arXiv subjects

V. A. Volkov

Publications and source records attributed to V. A. Volkov.

At least 19 recordsLinked to original sources

arXiv2024

Plasmons in two-dimensional electron systems with infinite and semi-infinite metal gratings

We analytically investigate the plasmons propagating in a homogeneous two-dimensional (2D) electron system, along the metal grating in the form of a periodic array of strip-shaped electrodes (gates) in the vicinity of the 2D system. We show that in the case of semi-infinite grating, the Tamm plasmon modes localized near and propagating along the grating edge can exist in the gaps of the plasmonic band structure provided that the last gate differs in width from the other gates. When the last gate is wider, the spectrum of the fundamental Tamm plasmon mode lies in the lowest frequency gap, below the first plasmonic band. Importantly, we find the mode to exist in this case only for finite values of the wave vector along the grating. Otherwise, if the width of the last gate is smaller, the Tamm plasmon modes occupy higher frequency gaps, and delocalized plasmons from the first frequency band become the lowest frequency excitations.

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arXiv2021

Quasi-stationary near-gate plasmons in van der Waals heterostructures

Near-gate plasmons are a new type of plasma oscillations emerging in homogeneous two-dimensional electron systems where a gate provides partial screening of electron-electron interaction. Here we develop a theory of the near-gate plasmons in van der Waals heterostructures comprising a conducting layer separated by a thin insulator from an uncharged disk-shaped gate. We show that in these structures the near-gate plasmons form gate-size-quantized quasi-stationary discrete modes even in the collisionless limit. Belonging to continuum spectrum of two-dimensional plasmons outside of the disk-gate, the near-gate plasmons are manifested as Fano-like resonances in frequency and magnetodispersions of scattering cross-section of the former scattered off the region under the gate. This enables to recover spectrum of the near-gate plasmons in the van der Waals heterostructures using near-field imaging techniques.

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arXiv2021

Electrically controllable cyclotron resonance

Cyclotron resonance (CR) is considered one of the fundamental phenomena in conducting systems. In this paper, we study CR in a gated two-dimensional (2D) electron system (ES). Namely, we analyze the absorption of electromagnetic radiation incident normal to the gated 2DES, where a standard dielectric substrate separates the 2D electron sheet and the metallic steering electrode ("gate"); the whole system is placed in the perpendicular magnetic field. Our analysis reveals the redshift of the absorption peak frequency compared to the electron cyclotron frequency. The redshift appears in low-frequency regime, when the resonant frequency is much less than the frequency of Fabry-Perot modes in natural resonator "2D electron sheet - substrate - gate". Moreover, we find this shift to be dependent on the electron density of 2DES. Therefore, it can be controlled by varying the gate voltage. We predict that the shift can be large in realistic gated or back-gated 2DESs. The obtained controllability of CR in gated 2DES opens the door for exploring new physics and applications of this phenomenon.

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arXiv2020

Plasmons and magnetoplasmons in partially bounded two-layer electron systems

We have analytically studied plasmons in an electron system comprised of two spatially separated layers -- an infinite two-dimensional electron system (2DES) and a 2D strip. Our analysis reveals the existence of plasmon modes that are localized near and propagate along the strip. These modes are characterized by the wave vector in the direction of the strip, as well as the number of charge density nodes, N, across the strip. In the long-wavelength limit, the fundamental mode N=0 is found to have gapless linear dispersion. When the external perpendicular magnetic field is applied, this mode remains gapless and exhibits peculiar magnetodispersion. We analyze the correlation between our findings and the previously established results on plasmons in gated and partially gated 2DESs.

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arXiv2019

Interaction of gated and ungated plasmons in two-dimensional electron systems

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 dielectric environment and under an infinite metallic gate, respectively. However, it is for the first time that we introduce an analytical theory of the interaction of gated and ungated plasmons in partly gated 2DES. Generally, a finitewidth 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,..., previously derived from numerical calculations. Unexpectedly, this fundamental plasmon mode has been found to differ substantially from the rest. In fact, it is characterised 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.

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arXiv2018

Quantum Confinement and Heavy Surface States of Dirac Fermions in Bismuth (111) Films: an Analytical Approach

Recent high-resolution angle-resolved photoemission spectroscopy experiments have given a reason to believe that pure bismuth is topologically non-trivial semimetal. We derive an analytic theory of surface and size-quantized states of Dirac fermions in Bi(111) films taking into account the new data. The theory relies on a new phenomenological momentum-dependent boundary condition for the effective Dirac equation. The boundary condition is described by two real parameters that are expressed by a linear combination of the Dresselhaus and Rashba interface spin-orbit interaction parameters. In semi-infinite Bi(111), near $\overline{\rm M}$-point the surface states possess anisotropical parabolic dispersion with very heavy effective mass in $\overline{\rm Γ}-\overline{\rm M}$ direction order of ten free electron masses, and light effective mass in $\overline{\rm M}-\overline{\rm K}$ direction order of one hundredth of free electron mass. In Bi(111) films with equivalent surfaces, the surface states from top and bottom surfaces are not splitted. In such symmetric film with arbitrary thickness, bottom of the lowest quantum confinement subband in conduction band coincides with the bottom of bulk conduction band in $\overline{\rm M}$-point.

