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We consider surface states in semiconductors with inverted-band structures, such as $\alpha$-Sn and HgTe. The main interest is the interplay of the effect of a strain of an arbitrary sign and that of the sample finite size. We consider, in particular, a model system comprised of a gapless semiconductor (e.g. HgTe or $\alpha$-Sn) of finite-width sandwiched between layers of a regular-band semiconductor (e.g. CdTe or InSb). We clarify the origin of various transitions that happen at a given strain with the change of the sample thickness, in particular the transition between the Dirac semimetal and quasi-3D (quantized) topological insulator. Our conclusion opposes those reached recently by the majority of researchers. We show that near the transition point the surface state cannot be treated as a truly topological one since the parameters of the problem are such that an appreciable overlap of the surface states' wave functions located at opposite boundaries occur. As a result, a spin-conserving, elastic impurity scattering between the states located at opposite boundaries will induce substantial backscattering and destroy the robustness of the surface state. For the k-p Kane model we derive hard-wall boundary conditions in the case when the regular-band materials form high barriers for the carriers of the inner inverted-band semiconductor (for example, CdTe/HgTe/CdTe and CdTe/$\alpha$-Sn/CdTe cases). We show that in this case the boundary conditions have universal and simple form and allow investigation of the realistic case of finite mass of the heavy-hole band, and comparison of the results obtained within the Kane and Luttinger models. In particular, a new type of surface states (wing states) developes with application of strain in the Kane model and is absent in the Luttinger model., Comment: 16 pages, 5 figures; Extended version; Discussions section , Appendix B, derivation of some formulas are added

We revisit the problem of surface states in semiconductors with inverted band structures, such as $\alpha$-Sn and HgTe. We unravel the confusion that arose over the past decade regarding the origin of the surface states, their topological nature, and the role of strain. Within a single minimalistic description, we reconcile different solutions found in the 1980s with the results obtained from modern-day numerical simulations, allowing us to unambiguously identify all branches of surface states around the $\Gamma$-point of the Brillouin zone in different regimes. We also show that strain is a smooth "deformation" to the surface states, following the usual continuity principle of physics, and not leading to any drastic change of the physical properties in these materials, in contrast to what has recently been advanced in the literature. We consider biaxial in-plane strain that is either tensile or compressive, leading to different branches of surface states for topological insulators and Dirac semimetals, respectively. Our model can help in interpreting numerous experiments on topological surface states originating from inverted-band semiconductors., Comment: 11 pages, 7 figures; extended version. New section IV (Dirac semimetal regime), two figures and references added

Entanglement of two different quantum orders is of an interest of the modern condensed matter physics. One of the examples is the dynamical multiferroicity, where fluctuations of electric dipoles lead to magnetization. We investigate this effect at finite temperature and demonstrate an elevated magnetic response of a ferroelectric near the ferroelectric quantum critical point (FE QCP). We calculate the magnetic susceptibility of a bulk sample on the paraelectric side of the FE QCP at finite temperature and find enhanced magnetic susceptibility near the FE QCP. We propose quantum paraelectric strontium titanate (STO) as a candidate material to search for dynamic multiferroicity. We estimate the magnitude of the magnetic susceptibility for this material and find that it is detectable experimentally., Comment: 9 pages, 1 Fig., contains a Supplemental Material (pdf); Accepted by Journal of Physics: Condensed Matter

In semiconductor nanostructures nonradiative Auger recombination is enhanced by the presence of boundaries which relax the momentum conservation and thereby removes the threshold reduction for these processes. We propose a method to strongly reduce the Auger recombination rate by injecting spin-polarized carriers. Our method is illustrated on the example of a quantum well in which the spin-orbit coupling of conduction band is negligible as compared to valence band and thus holes can be considered as spin-unpolarized. The suppression factor of the Auger recombination is determined by the two-dimensional character of the system, given by the ratio of the Fermi energy of electrons and the separation of the electron levels quantized in the growth direction. Our predictions can be tested experimentally and we discuss their implications for semiconductor lasers relying on injection of spin-polarized electrons., Comment: 4 pages, 1 figure

We have studied the edge spin accumulation in a high mobility two-dimensional electron gas formed in a symmetric well with two subbands. This study is strongly motivated by the recent experiment of Hernandez et al. [Phys. Rev. B {\bf 88}, 161305(R) (2013)] who demonstrated the spin accumulation near the edges of a bilayer symmetric GaAs structure in contrast to no effect in a single-layer configuration. The intrinsic mechanism of the spin-orbit interaction we consider arises from the coupling between two subband states of opposite parities. We obtain a parametrically large magnitude of the edge spin density for the two-subband sample as compared to the usual single-subband structure. We show that the presence of a gap in the system, i.e., the energy separation $\Delta$ between the two subband bottoms, changes drastically the picture of the edge spin accumulation. Thus one can easily proceed from the regime of weak spin accumulation to the regime of strong one by varying the Fermi energy (electron density) and/or $\Delta$. We estimate that by changing the gap $\Delta$ from zero up to $1\div 2$ K, the magnitude of the effect changes by three orders of magnitude. This opens up the possibility for the design of new spintronic devices., Comment: 6 pages, 2 figures, expanded text and added Supplementary Material

