Semiclassical energy levels of electrons in metals with band degeneracy lines

We show that in calculating the semiclassical energy levels of electrons in metals located in a magnetic field, one must determine whether or not the corresponding electron paths in the space of wave vectors k are attached to a band degeneracy line. Calculations in the two possible cases, i.e., with and without such attachment, differ by |e|ℏ/2m*c, where e is the electron charge and m* is the cyclotron mass of the electron. This shift in the energy levels is of a topological nature, and its existence depends neither on the specific form of the electron dispersion relation ε(k) near the electron path nor on the shape or size of this path. The reason for this shift lies in the fact that the electron orbit is attached to the band degeneracy line, which is the line of singular points of the Bloch wave functions. In many respects this effect is similar to the Aharonov-Bohm effect if the band degeneracy line is considered an infinitely thin “solenoid.” This shift in energy levels should become apparent in studies of oscillation phenomena in metals. We give examples of metals in which the conditions for observing the shift is probably the most favorable. Zh. éksp. Teor. Fiz. 114, 1375–1392 (October 1998)     

Berry curvature in graphene: a new approach

In the present paper we have directly computed the Berry curvature terms relevant for graphene in the presence of an inhomogeneous lattice distortion. We have employed the generalized Foldy–Wouthuysen framework, developed by some of us. We show that a non-constant lattice distortion leads to a valley–orbit coupling which is responsible for a valley–Hall effect. This is similar to the valley–Hall effect induced by an electric field proposed in the literature and is the analogue of the spin–Hall effect in semiconductors. Our general expressions for Berry curvature, for the special case of homogeneous distortion, reduce to the previously obtained results. We also discuss the Berry phase in the quantization of cyclotron motion.     

Magnetooptic measurements of the cyclotron mass and g-factor of light holes in GaAs

An emission line appearing in the hot-luminescence spectrum of GaAs at a frequency shifted from the laser line by the cyclotron energy of light holes is observed and investigated. Analysis of the magnetooscillations of the intensity of this line shows that the line is due to the recombination of a photoexcited electron and a light hole after the hole undergoes energy relaxation between Landau levels. The dependence of the cyclotron mass and g factor of light holes on the hole energy was measured directly and a very strong nonparabolicity of the valence band of GaAs, several times greater than the theoretical estimates, was observed. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 766–771 (10 December 1996)     

Manifestation of exitonic effects in the magneto-oscillations of the intensity of the recombination radiation of 2D electrons

A study is made of the temperature dependence of the magnetooscillations of the recombination radiation of 2D electrons from the photoexcited size-quantization subband in an isolated GaAs/AlGaAs quantum well. It is shown that at high temperatures (T>10 K) the period of the oscillations is determined by the ratio of the intersubband energy splitting and the sum of the electron and hole cyclotron energies. It is found that as the temperature decreases (T<5 K), a new series of oscillations (with the same period but with a larger phase shift), which are associated with the appearance of excitonic states under the Landau levels, appears. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 10, 719–724 (25 November 1996)     

Manipulation of Dirac points in graphene-like crystals

We review different scenarios for the motion and merging of Dirac points in 2D crystals. These different types of merging can be classified according to a winding number (a topological Berry phase) attached to each Dirac point. For each scenario, we calculate the Landau level spectrum and show that it can be quantitatively described by a semiclassical quantization rule for the constant energy areas. This quantization depends on how many Dirac points are enclosed by these areas. We also emphasize that different scenarios are characterized by different numbers of topologically protected zero energy Landau levels.     

Interband resonant tunneling in superconductor heterostructures in a quantizing magnetic field

The resonant tunneling of electrons through quasistationary levels in the valence band of a quantum well in double-barrier structures based on III–V materials with type-II heterojunctions is considered in a quantizing magnetic field directed perpendicularly to the interfaces. The transmission coefficients of the tunnel structure for transitions from states corresponding to different Landau levels are calculated using the Kane model. It is shown that transitions with a unit change in the Landau level index n as a result of mixing of the wave functions of states with opposite spin orientations are possible on the interfaces due to spin-orbit coupling. The probability of such transitions can be comparable to the probability of transitions without a change in the Landau level index for InAs/AlGaSb/GaSb resonant-tunneling structures. Fiz. Tverd. Tela (St. Petersburg) 40, 2121–2126 (November 1998)     

