental details .................................................................................................. . 5. Experiments on sum rule and n(k) ........................................................................ . 6. ARPES spectra: qualitative features ...................................................................... . 7. Normal state of optimally doped Bi2212 ............................................................... . 8. Extended saddle point singularity ........................................................................... . 9. Bilayer splitting? ............................................................. : ........................................... . 10.Superconducting gap and its anisotropy ................................................................ . 11. Pseudogap in the underdoped materials .............................................................. .. 12. Conclusions ................................................................................................................... .

ZHI-XUN SHEN - Angle-resolved photoemission study of high-temperature superconductors: Insulators, metals and supercondutors .............................. .

1. Angle-resolved photoemission as a tool to probe the electronic structure of novel materials ............................................................................................................. .

2. Doping-dependent electronic structure of cuprate materials ............................ . 3. Photoemission study of the excitation gaps in the normal and superconducting

state of underdoped Bi2Sr2CaCu20s +

INDICE VII

7. Fluctuation effects in underdoped cuprates .... :...................................................... pag. 168 7"1. Photoemission spectra: k-, X-, and T-dependence of the normal phase» 168 7"2. ~-phase fluctuations in underdoped supercondutors ................................. » 172 7"3. ~-amplitude fluctuations ................................................................................... » 173 7"4. Pairing pseudogap.............................................................................................. » 174

8. Conclusion ...................................................................................................................... » 174

T. M. RICE - Strongly correlated models for the cuprate high-Tc supercon-ductors ................................................................................................................................ . » 177

1. Introduction .................................................................................................................. . » 177 2. Electronic structure of cuprates: introduction of the t-J model ..................... . » 181 3. Properties of the t-J model in two dimensions .............•...................................... » 185 4. t-J ladders and cuprate ladder compounds .......................................................... . » 194 5. Conclusion ..................................................................................................................... . » 204

M. MARINARO and R. CITRO - Superconductivity in correlated electron systems ............................................................................................................................... . » 209

1. Introduction .................................................................................................................. . » 209 2. Acquired knowledge .................................................................................................... . 209

2'1. Two-dimensional systems ................................................................................ . » 209 2'2. Phase diagram ................................................................................................... . » 210 2'3. Electronic correlations ..................................................................................... . » 210 2'4. Feature in the density of states (DOS) ...................................................... . 212 2'5. Symmetry of the condensed phase ............................................................... . » 212 2'6. Linear resistivity at optimal doping ............................................................. . » 212

3. Controversial points .................................................................................................... . » 212 3'1. DOS features ...................................................................................................... . » 212 3'2. Role of the electron-phonon interaction ...................................................... . » 213 3'3. Phase separation ............................................................................................... . » 213 3'4. Superconducting phase .................................................................................... . » 213 3'5. Pairing mechanism ............................................................................................ . » 214

4. Theoretical models ...................................................................................................... . » 214 4'1. The p-d model ........ ; .......................................................................................... . » 215 4'2. Correlation functions ........................................................................................ . » 216

5. Results ........................................................................................................................... . » 217

H. TAKAGI and N. E. HUSSEY - Normal-state charge transport properties of high-Tc cuprates .............................................................................................................. . » 227

1. Introduction .................................................................................................................. . » 227 2. Generic phase diagram .............................................. ; ............................................... . » 227 3. Systematic evolution of the temperature-dependent in-plane resistivity with

doping ............................................................................................................................ . » 228 4. T-linear resistivity in the optimally doped superconductors ............................. . » 230 5. Normal-state gap and the in-plane resistivity ...................................................... . » 231 6. The out-of-plane transport ........................................................................................ . » 232 7. Anomalous temperature and carrier concentration dependence of the in-plane

Hall effect ..................................................................................................................... . » 235 8. Summary ...................................................................................................................... .. » 238

VIII

C. THOMSEN and G. KACZMARCZ1'K - Raman spectroscopy experiments in high-Tc superconductors .............................................................................................. .

1. Introduction to RaJIlan scattering ........................................................................... . 2. Vibrations in high-Tc's ............................................................................................... .

2'1. Lattice vibrations in YB3c2CUg07 _ a and related compounds ................... . 2'2. The Bi2Sr2Ca" _ 1 CUn 02n + 4 superconductor family ..................................... .

