We study spectra of surface states in 2D topological insulators based on HgTe/(Hg,Cd)Te quantum wells and 3D Bi₂Se₃-type compounds by constructing a class of feasible time-reversal invariant boundary conditions (BCs) for an effective kp-Hamiltonian and a tight-binding model of the topological insulators. The BCs contain some phenomenological parameters which implicitly depend on both bulk Hamiltonian parameters and crystal potential behavior near the crystal surface. Space symmetry reduces the number of the boundary parameters to four real parameters in the 2D case and three in the 3D case. We found that the boundary parameters may strongly affect not only an energy spectrum but even the very existence of these states inside the bulk gap near the Brillouin zone center. Nevertheless, we reveal in frames of the tight-binding model that when surface states do not exist in the bulk gap in the Brillouin zone center they cross the gap in other points of the Brillouin zone in agreement with the bulk-boundary correspondence.

Unique properties of plasmons in two-dimensional electron systems (2DESs) have been studied for many years. Existing theoretical approaches allow for analytical study of the properties of ungated and gated plasmons in two fundamental, ideal cases—the 2DES in a dielectric environment and under an infinite metallic gate, respectively. Here we introduce an analytical theory of the interaction of gated and ungated plasmons in partly gated 2DES. Generally, a finite-width gate is formed by a metallic strip placed over an infinite plane hosting 2D electrons. Our solution, in particular, describes the propagating plasmon modes with their charge density having $N$ nodes under the gate. In this regard, a new mode with $N=0$ has been found in addition to the gapped modes with $N=1,2,\cdots$ previously derived from numerical calculations. Unexpectedly, this fundamental plasmon mode has been found to differ substantially from the rest. In fact, it is characterized by gapless square root dispersion and represents a hybrid of gated and ungated plasmons. In contrast to the higher modes, the currents and lateral fields of the fundamental mode are localized mainly to the outside area in the vicinity of the gate. Heretofore, such a “near-gate plasmon” has never been considered.

We report on a contribution to the microwave response of a two-dimensional electron system in a magnetic field which originates from excitation of virtual Bernstein modes. These collective modes emerge as a result of interaction between the usual magnetoplasmon mode and cyclotron resonance harmonics. The electrons are found to experience a strongly enhanced radiation field when its frequency falls in a gap of the Bernstein modes spectrum. This field can give rise to nonlinear effects, one of which, the parametric cyclotron resonance, is discussed. We argue that this resonance leads to a plasma instability in the ultraclean system. The instability-induced heating is responsible for the giant photoresistivity spike recently observed in the vicinity of the second cyclotron resonance harmonic.

A brief survey is given of theoretical works on surface states (SSs) in Dirac materials. Within the formalism of envelope wave functions and boundary conditions for these functions, a minimal model is formulated that analytically describes surface and edge states of various (topological and non-topological) types in several systems with Dirac fermions (DFs). The applicability conditions of this model are discussed.Comment: Contribution for the JETP special issue dedicated to L.V. Keldys

The Kohn-Luttinger method of envelope functions is generalized to the case of heterostructures with atomically sharp heterojunctions based on lattice-matched layers of related semiconductors with zinc-blende symmetry. For electron states near the Γ point in (001) heterostructures the single-band effective-mass equation is derived, taking into account both the spatial dependence of the effective mass and effects associated with the atomically sharp heterojunctions. A small parameter is identified, in powers of which it is possible to classify the various contributions to this equation. For hole states only the main contributions to the effective Hamiltonian, due to the sharpness of the heterojunctions, are taken into account. An expression is derived for the parameter governing mixing of states of heavy and light holes at the center of the 2D Brillouin zone.