The study of condensed matter physics has evolved over the last decade or so. The scope of modern condensed matter physics has expanded significantly from traditional solid-state physics and has become a highly interdisciplinary field of research. This book connects modern experimental discoveries with theoretical and fundamental concepts. It introduces the interacting and non-interacting aspects of fermionic systems and the role of topology and symmetry in understanding material properties. The text emphasizes quantum Hall effect, topological insulators and how the discovery of graphene has incited brilliant ideas in both fundamental and applied aspects. The role of interactions is discussed to explain topics including magnetism and superconductivity. Topics such as Bose–Einstein condensation and superfluid properties of atomic systems in optical lattices are also a key feature of the text. The book offers something different to the field due to the range of topics covered in a pedagogical way for students.
Author(s): Saurabh Basu
Publisher: IOP Publishing
Year: 2022
Language: English
Pages: 355
City: Bristol
PRELIMS.pdf
Preface
Foreword
Acknowledgement
Author biography
Saurabh Basu
CH001.pdf
Chapter 1 Electron liquid
1.1 Introduction
1.2 Jellium model
1.2.1 The Hamiltonian
1.2.2 Hartree–Fock approximation
1.2.3 Hartree–Fock energy
1.3 Properties of the electron liquid
1.3.1 Effective mass
1.3.2 Magnetic properties
1.3.3 Screening and dielectric function
1.3.4 Conductivity
1.4 Determination of the Fermi surface: the de Haas–Van Alphen effect
1.5 Fermi liquid theory
1.6 Summary and outlook
References
CH002.pdf
Chapter 2 Magnetic phenomena in solids
2.1 Introduction
2.2 Magnetic ordering: diamagnetism and paramagnetism
2.3 Magnetic properties of filled and partially filled shell materials
2.4 Ferromagnetism and antiferromagnetism
2.5 Mean field theory
2.6 Linear spin wave theory
2.6.1 Quantum XY model
2.7 Ising model of ferromagnetism: transfer matrix
2.8 Critical exponent and the universality class
2.9 Quantum antiferromagnet
2.10 Itinerant electron magnetism
2.11 Magnetic susceptibility: Kubo formula
2.12 Hubbard model: an introduction
2.13 Symmetries of the Hubbard model
2.13.1 Spin-rotational invariance
2.13.2 Particle–hole symmetry
2.13.3 Extreme limits of the Hubbard model
2.14 Ferromagnetism in Hubbard model: Stoner criterion
2.15 Antiferromagnetism in the Hubbard model
2.15.1 Strong coupling limit
2.15.2 Summary and outlook
2.16 Appendix
2.17 RS coupling
2.18 jj Coupling
2.19 Hund’s rule
References
CH003.pdf
Chapter 3 Transport in electronic systems
3.1 Introduction
3.2 Quantum Hall effect
3.2.1 General perspectives
3.2.2 Translationally invariant system: classical limit of QHE
3.2.3 Charge particles in a magnetic field: Landau levels
3.2.4 Degeneracy of the Landau levels
3.2.5 Conductivity of the Landau levels: role of the edge modes
3.2.6 Spin and the electric field
3.2.7 Laughlin’s argument: Corbino ring
3.2.8 Edge modes and conductivity of the single Landau level
3.2.9 Incompressibility and the QH states
3.2.10 Hall effect in the symmetric gauge
3.3 Kubo formula and the Hall conductivity
3.3.1 Hall conductivity and the Chern number
3.4 Quantum Hall effect in graphene
3.4.1 Basic electronic properties of graphene
3.4.2 Experimental confirmation of the Dirac spectrum
3.4.3 Landau levels in graphene
3.4.4 Experimental observation of the Landau levels in graphene
3.4.5 Summary
References
CH004.pdf
Chapter 4 Symmetry and topology
4.1 Introduction
4.1.1 Gauss–Bonnet theorem
4.1.2 Berry phase
4.2 Symmetries and topology
4.2.1 Inversion symmetry
4.2.2 Time reversal symmetry
4.3 SSH model
4.3.1 Introduction
4.4 The SSH Hamiltonian