3. Electron-phonon interaction ...................................................................................... . 3'1. Self-energy effects in high-Tc's ...................................................................... . 3'2. Above Tc effects ................................................................................................ .

4. Summary ....................................................................................................................... .

J. P. FRANCK - Experiments on the isotope effect ............................................... .

1. Introduction .................................................................................................................. . 2. The isotope effect in doped cuprate high-Tc superconductors ......................... .

2'1. Doped YBa2CUg07 - a •.•..•....•....•.•..•..•.•..•..•.•..•.•..•............................................... 2'2. The isotope effect in oxygen-deficient YBa2CUg07 - a ..............................•. 2'3. The isotope effect in L3c2_"'Sr"'Cu04 ............................................................. .

3. Discussion ...................................................................................................................... . 3'1. Oxygen-deficient YB3c2Cug07 - a •.•..•.•..•.••.•..•.••.•.••.•..•.••.•....•..•......•................... 3'2. The Lal_",Sr",Cu04 system .............................................................................. .

4. The isotope effect in the "Colossal Magneto-Resistance" compounds Lal _ ",Ca.,MnOg ............................................................................................................. .

5. Conclusion ..................................................................................................................... .

J. T. DEVREESE - Bipolarons and high-Tc superconductivity ............................ .

1. Introduction: Frohlich polarons ............................................................................... . 2. Frohlich bipolarons ..................................................................................................... .

2'1. Introduction: history and main concepts ..................................................... . 2'2. Path-integral treatment ................................................................................... . 2'3. Stability of bipolarons ...................................................................................... . 2'4. Stability of bipolarons in a magnetic field .................................................. . 2'5. Magnetoabsorption of Frohlich bipolarons .................................................. .

3. Polarons and the optical spectra of oxides ........................................................... . 4. Many-polaron systems ................................................................................................ . 5. Many-polaron-bipolaron systems .............................................................................. .

5'1. Intuitive approach ............................................................................................. . 5'2. Polaron-bipolaron transitions and electron screening effects .................. .

6. Bipolarons and high-Tc superconductivity ............................................................. . Appendix A - A note on the thermodynamics of an interacting Bose gas ........ .

A. S. ALEXANDROV - Polaronic and bipolaronic high-Tc superconductivity ..

1. Introduction .................................................................................................................. . 2. Bloch states and correlations in doped semiconductors .................................... .

2'1. Effective mass approximation ........................................................................ . 2'2. Tight-binding approximation and the generic Hamiltonian ..................... .

INDICE

pag. 241

» 241 » 246 » 248 » 253 » 256 » 257 » 262 » 264

» 269

» 269 » 271

271 » 273 » 275 » 275 » 278 » 278

» 280 » 283

» 287

» 287 » 290

290 » 291 » 292 » 294 » 295

299 » 300 » 301 » 301

303 303 304

» 309

309 310 310

» 313

INDICE

3. The multi-polaron problem ....................................................................................... . 3"1. Small-polaron instability within the Migdal approach .............................. . 3'2. Exact solution of the multi-polaron problem for A ~ 00 ......................... .. 3'3. Polaron band ...................................................................................................... . 3'4. Electron Green's function and ARPES of polaronic systems ................ .

4. Polaronic and bipolaronic superconductivity ......................................................... . 4'1. Cooper pairing of nonadiabatic carriers ...................................................... . 4'2. High-Tc polaronic superconductivity ............................................................. . 4'3. Coherent tunneling and repulsion of bipolarons ........................................ . 4'4. Bipolaron anisotropic flat bands in high-Tc copper oxides ..................... . 4'5. Pseudospin representation of the bipolaronic Hamiltonian ..................... . 4'6. Superfluid vs. charged ordered ground state ............................................. . 4'7. Excitation spectrum of the bipolaronic liquid ............................................ . 4'8. T-n phase diagram of the bipolaronic liquid .............................................. .

5. Bipolaron theory of high-Tc cuprates ..................................................................... . 5'1. Hall density and the "boomerang" behavior of Tc with doping ............ . 5'2. Temperature dependence of the Hall effect and the in-plane resistivity» 5'3. c-axis transport and normal-state gap ......................................................... . 5'4. Violation of Kohler's rule ................................................................................ .

6. Thermodynamic VB. resistive transition in a magnetic field ............................. . 7. Conclusion ..................................................................................................................... .

