Dynamical theory for strongly correlated two-dimensional electron systems

Optical properties and plasmons in moiré structures

The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides. Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures.

Dielectric response function and plasmon dispersion in a strongly coupled two-dimensional Coulomb liquid

We have formulated a dielectric response function for strongly coupled two-dimensional Coulomb liquids in the T=0 quantum domain. The formulation is based on the classical quasilocalized charge approximation [G. Kalman and K.I. Golden, Phys. Rev. A 41, 5516 (1990); K.I. Golden and G. Kalman, Phys. Plasmas 7, 14 (2000)] and extends the QLCA formalism into the quantum domain. We calculate the dispersion of the longitudinal plasmon mode for r(s) =10, 20, 40 and the resulting dispersion curves are compared with recent experimental results. We also conjecture the possible existence of a new high-wave-number collective excitation in close proximity to the right boundary of the pair continuum.

Dynamical theory of strongly coupled two-dimensional Coulomb fluids in the weakly degenerate quantum domain

We study the problem of dynamical response and plasma mode dispersion in strongly coupled two-dimensional Coulomb fluids (2DCFs) in the weakly degenerate quantum domain. Adapting the nonlinear response function approach of Golden and Kalman [Phys. Rev. A 19, 2112 (1979)] to the 2DCF, we construct a self-consistent approximation scheme for the calculation of the density response functions and plasma mode dispersion at long wavelengths. The basic ingredients in the construction are (i). the first kinetic equation in the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, (ii). the velocity-average-approximation (VAA) hypothesis, (iii.) the quadratic fluctuation-dissipation theorem, and (iv). the dynamical superposition approximation (DSA) closure hypothesis. The reliability of the VAA-DSA theory can be assessed by observing that the principal coupling correction to the 2D temperature-dependent Lindhard function is identified as being precisely the part of the third-frequency-moment sum-rule coefficient proportional to the potential energy.