We consider a two-dimensional structure with spin-orbit-related splitting of the electron (hole) spectrum and calculate the edge spin density which appears due to the intrinsic mechanism of spin-orbit interaction in the presence of a charge current through the structure. We concentrate on the quasi-ballistic case when a mean free path, being much smaller than the sample size, is larger than the spin precession length determined by the value of the spin-orbit splitting. We show that regardless of the presence or absence of the bulk spin current the main source of the edge spin density is the boundary scattering itself. The character of the edge spin density depends on the smoothness of the bulk impurity potential. We have calculated the edge spin density profile for an arbitrary smoothness of the scattering potential in the bulk, and discussed relation to the existing experiments for two-dimensional holes., Comment: 6 pages, 1 fig

We propose a nano-scale realization of a phonon laser utilizing phonon-assisted spin flips in quantum dots to amplify sound. Owing to a long spin relaxation time, the device can be operated in a strong pumping regime, in which the population inversion is close to its maximal value allowed under Fermi statistics. In this regime, the threshold for stimulated emission is unaffected by spontaneous spin flips. Considering a nanowire with quantum dots defined along its length, we show that a further improvement arises from confining the phonons to one dimension, and thus reducing the number of phonon modes available for spontaneous emission. Our work calls for the development of nanowire-based, high-finesse phonon resonators., Comment: 5 pages, 2 figures

We consider a 2D ballistic and quasi-ballistic structures with spin-orbit-related splitting of the electron spectrum. The ballistic region is attached to the leads with a voltage applied between them. We calculate the edge spin density which arises in the presence of a charge current through the structure. We solve the problem with the use of the method of scattering states and clarify the important role of the unitarity of scattering. In the case of a straight boundary it leads to exact cancellation of long-wavelength oscillations of the spin density. In general, however, the smooth spin oscillations with the spin precession length may arise, as it happens, e.g., for the wiggly boundary. Moreover, we show that the result crucially depends on the form of the spin-orbit Hamiltonian., Comment: 5 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1007.1133

We consider a mesoscopic {\it ballistic} structure with Rashba spin-orbit splitting of the electron spectrum. The ballistic region is attached to the leads with a voltage applied between them. We calculate the edge spin density which appears in the presence of a charge current through the structure due to the difference in populations of electrons coming from different leads. Combined effect of the boundary scattering and spin precession leads to oscillations of the edge polarization with the envelope function decaying as a power law of the distance from the boundary. The problem is solved with the use of scattering states. The simplicity of the method allows to gain an insight into the underlaying physics. We clarify the role of the unitarity of scattering for the problem of edge spin accumulation. In case of a straight boundary it leads to exact cancellation of all long-wave oscillations of the spin density. As a result, only the Friedel-like spin density oscillations with the momentum 2k_F survive. However, this appears to be rather exceptional case. In general, the smooth spin oscillations with the spin precession length recover, as it happens, e.g., for the wiggly boundary. We demonstrate also, that there is no relation between the spin current in the bulk, which is zero in the considered case, and the edge spin accumulation., Comment: Latex, 6 pages, 2 figs

This paper has been withdrawn by the authors due to inadequate formula Eq. (105) and following arguments., Comment: This paper has been withdrawn

We study spin relaxation in a two-electron quantum dot in the vicinity of the singlet-triplet crossing. The spin relaxation occurs due to a combined effect of the spin-orbit, Zeeman, and electron-phonon interactions. The singlet-triplet relaxation rates exhibit strong variations as a function of the singlet-triplet splitting. We show that the Coulomb interaction between the electrons has two competing effects on the singlet-triplet spin relaxation. One effect is to enhance the relative strength of spin-orbit coupling in the quantum dot, resulting in larger spin-orbit splittings and thus in a stronger coupling of spin to charge. The other effect is to make the charge density profiles of the singlet and triplet look similar to each other, thus diminishing the ability of charge environments to discriminate between singlet and triplet states. We thus find essentially different channels of singlet-triplet relaxation for the case of strong and weak Coulomb interaction. Finally, for the linear in momentum Dresselhaus and Rashba spin-orbit interactions, we calculate the singlet-triplet relaxation rates to leading order in the spin-orbit interaction, and find that they are proportional to the second power of the Zeeman energy, in agreement with recent experiments on triplet-to-singlet relaxation in quantum dots., Comment: 29 pages, 14 figures, 1 table

