Manifestation of a semimetallic state in cyclotron resonance in low-symmetry HgTe-based quantum wells

Cyclotron-resonance measurements in 21-nm-thick HgTe/CdHgTe quantum wells of different crystallographic orientations have been performed. It has been found that, in contrast to the structures with the (001) orientation of the quantum-well plane, (013)-oriented quantum wells are semimetallic and their absorption spectra exhibit both electron and hole cyclotron-resonance lines. The simultaneous presence of the two types of charge carriers originates from an overlap between the upper heavy-hole quantum-confinement subbands hh1 and hh2. This overlap is caused by the strong interaction of these subbands with the Dyakonov-Khaetskii interface state. Calculations carried out using the eight-band kp-Hamiltonian indicate that, for known values of the band-structure parameters, the overlap between hh2 and hh1 subbands does not occur; this result is in agreement with the cyclotron-resonance data for (001)-oriented structures. The enhanced interaction between heavy-hole and interface states owing to the existence of steps at low-symmetry heterointerfaces may be the mechanism responsible for the appearance of an overlap between subbands in HgTe quantum wells with orientation different from (001).     

(<Emphasis Type="Italic">q</Emphasis><Subscript>1</Subscript>, <Emphasis Type="Italic">q</Emphasis><Subscript>2</Subscript>)-quasimetrics bi-Lipschitz equivalent to 1-quasimetrics

We prove that the conditions of (q₁, 1)- and (1, q₂)-quasimertricity of a distance function ρ are sufficient for the existence of a quasimetric bi-Lipschitz equivalent to ρ. It follows that the Box-quasimetric defined with the use of basis vector fields of class C₁ whose commutators at most sum their degrees is bi-Lipschitz equivalent to some metric. On the other hand, we show that these conditions are not necessary. We prove the existence of (q₁, q₂)-quasimetrics for which there are no Lipschitz equivalent 1-quasimetrics, which in particular implies another proof of a result by V. Schröder.     

Resonance phenomena in domain boundary movement in ferrites

The frequency dependence of magnetic losses in certain ferrites over the frequency range 20–110 MHz is studied. A series of absorption lines was observed in many ferrites. On the basis of an investigation of the change in absorption spectrum as a function of the magnetic history of the specimen, the size of the powder particles, and the external magnetic field, it was concluded that the resonance lines observed are produced by domain boundary resonance.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 41–45, July, 1973.     

Analytic properties of quasiconformal mappings on Carnot groups

The research was supported by the Russian Foundation for Fundamental Research (Grant 94-01-00378) and the International Science Foundation (Grant RAT000).     

On one class of Lipschitz vector fields in ℝ<Superscript>3</Superscript>

Under consideration are some continuous metric functions induced by one class of Lipschitz vector fields in ℝ³. These functions are showed to be quasimetrics within the domain of definition of the vector fields. We prove some analogs of the Rashevsky-Chow Theorem and the Ball-Box Theorem under some restriction on the class of vector fields. The methods of proofs do not use the existence of the nilpotent tangent cone.     

Peak values of the longitudinal conductivity under integer quantum Hall effect conditions for sharp and smooth chaotic potentials

The problem of the peak values of the longitudinal conductivity under integer quantum Hall effect conditions is studied. The limiting cases of sharp and smooth chaotic potentials are considered. In the case of a sharp chaotic potential, the first longitudinal conductivity peak (δ _xx ⁽⁰⁾ ) obtained by the extrapolation of numerical data to an infinite sample size L→∞ is (0.55±0.03)e ²/h. In the case of a smooth chaotic potential, the peak values of the longitudinal conductivity are independent of the Landau level number and decrease as the chaotic-potential correlation length λ increases. The results obtained for sharp and smooth chaotic potentials agree with the reported experimental and numerically calculated data.     

Theory of (<Emphasis Type="Italic">q</Emphasis> <Subscript>1</Subscript>, <Emphasis Type="Italic">q</Emphasis> <Subscript>2</Subscript>)-quasimetric spaces and coincidence points

We introduce (q₁, q₂)-quasimetric spaces and examine their properties. Covering mappings between (q₁, q₂)-quasimetric spaces are investigated. Sufficient conditions for the existence of a coincidence point of two mappings acting between (q₁, q₂)-quasimetric spaces such that one is a covering mapping and the other satisfies the Lipschitz condition are obtained.     

High-frequency modulation of light in diffraction by the Bragg grating with a refractive index traveling wave

The diffraction by a Bragg grating with high-frequency modulation of the refractive index of the medium is analyzed theoretically. The effect of the grating parameters and parameters of an rf signal on the efficiency of modulation of optical signals at frequencies above 10 GHz is investigated.