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Copy of Phases

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by

Noah Yuan

on 6 May 2015

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Transcript of Copy of Phases

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

Superconducting
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

Ordered
Free
Partially Ordered
Proton
Quantum Chromodynamics
Neutron
Quantum Chromodynamics
Electron
Nucleus
Full transcript