We have described the electron spin dynamics in the presence of Rashba spin- orbit interaction and disorder using the spin-density matrix method. We showed that in the Born approximation in the scattering amplitude the spin current is zero for an arbitrary ratio of the spin-orbit splitting and the scattering rate and for an arbitrary disorder potential. We also describe some magnetotransport phenomena such as negative magnetoresistance and a negative charge Hall effect which occur in the presence of spin-orbit coupling., Comment: Proceedings of LT24 Conference, Invited talk, 4 pages

We have described electron spin dynamics in the presence of the spin-orbit interaction and disorder using the spin-density matrix method. Exact solution is obtained for an arbitrary 2D spin-orbit Hamiltonian and arbitrary smoothness of the disorder potential. Spin current depends explicitely on the disorder properties, namely the smoothness of the disorder potential, even in the ballistic limit when broadening by scattering is much smaller than the spin-orbit related splitting of the energy spectrum. In this sense universal intrinsic spin current does not exist., Comment: LaTeX, 6 pages, 1 fig., Eqs.22,28 are corrected

We have described the electron spin dynamics in the presence of the spin-orbit interaction and disorder using the spin-density matrix method. We showed that in the Born approximation in the scattering amplitude the spin current is zero for an arbitrary ratio of the spin-orbit splitting and the scattering rate. Various types of the disorder potential are studied. We argue that the bulk spin current has always an {\it extrinsic} nature and depends explicitely on scattering by impurities since it appears only beyond the Born approximation in the scattering amplitude., Comment: 5 pages, RevTex, 1 Fig

We have reconsidered the problem of spin injection across ferromagnet/non-magnetic-semiconductor (FM/NMS) and dilute-magnetic-semiconductor/non-magnetic-semiconductor interfaces, for structures with \textit{finite} magnetic layers (FM or DMS). By using appropriate physical boundary conditions, we find expressions for the resistances of these structures which are in general different from previous results in the literature. When the magnetoresistance of the contacts is negligible, we find that the spin-accumulation effect alone cannot account for the $d$ dependence observed in recent magnetoresistance data. In a limited parameter range, our formulas predict a strong $d$ dependence arising from the magnetic contacts in systems where their magnetoresistances are sizable., Comment: 6 pages, 3 eps figs. (extended version- new title + two new figures added)

We review and summarize recent theoretical and experimental work on electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with surrounding nuclear spins. This topic is of particular interest with respect to several proposals for quantum information processing in solid state systems. Specifically, we investigate the hyperfine interaction of an electron spin confined in a quantum dot in an s-type conduction band with the nuclear spins in the dot. This interaction is proportional to the square modulus of the electron wave function at the location of each nucleus leading to an inhomogeneous coupling, i.e. nuclei in different locations are coupled with different strength. In the case of an initially fully polarized nuclear spin system an exact analytical solution for the spin dynamics can be found. For not completely polarized nuclei, approximation-free results can only be obtained numerically in sufficiently small systems. We compare these exact results with findings from several approximation strategies., Comment: 26 pages, 9 figures. Topical Review to appear in J. Phys.: Condens. Matter

We study spin relaxation and decoherence in a GaAs quantum dot due to spin-orbit interaction. We derive an effective Hamiltonian which couples the electron spin to phonons or any other fluctuation of the dot potential. We show that the spin decoherence time $T_2$ is as large as the spin relaxation time $T_1$, under realistic conditions. For the Dresselhaus and Rashba spin-orbit couplings, we find that, in leading order, the effective magnetic field can have only fluctuations transverse to the applied magnetic field. As a result, $T_2=2T_1$ for arbitrarily large Zeeman splittings, in contrast to the naively expected case $T_2\ll T_1$. We show that the spin decay is drastically suppressed for certain magnetic field directions and values of the Rashba coupling constant. Finally, for the spin coupling to acoustic phonons, we show that $T_2=2T_1$ for all spin-orbit mechanisms in leading order in the electron-phonon interaction., Comment: 5 pages, 1 figure

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei for times smaller than the nuclear spin relaxation time. The decay is caused by the spatial variation of the electron envelope wave function within the dot, leading to a non-uniform hyperfine coupling $A$. We show that the usual treatment of the problem based on the Markovian approximation is impossible because the correlation time for the nuclear magnetic field seen by the electron spin is itself determined by the flip-flop processes. The decay of the electron spin correlation function is not exponential but rather power (inverse logarithm) law-like. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by $\hbar N/A$, where $N$ is the number of nuclei inside the dot. The amplitude of precession, reached as a result of the decay, is finite. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots., Comment: Revtex, 11 pages, 5 figures

