Candidacy Topic - Condensed Matter


Length, energy, and time scales:   Interatomic spacings in solids, elastic and inelastic mean free paths for electrons, phonon energy scales, typical band widths and band gaps, vibrational time scales, electronic time scales, plasma frequency. Unit conversions (eV, K, T, cm-1)

Electricity and magnetism: Basic E&M of light, polarization, standing and traveling waves, density of states, blackbody radiation, 2nd quantization, what is a gauge

Basic quantum mechanics:   Bohr atom, one electron atom (Lande g factor); hyperfine structure, , multi-electron atoms (Hund's rules), harmonic oscillator, Aharonov-Bohm phase, particle-in-a-box, perturbation theory, time-dependent perturbation theory, Fermi’s golden rule, Landau levels, Zeeman effect, Born-Oppenheimer approximation, WKB approximation, sudden vs. adiabatic approximations

Statistical mechanics:  Boltzmann factor, partition functions, Maxwell distribution, Fermi gas, Bose gas, density of states, degeneracy, kinetic concepts, chemical potential, diffusion, Debye model, heat capacity, first and second order phase transitions, Landau-Ginsburg theory of phase transitions 

Solid state physics: 

Tight binding, nearly-free electron picture, band structure, reciprocal space, diffraction, Bloch states, crystal momentum, acoustic vs. optical phonons, semiconductors, quasiparticles, holes, Fermi velocity, effective mass, valley degeneracy, p-n junctions, depletion widths, screening, plasma frequency

Magnetism:  Exchange energy, Pauli paramagnetism, Landau diamagnetism, types of magnetic order, Curie and Curie-Weiss laws, local vs. itinerant magnetism, Stoner criterion, Bohr-Van Leeuwen theorem

Thermodynamic and transport properties: heat capacity, resistivity (different contributions in metals, semiconductors etc.), Wiedemann-Franz Law, Nernst effect

Dielectric and optical properties:  Kramers-Kronig relations, piezoelectricity, Claussius-Mossotti relation, selection rules, lasers

Superconductivity:   Meissner effect, Cooper pairs, penetration depth, coherence length, Type I vs. Type II, Josephson effect, flux quantization, superconducting quantum interference devices

Nanoscale physics:  Coulomb blockade, conductance quantization, 2d electron systems, Landau quantization, integer quantum Hall effect, fractional quantum Hall effect, weak localization, universal conductance fluctuations, Aharonov-Bohm effect, tunneling density of states, van der Waals/Casimir forces, radiation pressure

Miscellaneous: Landau-Zener crossing, crystal structures (space groups, point group symmetry)

Experimental emphasis

Characterization techniques (how they work & what they tell us):  x-ray diffraction, electron diffraction, neutron diffraction, photoemission, ARPES, Mossbauer, heat capacity, thermal conductivity, resistivity, Hall coefficient, magnetic susceptibility, muSR

Electronic methods:  two-terminal vs. four-terminal measurements, lock-in techniques, van der Pauw technique, Hall resistance, shot noise, Johnson-Nyquist noise, 1/f noise

Magnetic methods:  NMR, EPR, FMR, magnetization, magnetoresistance

Nanoscale methods:  STM, AFM, MFM, EFM, Kelvin probe

Low-temperature methods:  accessible temperatures for 4He, 3He, and dilution refrigerators; principles of operation; superconducting magnets

Data analysis:  error analysis, confidence intervals, chi^2, lineshapes – Gaussians, Lorentzians

Theoretical emphasis

Basic Theory Models: Ising Model, Heisenberg model, Hubbard model, t-J model, Kondo/Anderson (single-impurity/lattice) models, luttinger liquid, Sine-Gordon model, non-linear sigma model, valencebond models, spin-ice models

Many-body formalism: Landau theory of Fermi liquids, Second quantization, Static-mean-field approaches, Green functions and Feynman diagrams (zero temperature, Matsubara, Keldysh), hydrodynamic approach (memory functional), Diagram resumations, functional integrals, large-N/S expansions (slave particles, Schwinger bosons, Holstein-Primakov bosons, etc.), Hubbard-Stratonovich decoupling, 1-d methods (bosonization, conformal symmetry, integrability), renormalization group theory (bosons, fermions), quantum phase transitions (Hertz theory), (high/low-T) series expansions, solitons and instantons

Computational methods: exact diagonalization, Lanczos, (quantum) Monte Carlo, numerical/densitymatrix renormalization group, dynamical mean field theory (LISA, DCA, etc.), ab-initio and density functional methods (Thomas Fermi, LDA, LSD, pseudopotentials), molecular dynamics

Disordered Systems: weak/strong(Anderson) localization, replica theory, supersymmetric methods, time-loop methods, random matrix theory.

Optical effects emphasis

Plasmonics: Localized Surface Plasmon, Surface Plasmon-Polariton, Plasmon Hybridization, Quantum Plasmonics, Nonlocal screening, Surface Enhanced Raman Scattering, Surface Enhanced InfraredAbsorption, LSPR sensing, Dark-field scattering spectroscopy, Cathodoluminescence, EELS, Plasmonic Fano resonances, Chirality

Electromagnetics: Purcell effect, superradiance, subradiance

Photonics: Photonic bandgap, Photonic crystals, Metamaterials

Excitonics: Exciton, Quantum Dots, Quantum Confinement effect, Luminescence

Computational: Finite Difference Time-Domain method, Finite Element Method, Mie theory, Discrete Dipole Approximation