Spin–orbit coupling and semiclassical electron dynamics in noncentrosymmetric metals

Spin–orbit coupling of electrons with the crystal lattice plays a crucial role in materials without inversion symmetry, lifting spin degeneracy of the Bloch states and endowing the resulting nondegenerate bands with complex spin textures and topologically nontrivial wavefunctions. We present a detailed symmetry-based analysis of the spin–orbit coupling and the band degeneracies in noncentrosymmetric metals. We systematically derive the semiclassical equations of motion for fermionic quasiparticles near the Fermi surface, taking into account both the spin–orbit coupling and the Zeeman interaction with an applied magnetic field. Some of the lowest-order quantum corrections to the equations of motions can be expressed in terms of a fictitious “magnetic field” in the momentum space, which is related to the Berry curvature of the band wavefunctions. The band degeneracy points or lines serve as sources of a topologically nontrivial Berry curvature. We discuss the observable effects of the wavefunction topology, focusing, in particular, on the modifications to the Lifshitz–Onsager semiclassical quantization condition and the de Haas-van Alphen effect in noncentrosymmetric metals.     

Semiclassical diagonalization of quantum Hamiltonian and equations of motion with Berry phase corrections

It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum systems may be affected by Berry phase terms. It is therefore important to find a general procedure allowing for the determination of semiclassical Hamiltonian with Berry Phase corrections. This article presents a general diagonalization method at order ħ for a large class of quantum Hamiltonians directly inducing Berry phase corrections. As a consequence, Berry phase terms on both coordinates and momentum operators naturally arise during the diagonalization procedure. This leads to new equations of motion for a wide class of semiclassical system. As physical applications we consider here a Dirac particle in an electromagnetic or static gravitational field, and the propagation of a Bloch electrons in an external electromagnetic field.     

Breakdown of Luttinger's theorem in two-orbital Mott insulators

An analysis of Luttinger's theorem shows that – contrary to recent claims – it is not valid for a generic Mott insulator. For a two-orbital Hubbard model with two electrons per site the crossover from a non-magnetic correlated insulating phase (Mott or Kondo insulator) to a band insulator is investigated. Mott insulating phases are characterized by poles of the self-energy and corresponding zeros in the Greens functions defining a “Luttinger surface” which is absent for band insulators. Nevertheless, the ground states of such insulators with two electrons per unit cell are adiabatically connected.     

Excitonic effects in the recombination radiation spectra of completely filled Landau levels of two-dimensional electrons

The recombination radiation spectra of two-dimensional electrons in an asymmetrically doped GaAs/AlGaAs quantum well are investigated at different temperatures and laser-excitation energies. At low temperatures and in high magnetic fields the recombination lines of the electrons from completely filled Landau levels are split into narrow sublevels. It is shown that this fine structure of the Landau levels is due to the presence of excitonic effects in the initial and final states of the photoexcited system. It is demonstrated that the recombination process is accompanied by the excitation of intersubband and cyclotron magnetoplasma modes. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 38–43 (10 January 1997)     

Orbital magnetism of 2D chaotic lattices

We study the orbital magnetism of 2D lattices with chaotic motion of electrons within a primitive cell. Using the temperature diagrammatic technique, we evaluate the averaged value and rms fluctuation of the magnetic response in the diffusive regime within the model of noninteracting electrons. The fluctuations of the magnetic susceptibility turn out to be large and at low temperature can be of the order of χL(k _Fl)^3/2, where k _F is the Fermi wave vector, l is the mean free path, and χL is the Landau susceptibility. In a certain region of magnetic fields the paramagnetic contribution to the averaged response is field-independent and larger than the absolute value of the Landau response. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 979–983 (25 June 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Landau quantization and equatorial states on the surface of a nanosphere

The Landau quantization for the electron gas on the surface of a sphere is considered. It is shown that in the regime of strong fields the lowest energy states are those with magnetic quantum numbers m of order of Φ /Φ₀, the number of magnetic flux quanta piercing the sphere. For an electron gas of low density (semiconducting situation) it leads to the formation of an electronic stripe on the equator of the sphere in high fields. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 6, 405–409 (25 September 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Quantum Hall effect in a quasi-three-dimensional HgTe film