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arXiv2018

Effective Dresselhaus and Rashba spin-orbit interactions in narrow quantum wells

Rashba and linear Dresselhaus interactions are believed to yield dominant contribution to the spin splitting of two-dimensional electrons in the quantum wells based on A$_3$B$_5$ compounds. We show that the interfacial spin-orbit interaction significantly renormalizes the value of the corresponding Rashba ($α_{SIA}$) and Dresselhaus ($α_{BIA}$) parameters. For this purpose, we solve the effective mass equation in a quantum well supplemented by the original boundary conditions on the atomically sharp interfaces and calculate the interfacial contributions to $α_{SIA}$ and $α_{BIA}$. Our results explain a considerable spread in the experimental data on spin-orbit parameters in GaAs/AlGaAs quantum wells. We also demonstrated that the non-equivalence of the interfaces leads to the anisotropy of the spin splitting even in quantum wells with zero average electric field.

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arXiv2017

Resonance Absorption of Terahertz Radiation in Nanoperforated Graphene

Recent measurements of the conductivity of nanoperforated graphene are interpreted in terms of edges states existing near the edge of each nanohole. The perimetric quantization of edge states should result in the formation of a quasi-equidistant ladder of quasistationary energy levels. Dirac fermions filling this ladder rotate about each nanohole in the direction determined by the valley index. It is shown that the irradiation of this system by circularly polarized terahertz radiation leads to a resonance in absorption in one of the valleys. The magnitude of absorption at the resonance frequency can be controlled by means of gate voltage.

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arXiv2017

Aharonov-Bohm oscillations caused by non-topological surface states in Dirac nanowires

One intriguing fingerprint of surface states in topological insulators is the Aharonov-Bohm effect in magnetoconductivity of nanowires. We show that surface states in nanowires of Dirac materials (bismuth, bismuth antimony, and lead tin chalcogenides) being in non-topological phase, exhibit the same effect as amendment to magnetoconductivity of the bulk states. We consider a simple model of a cylindrical nanowire, which is described by the 3D Dirac equation with a general $T$-invariant boundary condition. The boundary condition is determined by a single phenomenological parameter whose sign defines topological-like and non-topological surface states. The non-topological surface states emerge outside the gap. In longitudinal magnetic field $B$ they lead to Aharonov-Bohm amendment for the density of states and correspondingly for conductivity of the nanowire. The phase of these magnetooscillations increases with $B$ from $π$ to $2π$.

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arXiv2017

Surface States of a System of Dirac Fermions: A Minimal Model

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.

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arXiv2017

Fermi arcs formation in Weyl semimetals: the key role of intervalley interaction

We propose an analytical model describing Fermi arc surface states observed in the recent investigations of Weyl semimetals. The effective two-valley Hamiltonian is supplemented by the boundary conditions taking into account both the intravalley and intervalley interfacial interaction. We demonstrate that the latter is crucial for the formation of the surface states having the form consistent with the experimental data. Depending on the magnitude and interplay between the intravalley and intervalley interactions, the Fermi arc connects two nearby or distant valleys. Moreover, the emergence of additional Fermi contours (closed curves not intersecting the Weil points) can be understood in the simplest four-valley approximation. These results open the opportunities for search of new effects in Weyl semimetals under the external fields.

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arXiv2016

Edge plasmon polaritons on a half-plane

The effect of electromagnetic retardation on the spectrum of edge plasmons in a semi-infinite two-dimensional electron system is considered. The problem is reduced to complicated integral equations for the potentials, which are solved upon a major simplification of the kernel. The spatial distribution of the potentials, charges, and currents is analyzed. It is shown that edge plasmon polaritons in the high-conductivity two dimensional system are characterized by a high Q factor at all frequencies, including those lower than the inverse electron relaxation time.

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arXiv2016

Undamped relativistic magnetoplasmons in lossy two-dimensional electron systems

We address electrodynamic effects in plasma oscillations of a lossy 2D electron system whose dc 2D conductivity is comparable to the speed of light. We argue that the perpendicular constant magnetic field B causes astonishing features of magnetoplasma dynamics. We show that plasmon-polariton spectra can be classified using a 'relativistic' phase diagram 2D conductivity divided by the speed of light versus B. An extraordinarily low damping branch in magnetoplasmon-polariton spectra emerges at two phases of this diagram. Some magnetoplasmons at these phases are predicted to be undamped waves.

