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In this work we analyze the statistical thermodynamics of Diced lattice carriers employing a Greens function formulation to examine the grand potential, Helmholtz free energy, the grand and ordinary partition functions and entropy. This facilitates the calculation of the specific heat, and all evaluations are carried out for both the degenerate and nondegenerate statistical regimes.

A detailed numerical study of the Helmholtz Green's function for the description of scalar wave propagation through a nano-hole on a plasmonic layer is presented here. In conjunction with this, we briefly review the analytic formulation taking the nano-hole radius as the smallest length parameter of the system. Figures exhibiting the numerical results for this Green's function in various ranges of the transmission region are presented., Comment: 15 pages, 20 figures. arXiv admin note: substantial text overlap with arXiv:1802.01573

We have developed an analytical formulation to calculate the plasmon dispersion relation for a two-dimensional layer which is encapsulated within a narrow spatial gap between two bulk half-space plasmas. This is based on a solution of the inverse dielectric function integral equation within the random-phase approximation (RPA). We take into account the nonlocality of the plasmon dispersion relation for both gapped and gapless graphene as the sandwiched two-dimensional (2D) semiconductor plasma. The associated nonlocal graphene plasmon spectrum coupled to the "sandwich" system is exhibited in density plots, which show a linear mode and a pair of depolarization modes shifted from the bulk plasma frequency., Comment: 14 pages, 4 figures

An integral equation is formulated to describe electromagnetic wave transmission through a sub-wavelength nano-hole in a thin plasmonic sheet in terms of the dyadic Green's function for the associated Helmholtz problem. Taking the subwavelength radius of the nano-hole to be the smallest length of the system, we have obtained an exact solution of the integral equation for the dyadic Green's function analytically and in closed form. This dyadic Green's function is then employed in the numerical analysis of electromagnetic wave transmission through the nano-hole for normal incidence of the incoming wave train. The electromagnetic transmission involves two distinct contributions, one emanating from the nano-hole and the other is directly transmitted through the thin plasmonic layer itself (which would not occur in the case of a perfect metal screen). The transmitted radiation exhibits interference fringes in the vicinity of the nano-hole, and they tend to flatten as a function of increasing lateral separation from the hole, reaching the uniform value of transmission through the sheet alone at large separations., Comment: 14 pages, 24 individual figures organized in 9 captioned groups

Considering screeening of electron scattering interactions in terms of the finite-temperature STLS theory and solving the linearized Boltzmann equation (with no appeal to a relaxation time approximation), we present a theoretical analysis of the low-temperature Seebeck effect in two-dimensional semiconductors with dilute electron densities. We find that the temperature ($T$) dependencies of the diffusion and phonon-drag thermoelectric powers ($S_d$ and $S_g$) can no longer be described by the conventional simple power-laws. As temperature increases, $|S_d|/T$ decreases when $T\gtrsim 0.1 \epsilon_F$ ($\epsilon_F$ is the Fermi energy), while $|S_g|$ first increases and then falls, resulting a peak located at a temperature between Bloch-Gr\"uneisen temperature and $\epsilon_F$., Comment: 12 pages, 5 figures

We analyze inelastic cotunneling through an interacting quantum dot subject to an ambient magnetic field in the weak tunneling regime under a non-adiabatic time-dependent bias-voltage. Our results clearly exhibit photon-assisted satellites and an overall suppression of differential conductance with increasing driving amplitude, which is consistent with experiments. We also predict a zero-anomaly in differential conductance under an appropriate driving frequency., Comment: Phys. Lett. A (in press)

We present a kinetic equation approach to investigate dc transport properties of graphene in the diffusive regime considering long-range electron-impurity scattering. In our study, the effects of interband correlation (or polarization) on conductivity are taken into account. We find that the conductivity contains not only the usual term inversely proportional to impurity density $N_i$, but also an anomalous term that is linear in $N_i$. This leads to a minimum in the density dependence of conductivity when the electron density $N_{\rm e}$ is equal to a critical value, $N_c$. For $N_{\rm e}>N_c$ the conductivity varies almost linearly with the electron density, while it is approximately inversely proportional to $N_{\rm e}$ when $N_{\rm e}