Magnetotransport of a quasi-three-dimensional (100-nm) HgTe film in quantized magnetic fields has been experimentally investigated. It has been found that the film exhibits pronounced quantization of the Hall resistance accompanied by deep minima of the dissipative resistance. A transition from the three-dimensional behavior of Shubnikov-de Haas oscillations in semiclassical magnetic fields (ω_cτ _q ≤ 1) to a two-dimensional one in the quantum-Hall-effect regime has been discovered. The conduction electron cyclotron effective mass in mercury telluride has been determined from the temperature dependence of the Shubnikov-de Hass oscillations in such magnetic fields.     

The effect of C atom concentration on the electronic properties of boron carbonitride alloy nanotube in zig-zag form

Electronic properties of single-walled boron nitride nanotube in zig-zag form are numerically investigated by replacing B atoms with C atoms. Using a tight-binding Hamiltonian, the methods based on Green’s function theory, Landauer formalism and Dyson equation, the electronic density of states and electronic conductance in boron nitride nanotube and boron carbonitride nanotube are calculated. Our calculations indicate that in a boron nitride nanotube, the localized states associated with C impurities appear as the concentration of C atoms increases. The boron carbonitride nanotube thus behaves like a semiconductor. Also, by increasing the C atom concentration, the voltage in the first step on the I–V characteristics decreases, whereas the corresponding current increases.     

Wave-packet dynamics of Bloch electrons—Role of Berry phase

Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest in the role of Berry phase in spintronics, we reconsidered the problem of adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We showed, using only the fundamental principles of quantum mechanics, that the effective wave-packet dynamics of Bloch electrons is conveniently described by a set of equations of motion (EOM) in which a non-Abelian Berry phase associated with the internal degree of freedom appears.     

Quantum Hall effect in the bulk semiconductors bismuth and antimony tellurides: Proof of the existence of a current-carrier reservoir

The quantization of the Hall resistivity ρ_xy in the form of plateaus in the dependence of ρ_xy on the magnetic field B is observed in the semiconductors Bi₂Te₃ and Sb₂Te₃; the minima of the transverse magnetoresistivity ρ_xx correspond to the start of the plateaus. The quantization of ρ_xy is due to the presence of a current-carrier reservoir. An impurity band with a high density of states or a different band with a much higher current-carrier effective mass serves as the reservoir. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 11, 754–758 (10 December 1999)     

Kinetics of two-dimensional electrons on a curved surface

A number of effects associated with the curvature of the surface on which a two-dimensional (2D) electron gas is placed are studied. The most significant effect in an external magnetic field (which for 2D electrons becomes effectively nonuniform) is the lifting of the degeneracy of the Landau levels. The intensity and shape of the cyclotron resonance line (inhomogeneously broadened) for different polarizations and the corrections to the Hall constant are found for the example of a circular cylinder. A picture of the quantization of the conductance that is qualitatively different from the case of a flat strip is obtained for a quasi-one-dimensional quantum wire in the form of a hollow cylinder. It is shown that in contradistinction to the planar case the spectrum of 2D electrons on the curved surface is sensitive to the sign of the spin-orbit coupling constant (for a fixed sign of the curvature). For hetero-junctions, for example, this opens up new possibilities for extracting information about their “hidden parameters.” Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 421–426 (25 September 1996)     

Magneto-intersubband zener tunneling in a wide GaAs quantum well at high filling factors

The dependence of the differential resistance r _xx on the dc current density J _dc in a wide GaAs quantum well with two occupied size quantization subbands has been investigated at the temperature T = 4.2 K in the magnetic fields B < 1 T. A peak, whose position is given by the relation 2R _c eE _H = ħω_c/2, where R _c is the cyclotron radius, E _H is the Hall electric field, and ω_c is the cyclotron frequency, has been observed in the r _xx (J _dc) curves at high filling factors. The experimental results are attributed to Zener tunneling of electrons between the Landau levels of different subbands.