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arXiv2015

Transport of Massless Dirac Fermions in Non-topological Type Edge States

There are two types of intrinsic surface states in solids. The first type is formed on the surface of topological insulators. Recently, transport of massless Dirac fermions in the band of "topological" states has been demonstrated. States of the second type were predicted by Tamm and Shockley long ago. They do not have a topological background and are therefore strongly dependent on the properties of the surface. We study the problem of the conductivity of Tamm-Shockley edge states through direct transport experiments. Aharonov-Bohm magneto-oscillations of resistance are found on graphene samples that contain a single nanohole. The effect is explained by the conductivity of the massless Dirac fermions in the edge states cycling around the nanohole. The results demonstrate the deep connection between topological and non-topological edge states in 2D systems of massless Dirac fermions.

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arXiv2015

Orbital Quantization in a System of Edge Dirac Fermions in Nanoperforated Graphene

The dependence of the electric resistance R of nanoperforated graphene samples on the position of the Fermi level, which is varied by the gate voltage Vg, has been studied. Nanoperforation has been performed by irradiating graphene samples on a Si/SiO$_2$ substrate by heavy (xenon) or light (helium) ions. A series of regular peaks have been revealed on the R(Vg) dependence at low temperatures in zero magnetic field. These peaks are attributed to the passage of the Fermi level through an equidistant ladder of levels formed by orbitally quantized states of edge Dirac fermions rotating around each nanohole. The results are in agreement with the theory of edge states for massless Dirac fermions.

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arXiv2015

Boundary Conditions and Surface States Spectra in Topological Insulators

We study spectra of surface states in 2D topological insulators (TIs) based on HgTe/(Hg,Cd)Te quantum wells and 3D Bi$_2$Se$_3$-type compounds by constructing a class of feasible time-reversal invariant boundary conditions (BCs) for an effective ${\bf k}{\bf p}$-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.

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arXiv2014

Spin splitting of two dimensional states in the conduction band of asymmetric heterostructures: contribution from the atomically sharp interface

The effect of an atomically sharp impenetrable interface on the spin splitting of the spectrum of two-dimensional electrons in heterostructures based on (001) III-V compounds has been analyzed. To this end, the single band Hamiltonian $Γ_{6c}$ for envelope functions is supplemented by a general boundary condition taking into account the possibility of the existence of Tamm states. This boundary condition also takes into account the spin-orbit interaction, the asymmetry of a quantum well, and the lack of inversion symmetry in the crystal and contains the single phenomenological length $R$ characterizing the structure of the interface at atomic scales. The model of a quasitriangular well created by the electric field $F$ has been considered. After the unitary transformation to zero boundary conditions, in the modified Hamiltonian interfacial contribution appears, from which the two-dimensional spin Hamiltonian is obtained through averaging over the fast motion along the normal. In the absence of magnetic field $\boldsymbol B$, this contribution is the sum of the Dresselhaus and the Bychkov-Rashba terms with the constants renormalized owing to the interfacial contribution. In the field $\boldsymbol B$ containing the quantizing component $B_z$, the off - diagonal (in cubic axes) components of the $g$-factor tensor are linear functions of $|B_z|$ and the number of the Landau level $N$. The results are in qualitative agreement with the experimental data.

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arXiv2014

Interface Contributions to the Spin-Orbit Interaction Parameters of Electrons at the (001) GaAs/AlGaAs Interface

One-body mechanisms of spin splitting of the energy spectrum of 2D electrons in a one-side doped (001) GaAs/Al$_x$Ga$_{1-x}$As quantum well have been studied theoretically and experimentally. The interfacial spin splitting has been shown to compensate (enhance) considerably the contribution of the bulk Dresselhaus (Bychkov-Rashba) mechanism. The theoretical approach is based on the solution of the effective mass equation in a quasitriangular well supplemented by a new boundary condition at a high and atomically sharp heterobarrier. The model takes into account the spin-orbit interaction of electrons with both bulk and interfacial crystal potential having C$_{2v}$ symmetry, as well as the lack of inversion symmetry and nonparabolicity of the conduction band in GaAs. The effective 2D spin Hamiltonian including both bulk and interfacial contributions to the Dresselhaus ($α_{BIA}$) and Rashba ($α_{SIA}$) constants has been derived. The analytical relation between these constants and the components of the anisotropic nonlinear $g$-factor tensor in an oblique quantizing magnetic field has been found. The experimental approach is based, on one hand, on the detection of electron spin resonance in the microwave range and, on the other hand, on photoluminescence measurements of the nonparabolicity parameter. The interfacial contributions to $α_{BIA}$ and $α_{SIA}$ have been found from comparison with the theory.

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