P. CAINANI - Infrared polaronic bands in cuprates and related perovskites

1. Introduction .................................................................................................................. . 2. Optical conductivity of charges strongly coupled to a polar lattice ................ .

2'1. Charge density waves and polaron ordering ............................................. .. 2'2. Modeling the optical conductivity of itinerant polarons ........................... . 2'3. The small-polaron model ................................................................................. . 2'4. The large-polaron model ................................................................................. . 2'5. The Infrared Active Vibrations ..................................................................... . 2'6. Fano lineshapes in the cuprates ................................................................... .

3. The optical conductivity of high-Tc superconductors in the normal phase ... . 3'1. One-component and multi-component models for a(w) ............................ . 3'2. The polaron d-band at intermediate doping ............................................... . 3'3. Polaron bands in CU02 infinite-layer films ................................................. . 3'4. Polaron bands in the metallic phase of cuprates ...................................... .

4. Conclusion ..................................................................................................................... .

V. CATAUDELLA, G. IADONISI, D. NINNO, E. PIEGARI, G. CAPONE, M. L. CHIO-FALO and G. DE FILIPPIS - Large polarons and high-Tc superconductivity

1. Introduction .................................................................................................................. . 2. Frohlich polaron formation ....................................................................................... .

2'1. Screening effects in Frohlich polarons ........................................................ . 2'2. Screening and narrow-band effects in Frohlich polarons ....................... . 2'3. Many-body RP A approach to the polaron formation ............................... .

3. Infrared absorbtion spectra in high-Tc superconductors and large polarons 4. Large-bipolaron formation ........................................................................................ . 5. The boson-fermion model of superconductivity .................................................... . 6. Conclusions ................................................................................................................... .

IX

pag. 315 » 315 » 318 » 319 » 321 » 323 » 324 » 325 » 328 » 331 » 335 » 336 » 337 » 340 » 342 » 343

345 » 350 » 355 » 356 » 360

» 365

» 365 » 366 » 366 » 370 » 371 » 373 » 375 » 378 » 378 » 378 » 383 » 385 » 388 » 389

» 393

» 393 » 395 » 395 » 397 » 401 » 402 » 403 » 405 » 408

x INDICE

J. RANNINGER and E. V. L. DE MELLO - Small polarons .................................. . pag. 411

1. Introduction .................................................................................................................. . » 411 2. The model ..................................................................................................................... . » 412 3. Internal structure of small polarons and their quasi-particle properties ...... . » 414 4. Correlated charge-deformation dynamics .............................................................. . » 422 5. Summary ....................................................................................................................... . » 424

J. RANNINGER and J.-M. ROBIN - From localized to itinerant bi-polarons in high-To superconductors .............................................................................................. . » 425

1. Introduction .................................................................................................................. . » 425 2. The boson-fermion model .......................................................................................... . » 427 3. The pseudogap in high-To superconductors .......................................................... . » 428 4. Various manifestations of the pseudogap .............................................................. . » 431 5. Discussion ..................................................................................................................... . » 434

C. GRIMALDI, E. CAPPELLUTI, L. PIETRONERO - Superconducting and nor-mal-state effects due to the breakdown of Migdal's theorem .................... . » 437

1. Introduction .................................................................................................................. . » 437 2. Migdal's theorem ......................................................................................................... . » 439 3. The vertex function .................................................................................................... . 440 4. Electron mass isotope effects .................................................................................. . » 444

4·1. Small polaron ..................................................................................................... . » 445 4·2. Vertex correction ............................................................................................... . 446 4·3. van Hove singularity ........................................................................................ . » 448

5. Conclusions and perspectives ................................................................................... . 449

P. MINNHAGEN - Vortex physics for superconductors from a two-dimensional perspective ........................................................................................................................ . » 451

1. Introduction .................................................................................................................. . » 451 2. Vortices .......................................................................................................................... . » 452

2·1. Coulomb gas model .......................................................................................... . » 455 2·2. XY-model ............................................................................................................. . » 458

3. Properties of the Coulomb gas model ................................................................... . 461 3·1. Charge unbinding transition ........................................................................... . » 461 3·2. Dynamics ............................................................................................................. . » 469 3·3. Non-linear I-V exponent .................................................................................. . » 476 3·4. Comparison with experiments ........................................................................ . 480

