**Normal State**

Example: Graphene

Atomic Interaction J~8 eV~80000 K

At room temperature,

graphene is definitely solid.

[1] G. Graziano et al., J. Phys.: Condens. Matter 24, 424216 (2012).

[2] M. Hasegawa and K. Nishidate, Phys. Rev. B 70, 205431 (2004).

[3] A. Hansson et al., Phys. Rev. B 86, 195416 (2012).

[4] H. Shin et al., arXiv:1401.0105v2 (2014).

Crystals

Bravais lattice

First Brillouin zone

Fourier Transform

Soup of

Quasiparticles

Band structure of

graphene

Low energy physics

of graphene

Unit cell (A+B) and Brillouin zone

Tight binding method

photons

Dynamics of Electrons

Carbon Atom

Carbon Nucleus

Tightly bounded

**Topological**

State

State

**Superconducting**

State

State

Move in the periodic electromagnetic field

Phonon dispersion of graphene

Specific heat of graphene and diamond

Dynamics and thermodynamics

of vibrating lattice

MRS BULLETIN • VOLUME 37 • DECEMBER 2012

Classical limit 3

R

**Solid State Physics**

Fermions: electrons

Bosons: phonons

Magnetic

Response

Pauli

Curie & Brilouin

Paramagnetism

Diamagnetism

Itinerant

electrons

Bounded

ions

Langevin

Quantum Hall Trio

Landau levels

Topological

insulators

diamond

Solid State Communications 164 (2013) 47–49

M/B

Landau

Curie's law

Brillouin functions

Susceptibility

V(x)

B

Landau level degeneracy

Flux quantum

Landau levels

Transport Properties

Conductance tensor

Resistance tensor

TKNN formula

2D TI

3D TI

Electrodynamics

Zero Electric Resistance

Complete Diamagnetism

H

Electron

M=-H

B=M+H=0

Thermodynamics

Experiments

Science 338, 1193 (2012)

J. Phys.: Condens. Matter 24 055701

Specific heat

Modern Physics from a to Z0, Wiley 1994

Phase diagram

**Theories**

Phenomenological

London Theory

Ginzburg-Landau

mean field theory

Pairing instability

Soup of

Quasiparticles

Cooper

Pairs

Condensation energy

Pairing potential

Gap equation

GL free energy density

Supercurrent

Microscopic

BCS

In general, the Hamiltonian for electrons should contain the interaction part.

Due to the interaction, electrons can form pairs to lower the free energy. The order parameter describing this pairing instability is defined as

Interaction and pairing instability

PDW

Pair density wave

FFLO state

Amperean phase

Josephson effect: convert DC voltage to AC current.

Flux quantization

Tunneling: coherent peak and Andreev reflection.

Specific heat jump

Thermodynamic critical field and upper critical field.

Abrikosov vortex lattice.

Supercurrent

London penetration depth

Group theory

in SC

Group theory

in normal state

Topology in band theory

**Atoms**

**Phases**

**Interaction Between Atoms**

**Three Phases**

of Matter

of Matter

Ordered

Free

Partially Ordered

Proton

Quantum Chromodynamics

Neutron

Quantum Chromodynamics

Electron

Nucleus