We employ a helicity-basis kinetic equation approach to investigate the anomalous Hall effect in two-dimensional narrow-band semiconductors considering both Rashba and extrinsic spin-orbit (SO) couplings, as well as a SO coupling directly induced by an external driving electric field. Taking account of long-range electron-impurity scattering up to the second Born approximation, we find that the various components of the anomalous Hall current fit into two classes: (a) side-jump and (b) skew scattering anomalous Hall currents. The side-jump anomalous Hall current involves contributions not only from the extrinsic SO coupling but also from the SO coupling due to the driving electric field. It also contains a component which arises from the Rashba SO coupling and relates to the off-diagonal elements of the helicity-basis distribution function. The skew scattering anomalous Hall effect arises from the anisotropy of the diagonal elements of the distribution function and it is a result of both the Rashba and extrinsic SO interactions. Further, we perform a numerical calculation to study the anomalous Hall effect in a typical InSb/AlInSb quantum well. The dependencies of the side-jump and skew scattering anomalous Hall conductivities on magnetization and on the Rashba SO coupling constant are examined., Comment: 16 pages, 4 figures, accepted for publication in PRB

Motivated by a recent experiment[Nature {\bf 442}, 176 (2006)], we present a quantitative microscopic theory to investigate the inverse spin-Hall effect with spin injection into aluminum considering both intrinsic and extrinsic spin-orbit couplings using the orthogonalized-plane-wave method. Our theoretical results are in good agreement with the experimental data. It is also clear that the magnitude of the anomalous Hall resistivity is mainly due to contributions from extrinsic skew scattering, while its spatial variation is determined by the intrinsic spin-orbit coupling., Comment: 5 pages, 3 figures

Employing a nonequilibrium Green's function approach, we examine the effects of long-range hole-impurity scattering on spin-Hall current in $p$-type bulk semiconductors within the framework of the self-consistent Born approximation. We find that, contrary to the null effect of short-range scattering on spin-Hall current, long-range collisions do produce a nonvanishing contribution to the spin-Hall current, which is independent of impurity density in the diffusive regime and relates only to hole states near the Fermi surface. The sign of this contribution is opposite to that of the previously predicted disorder-independent spin-Hall current, leading to a sign change of the total spin-Hall current as hole density varies. Furthermore, we also make clear that the disorder-independent spin-Hall effect is a result of an interband polarization directly induced by the dc electric field with contributions from all hole states in the Fermi sea., Comment: 9 pages, 1 figure

We employ a quantum Langevin equation approach to establish non-Markovian dynamical equations, on a fully microscopic basis, to investigate the measurement of the state of a coupled quantum dot qubit by a nearby quantum point contact. The ensuing Bloch equations allow us to examine qubit relaxation and decoherence induced by measurement, and also the noise spectrum of meter output current with the help of a quantum regression theorem, at arbitrary bias-voltage and temperature. Our analyses provide a clear resolution of a recent debate concerning the occurrence of a quantum oscillation peak in the noise spectrum., Comment: 5 pages, 3 figures, submitted, published version in Phys. Rev. B

We present a quantum Boltzmann equation analysis of the spin-Hall effect in a diffusive Rashba two-dimensional electron system. Within the framework of the self-consistent Born approximation, we consider the roles of disorder-induced quasiclassical relaxation, collisional broadening of the quasiparticles, and the intracollisional field effect in regard to spin-Hall dynamics. We present an analytical proof that the spin-Hall current vanishes, independently of the coupling strength, of the quasiparticle broadening, of temperature and of the specific form of the isotropic scattering potential. A sum relation of the collision terms in a helicity basis is also examined., Comment: final version, 11 pages, no figure

We explore inelastic cotunneling through a strongly Coulomb-blockaded quantum dot attached to two ferromagnetic leads in the weak coupling limit using a generic quantum Langevin equation approach. We first develop a Bloch-type equation microscopically to describe the cotunneling-induced spin relaxation dynamics, and then develop explicit analytical expressions for the local magnetization, current, and its fluctuations. On this basis, we predict a novel zero-bias anomaly of the differential conductance in the absence of a magnetic field for the anti-parallel configuration, and asymmetric peak splitting in a magnetic field. Also, for the same system with large polarization, we find a negative zero-frequency differential shot noise in the low positive bias-voltage region. All these effects are ascribed to rapid spin-reversal due to underlying spin-flip cotunneling., Comment: 7 pages, 5 figures, submitted

