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Bias voltage dependent scattering of the topological surface state is studied by scanning tunneling microscopy/spectroscopy for a clean surface of the topological insulator Bi$_2$Te$_2$Se. A strong warping of constant energy contours in the…
Two-dimensional topological insulators are characterized by gapped bulk states and gapless helical edge states, i.e. time-reversal symmetric edge states accommodating a pair of counter-propagating electrons. An external magnetic field…
We calculate the local density of states of a two-dimensional electron system under strong crossed magnetic and electric fields. We assume a strong perpendicular magnetic field which, in the absence of in-plane electric fields and collision…
We study two-particle states in a Su-Shrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with…
Motivated by recent experiments with ultracold magnetic atoms trapped in optical lattices where the orientation of atomic dipoles can be fully controlled by external fields, we study the ground state properties of dipolar bosons trapped in…
Recent transport experiments have established that two-dimensional electron systems with high-index partial Landau level filling, $\nu^{*} =\nu - \lbrack \nu \rbrack$, have ground states with broken orientational symmetry. In a mean-field…
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
Quantum spin Hall edge transport in two-dimensional transition-metal dichalcogenides depends on whether their one-dimensional edge channels are preserved under realistic substrates and device boundaries. Here we implement spin-orbit…
We discuss dynamic spin susceptibility (DSS) in two-dimensional (2D) Dirac electrons with spin-orbit interactions to characterize topological insulators. The imaginary part of the DSS appears as an absorption rate in response to a…
We analyze theoretically and experimentally how nonlinear differential-transmission spectroscopy of a lambda-system medium can provide quantitative understanding of the optical dipole moments and transition energies. We focus on the…
In this thesis we analyze extensions of classical electromagnetic dualities to the noncommutative (NC) 3D and 4D space-times. It is known that the noncomutativity parameter theta becomes its Hodge dual *theta through the NC 4D…
We explore a model akin to axion electrodynamics in which the axion field $\theta (t,\mathbf{x})$ rather than being dynamical is a piecewise constant effective parameter $\theta$ encoding the microscopic properties of the medium inasmuch as…
We re-examine the band structure of the stripe charge ordered state of $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure by using an extended Hubbard model within the Hartree mean-field theory. By increasing pressure, we find a topological…
We investigate the scattering problem of a two-particle composite system on a delta-function potential. Using the time independent scattering theory, we study how the transmission/reflection coefficients change with the height of external…
A theory of equilibrium states of electrons above a liquid helium surface in the presence of an external clamping field is built based on the first principles of quantum statistics for the system of many identical Fermi-particles. The…
The non-relativistic interacting electron gas in an external field of positively charged massive cores is dealt with in the scheme of second quantization. Ladder operators that change between stationary states of contiguous energy…
We develop a simple model of surface states for topological insulators, developing matching relations for states on surfaces of different orientations. The model allows one to write simple Dirac Hamiltonians for each surface, and to…
The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $\theta$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous…
We investigate the propagation of a massless scalar field on a star graph, modeling the junction of $n$ quantum wires. The vertex of the graph is represented by a point-like impurity (defect), characterized by a one-body scattering matrix.…
We review the application of the spectral zeta-function to the 1- loop properties of quantum field theories on manifolds with boundary, with emphasis on Euclidean quantum gravity and quantum cosmology. As was shown in the literature some…