We study the time evolution of a single spin coupled inhomogeneously to a spin environment. Such a system is realized by a single electron spin bound in a semiconductor nanostructure and interacting with surrounding nuclear spins. We find striking dependencies on the type of the initial state of the nuclear spin system. Simple product states show a profoundly different behavior than randomly correlated states whose time evolution provides an illustrative example of quantum parallelism and entanglement in a decoherence phenomenon., Comment: 6 pages, 4 figures included, version to appear in Phys. Rev. B

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei for times smaller than the nuclear spin relaxation time. The decay is caused by the spatial variation of the electron envelope wave function within the dot, leading to a non-uniform hyperfine coupling. We evaluate the spin correlation function with and without magnetic fields and find that the decay of the spin precession amplitude is not exponential but rather power (inverse logarithm) law-like. For fully polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The corresponding decay time is given by $\hbar N/A$, where $A$ is a hyperfine interaction constant and $N$ the number of nuclei inside the dot. The amplitude of precession, reached as a result of the decay, is finite. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots., Comment: 4 pages, Revtex

W. Apel and Yu.A. Bychkov have recently considered the spin relaxation in a 2D quantum Hall system for the filling factor close to unity [PRL v.82, 3324 (1999)]. The authors considered only one spin flip mechanism (direct spin-phonon coupling) among several possible spin-orbit related ones and came to the conclusion that the spin relaxation time due to this mechanism is quite short: around $10^{-10}$ s at B=10 T (for GaAs). This time is much shorter than the typical time ($10^{-5}$ s) obtained earlier by D. Frenkel while considering the spin relaxation of 2D electrons in a quantizing magnetic field without the Coulomb interaction and for the same spin-phonon coupling. I show that the authors' conclusion about the value of the spin-flip time is wrong and have deduced the correct time which is by several orders of magnitude longer. I also discuss the admixture mechanism of the spin-orbit interaction., Comment: 1 page

We have studied spin-flip transitions between Zeeman sublevels in GaAs electron quantum dots. Several different mechanisms which originate from spin-orbit coupling are shown to be responsible for such processes. It is shown that spin-lattice relaxation for the electron localized in a quantum dot is much less effective than for the free electron. The spin-flip rates due to several other mechanisms not related to the spin-orbit interaction are also estimated., Comment: RevTex, 7 pages (extended journal version, PRB, in press)

We have studied the physical processes responsible for the spin -flip in GaAs quantum dots. We have calculated the rates for different mechanisms which are related to spin-orbit coupling and cause a spin-flip during the inelastic relaxation of the electron in the dot both with and without a magnetic field. We have shown that the zero-dimensional character of the problem when electron wave functions are localized in all directions leads to freezing out of the most effective spin-flip mechanisms related to the absence of the inversion centers in the elementary crystal cell and at the heterointerface and, as a result, to unusually low spin-flip rates., Comment: 6 pages, RevTex

We investigated theoretically the Coulomb drag effect in coupled 2D electron gases in a wide interval of magnetic field and temperature $ 1/\tau \ll \omega_c \ll E_F/\hbar$, $T \ll E_F$, $\tau$ being intralayer scattering time, $\omega_c$ being the cyclotron frequency. We show that the quantization of the electron spectrum leads to rich parametric dependences of drag transresistance on temperature and magnetic field. This is in contrast to usual resistance. New small energy scales are found to cut typical excitation energies to values lower than temperature. This may lead to a linear temperature dependence of transresistance even in a relatively weak magnetic field and can explain some recent experimental data. We present a novel mechanism of Coulomb drag when the current in the active layer causes a magnetoplasmon wind and the magnetoplasmons are absorbed by the electrons of the passive layer providing a momentum transfer. We derived general relations that describe the drag as a result of resonant tunneling of magnetoplasmons., Comment: ZIP archive,10 pages, 3 ps figures, submitted to PRB

We consider the influence of the electron-electron interaction on the nonlinearity of the current-voltage characteristic of the tunnel junction at low bias (diffusive anomaly) in the presence of the classical magnetic field. We present the theory of a new phenomenon which manifests itself in the strong anisotropy of a diffusive anomaly for different orientations of the magnetic field with respect to the interface of the tunnel junction. The nonlinear differential tunneling conductance has a universal magnetic field dependence, so that only the magnetic field component perpendicular to the interface is involved. In particular, when the magnetic field is parallel to the interface, the I-V characteristic does not depend on the value of the magnetic field., Comment: 12 pages, LaTeX format, 2 figures (available from the authors), accepted for publication by PRB

We investigate the ground state of 2D electron gas in Quantum Hall regime at the filling factor slightly deviating from unity, that can be viewed as a sparse lattice of skyrmions. We have found that in the low density limit skyrmions are bound in pairs, those forming the actual lattice. We have shown that at further density increase the lattice undergoes a quantum phase transition, an analogue of superconducting phase transition in Josephson junction arrays., Comment: 4 pages REVTEX, 3 Postscript figures