3·4.1. Coulomb gas scaling ........................................................................... . » 480 3·4.2. Complex impedance ............................................................................ . » 481 3·4.3. 1-V characteristics ............................................................................... . 484

4. Anisotropic 3D XY-model .......................................................................................... . » 485 4·1. Plane decoupling ................................................................................................ . 487 4·2. Non-linear I-V and critical current .............................................................. . » 488 4·3. Comparison with experiments ........................................................................ . » 490

5. Anisotropic 3D XY-model in a magnetic field ..................................................... . 491 6. Concluding remarks .................................................................................................... . » 493

Elenco dei partecipanti ....................................................................................................... . 497

Foreword

Superconductivity is undoubtely one of the most exciting fields in the physics of the present century both from the experimental as well as from the theoretical viewpoint. The discovery of new superconducting materials has pushed forward the development of experimental low-temperature physics. The search for microscopic models to explain the many superconducting substances has introduced seminal concepts and techniques in many-body physics and in statistical mechanics.

The properties of the new compounds in their normal state are just as puzzling as the superconducting phase properties were in the low-temperature conventional materi-als. The complexity of the high-temperature superconductors has required a remarkable refinement of experimental techniques in order to allow a reliable characterization of the samples, and this is partly the reason why so many different microscopic models have so far been proposed.

Although we were a priori convinced that it would not be possible to give a complete overview of all the topics related to superconductivity; nevertheless we hope that the present selection may be useful to young researchers who are entering this rapidly evolving field as well as to more experienced scientists.

The large volume of experimental and theoretical work and the lack of a generally ac-cepted theoretical framework needed to understand high-Tc superconductivity has made the choice of the topics to be included in the Course difficult. Inasmuch as the School is named after Enrico Fermi, our first choice has been to give equal weight to experi-mental and theoretical topics. We focused our attention on those reliable measurements which are expected to provide the theory with key constraints, viz: Raman and Infrared Spectroscopy, Nuclear Spin Resonance, Angular Resolved Photoemission Spectroscopy, transport measurements, Josephson effect. From a pedagogical point of view, the purpose

XI

XII FOREWORD

of the lectures is to provide the students with a general background on these techniques and then to focus on specific results relevant to the physics of super conducting materials.

The choice of the theoretical topics has been even more difficult. We believe that the lectures devoted to the overview of the BCS theory and to the discussion of minimal models and of the crossover from BCS to Bose-Einstein condensation may be particularly useful to students. The remaining part of the program is shared between phonon- and non-phonon-based mechanisms. On the one hand, special emphasis has been devoted to the breakdown of the Migdal theorem and to polaronic theories. On the other hand, the book contains an overview of strongly correlated electron theories, including magnetic interactions. A survey of the physics of vortices completes the theoretical part of the lectures.

The organization of the CXXXVI Course of the "Enrico Fermi" School, the choice of the topics and of the speakers bears the fruits of the enthusiastic participation of Sir Nevill Mott, who started with us along this way on June 1996. We believe to interpret the wish of everybody in dedicating this volume to his memory. It certainly contains a large part of his ideas and of his recent work on high-temperature superconductivity. For this reason the book opens with the lecture which Sasha Alexandrov has dedicated to his memory. We wish to thank the Italian Physical Society (SIF) for financial and logistical support. We wish to thank the SIF Secretariat (in particular, Mrs. Enrica Mazzi) as well as the Editorial Staff for the much needed help with the local organization and with the publication of these Proceedings. We wish to thank all the lecturers for the enthusiasm with which they took part in the Course, fruitfully interacting with the participants. We thank them all who enthusiastically contributed to the success of the School and were not hampered by the inclement weather. We finally thank the Consiglio Nazionale delle Ricerche, the Gruppo Nazionale di Struttura della Materia of the CNR and the Istituto Nazionale di Fisica Nucleare for their sponsorship.

G. IADONISI, J. R. SCHRIEFFER and M. L. CHIOFALO

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SOCIETA ITALIANA Dr FISICA

SCUOLA INTERNAZIONALE DI FISICA «E. FERMI » CXXXVI CORSO - VARENNA SUL LAGO DI COMO

VILLA MONASTERO - 24 Giugno - 4 Luglio 1997