4.4.1 Topological properties
4.4.2 Chiral symmetry
4.5 Topology in 2D: graphene as a topological insulator
4.5.1 Berry phase of graphene
4.5.2 Symmetries of graphene
4.5.3 Semenoff insulator
4.5.4 Haldane (Chern) insulator
4.5.5 Quantum anomalous Hall effect
4.6 Quantum spin Hall insulator
4.6.1 Kane–Mele model
4.7 Bulk-boundary correspondence
4.8 Spin Hall conductivity
4.8.1 Rashba spin–orbit coupling
4.8.2 Rashba spin–orbit coupling in graphene
4.8.3 Z2 invariant
4.9 Spin Hall effect
4.9.1 Spin current
4.9.2 Summary and outlook
References
CH005.pdf
Chapter 5 Green’s functions
5.1 Introduction
5.2 Second quantization
5.2.1 Fock basis
5.2.2 Representation of a one-body operator in second quantized notation
5.2.3 Representation of a two-body operator
5.2.4 Applications of the second quantized method
5.3 Green’s function
5.3.1 Green’s function for a single particle
5.3.2 Green’s function for a many-particle system
5.3.3 Representations in quantum mechanics
5.3.4 Electron Green’s function at zero temperature
5.3.5 Example: a degenerate electron gas
5.4 Retarded and advanced Green’s functions
5.4.1 Spectral representation
5.4.2 Wick’s theorem and Feynman diagrams
5.5 Self-energy: Dyson equation
5.5.1 Self-energy for a two-site chain: an example
5.5.2 Hartree–Fock approximation
5.6 Finite temperature Green’s function
5.6.1 Properties of the Matsubara Green’s function
5.6.2 Matsubara Green’s function and the retarded propagator at T = 0
5.6.3 Matsubara frequency sums
5.7 Summary and outlook
References
CH006.pdf
Chapter 6 Superconductivity
6.1 Introduction
6.1.1 Historical developments
6.1.2 Physical properties
6.1.3 Meissner effect
6.1.4 Perfect conductors and superconductors
6.1.5 Electrodynamics of superconductors: London theory
6.1.6 Penetration depth
6.1.7 Flux quantization
6.1.8 Non-local electrodynamics
6.2 Magnetic phase diagram of superconductors
6.2.1 Thermodynamics of superconductors
6.2.2 Specific heat
6.2.3 Density of states
6.3 BCS theory
6.3.1 Introduction
6.3.2 Isotope effect
6.3.3 Origin of attractive interaction
6.3.4 The BCS ground state
6.3.5 Statistical description of the BCS ground state
6.4 The variational calculation
6.4.1 Temperature dependence of the gap
6.4.2 Thermodynamics from BCS theory
6.5 Electromagnetic considerations
6.5.1 Meissner effect
6.5.2 Electromagnetic response in the transverse gauge
6.6 Ginzburg–Landau (GL) theory
6.6.1 Coherence length and the penetration depth
6.7 Experimental determination of energy gap
6.7.1 Absorption of electromagnetic radiation
6.7.2 Ultrasound absorption
6.7.3 Tunneling experiment
6.7.4 Unconventional superconductivity
6.7.5 High-Tc cuprates
6.8 The pseudogap phase
6.8.1 Summary and outlook
References
CH007.pdf
Chapter 7 Superfluidity
7.1 Introduction
7.2 Bose–Einstein condensation
7.3 Superfluidity
7.3.1 Gross–Pitaevskii equation
7.3.2 Quantized vortices
7.4 Many-body physics with cold atomic systems
7.4.1 BEC in weakly interacting systems
7.5 Strongly correlated systems
7.5.1 Optical lattice
7.5.2 Atom–atom interaction: Feshbach resonance
7.5.3 Ultracold atoms on optical lattice and Bose–Hubbard model
7.6 Various aspects of ultracold atoms in optical lattices
7.6.1 Disorder optical potential
7.6.2 Synthetic magnetic field
7.6.3 Dipole–dipole interaction
7.6.4 Bose glass phase
7.6.5 Methods of solution of the BHM
7.6.6 Single-site MFT
7.6.7 Superfluid–Mott insulator (SF–MI) transition
7.6.8 Limitations of MFT
7.6.9 Optical dipole trap (ODT)
7.6.10 Spin-1 Bose gas: an era of quantum magnetism
7.6.11 A comparison between spin-0 (spinless) and spin-1 Bose gases
7.6.12 Phase diagrams
7.7 Summary and outlook
7.8 Appendix
7.8.1 Derivation of the Gross–Pitaevskii equation
References
