Strongly Correlated Fermi Systems: A New State of Matter

1 Introduction

1.1 General considerations

1.2 Strong and weak interparticle interactions

1.3 Theoretical approaches to strongly correlated systems

1.5 Main goals of the book

References

2 Landau Fermi liquid theory

2.1 Quasiparticle paradigm

2.2 Pomeranchuk stability conditions

2.3 Thermodynamic and transport properties

2.3.1 Equation for the effective mass

3 Density Functional Theory of Fermion Condensation

3.1 Introduction

3.2 Functional equation for the effective interaction

3.3 DFT and fermion condensation

3.4 DFT, the fermion condensation and superconductivity

3.5 Summary

References

4 Topological fermion condensation quantum phase transition

4.1 The fermion-condensation quantum phase transition

4.1.1 The FCQPT order parameter

4.1.3 The in uence of FCQPT at finite temperatures

4.1.4 Two Scenarios of the Quantum Critical Point

4.1.5 Phase diagram of Fermi system with FCQPT

References

5 Rearrangement of the single particle degrees of freedom

5.1 Introduction

5.2 Basic properties of systems with the FC

5.2.1 The case Tc < T < Tf0

5.2.2 The case T < Tc. Super uid systems with the FC

5.3 Validity of the quasiparticle pattern

5.3.1 Finite systems

5.3.2 Macroscopic systems

5.4 Interplay between fermion condensation and density-wave instability

5.5 Discussion

6 Topological FCQPT in strongly correlated Fermi systems

6.1 The superconducting state with FC at T = 0

6.1.1 Green's function of the superconducting state with FC at T = 0

6.1.2 The superconducting state at finite temperatures

6.1.3 Bogolyubov quasiparticles

6.1.4 The dependence of superconducting phase transition temperature Tc on doping

6.1.5 The gap and heat capacity near Tc

6.2 The dispersion law and lineshape of single-particle excitations

6.3 Electron liquid with FC in magnetic fields

6.3.1 Phase diagram of electron liquid in magnetic field

6.3.2 Magnetic field dependence of the effective mass in HF metals and high-Tc superconductors

6.4 Appearance of FCQPT in HF compounds

References

7 Effective mass and its scaling behavior

7.2 T/B scaling in heavy fermion compounds

References

8 Quantum spin liquid in geometrically frustrated magnets and the new state of matter

8.1 Introduction

8.2 Fermion condensation

8.3 Scaling of the physical properties

8.4 The frustrated insulator Herbertsmithite ZnCu3(OH)6Cl2

8.4.1 Thermodynamic properties

References

9 One dimensional quantum spin liquid

9.1 Introduction

9.2 General considerations

9.3 Scaling of the thermodynamic properties

9.4 T - H phase diagram of 1D spin liquid

9.5 Discussion and summary

References

10 Dynamic magnetic susceptibility of quantum spin liquid

10.1 Dynamic spin susceptibility of quantum spin liquids and HF metals

10.2 Theory of dynamic spin susceptibility of quantum spin liquid and heavy-fermion metals

10.3 Scaling behavior of the dynamic susceptibility

References

11 Spin-lattice relaxation rate and optical conductivity of quantum spin liquid

11.1 Spin-lattice relaxation rate of quantum spin liquid

11.2 Optical conductivity

References

12 Quantum spin liquid in organic insulators and ³He

12.1 The organic insulators EtMe³Sb[Pd(dmit)2]2 and - (BEDT - TTF)2Cu₂(CN)³

12.2 Quantum spin liquid formed with 2D ³He

12.3 Discussion

12.4 Outlook

References

13 Universal behavior of the thermopower of HF compounds

13.2 Extended quasiparticle paradigm and the scaling behavior of HF metals

13.2.1 Topological properties of systems with fermion condensate

13.2.2 Scaling behavior of HF metals

13.2.3 Universal behavior of the thermopower ST of heavy-fermion metals

13.3 Schematic T - B phase diagram

13.4 Summary

References

14 Universal behavior of the heavy-fermion metal beta - YbAlB4

14.1 Introduction

14.2 Universal scaling behavior

14.3 The Kadowaki-Woods ratio

14.4 The schematic phase diagrams of HF compounds

14.5 Summary

References

15 The universal behavior of the archetypical heavy-fermion metals YbRh2Si2

15.1 Introduction

15.2 Scaling behavior of the effective mass

15.3 Non-Fermi liquid behavior in YbRh2Si2

15.3.2 Average magnetization

15.3.3 Longitudinal magnetoresistance

15.3.4 Magnetic entropy

15.4 Summary

References

16 Heavy fermion compounds as the new state of matter

16.1 Introduction

16.2 General properties of heavy-fermion metals

16.3 Common field-induced quantum critical point

16.4 Summary

References

17 Quasi-classical physics within quantum criticality in HF compounds

17.1 Second wind of the Dulong-Petit law at a quantum critical point

17.2 Transport properties related to the quasi-classical behavior

17.3 Quasi-classical physics and T-linear resistivity

References

18 Asymmetric conductivity of strongly correlated compounds

18.1 Normal state

18.1.1 Suppression of the asymmetrical differential resistance in YbCu5-xAlx in magnetic fields

18.2 Superconducting state

18.3 Relation to the baryon asymmetry in the early Universe

18.4 Conclusion

References

19 Asymmetric conductivity, pseudogap and violations of time and charge symmetries

19.1 Introduction

19.2 Asymmetric conductivity and the NFL behavior

19.3 Schematic phase diagram

19.4 Heavy fermion compounds and asymmetric conductivity

19.5 Conclusions

References

20 Violation of the Wiedemann-Franz law in Strongly Correlated Electron Systems

20.1 Introduction

20.2 Wiedemann-Franz law violations

20.3 Conclusion

References

21 Quantum criticality of heavy-fermion compounds

21.1 Quantum criticality of high-temperature superconductors and HF metals

21.2 Quantum criticality of quasicrystals

21.3 Quantum criticality at metamagnetic phase transitions

21.3.1 Typical properties of the metamagnetic phase transition in Sr3Ru2O7

21.3.2 Metamagnetic phase transition in HF metals

21.4 Universal Behavior of two-dimensional 3He at low temperatures

21.5 Scaling behavior of HF compounds and kinks in the thermodynamic functions

21.6 New state of matter

References

22 Quantum criticality, T -linear resistivity and Planckian limit

22.1 Introduction

22.2 Phase diagram

22.3 Planckian limit and quasi-classical physics

22.4 Universal scaling relation

22.5 Summary

References

23 Forming high-Tc superconductors by the topological FCQPT

23.1 Introduction

23.2 Fermion condensation as two component system

23.3 Super uid density in the presence of fermion condensation

23.4 Penetration depth, fermion condensation and Uemura's law

23.5 Concluding remarks

References

24 Conclusions

References

Index