We present a theoretical analysis of several aspects of nonequilibirum cotunneling through a strong Coulomb-blockaded quantum dot (QD) subject to a finite magnetic field in the weak coupling limit. We carry this out by developing a generic quantum Heisenberg-Langevin equation approach leading to a set of Bloch dynamical equations which describe the nonequilibrium cotunneling in a convenient and compact way. These equations describe the time evolution of the spin variables of the QD explicitly in terms of the response and correlation functions of the free reservoir variables. This scheme not only provides analytical expressions for the relaxation and decoherence of the localized spin induced by cotunneling, but it also facilitates evaluations of the nonequilibrium magnetization, the charge current, and the spin current at arbitrary bias-voltage, magnetic field, and temperature. We find that all cotunneling events produce decoherence, but relaxation stems only from {\em inelastic} spin-flip cotunneling processes. Moreover, our specific calculations show that cotunneling processes involving electron transfer (both spin-flip and non-spin-flip) contribute to charge current, while spin-flip cotunneling processes are required to produce a net spin current in the asymmetric coupling case. We also point out that under the influence of a nonzero magnetic field, spin-flip cotunneling is an energy-consuming process requiring a sufficiently strong external bias-voltage for activation, explaining the behavior of differential conductance at low temperature: in particular, the splitting of the zero-bias anomaly in the charge current and a broad zero-magnitude "window" of differential conductance for the spin current near zero-bias-voltage., Comment: 15 pages, 5 figures, published version, to appear in Phys. Rev. B

We present a theoretical analysis of the effect of inelastic electron scattering on current and its fluctuations in a mesoscopic quantum dot (QD) connected to two leads, based on a recently developed nonperturbative technique involving the approximate mapping of the many-body electron-phonon coupling problem onto a multichannel single-electron scattering problem. In this, we apply the B\"uttiker scattering theory of shot noise for a two-terminal mesoscopic device to the multichannel case with differing weight factors and examine zero-frequency shot noise for two special cases: (i) a single-molecule QD and (ii) coupled semiconductor QDs. The nonequilibrium Green's function method facilitates calculation of single-electron transmission and reflection amplitudes for inelastic processes under nonequilibrium conditions in the mapping model. For the single-molecule QD we find that, in the presence of the electron-phonon interaction, both differential conductance and differential shot noise display additional peaks as bias-voltage increases due to phonon-assisted processes. In the case of coupled QDs, our nonperturbative calculations account for the electron-phonon interaction on an equal footing with couplings to the leads, as well as the coupling between the two dots. Our results exhibit oscillations in both the current and shot noise as functions of the energy difference between the two QDs, resulting from the spontaneous emission of phonons in the nonlinear transport process. In the "zero-phonon" resonant tunneling regime, the shot noise exhibits a double peak, while in the "one-phonon" region, only a single peak appears., Comment: 10 pages, 6 figures, some minor changes, accepted by Phys. Rev. B

We examine the high-frequency differential conductivity response properties of semiconductor superlattices having various miniband dispersion laws. Our analysis shows that the anharmonicity of Bloch oscillations (beyond tight-binding approximation) leads to the occurrence of negative high-frequency differential conductivity at frequency multiples of the Bloch frequency. This effect can arise even in regions of positive static differential conductivity. The influence of strong electron scattering by optic phonons is analyzed. We propose an optimal superlattice miniband dispersion law to achieve high-frequency field amplification.

A fully microscopic theory of electron spin relaxation by the D'yakonov-Perel' type spin-orbit coupling is developed for a semiconductor quantum well with a magnetic field applied in the growth direction of the well. We derive the Bloch equations for an electron spin in the well and define microscopic expressions for the spin relaxation times. The dependencies of the electron spin relaxation rate on the lowest quantum well subband energy, magnetic field and temperature are analyzed., Comment: Revised version as will appear in Physical Review B

We analyze the dynamics of a nanomechanical oscillator coupled to an electrical tunnel junction with an arbitrary voltage applied to the junction and arbitrary temperature of electrons in leads. We obtain the explicit expressions for the fluctuations of oscillator position, its damping/decoherence rate, and the current through the structure. It is shown that quantum heating of the oscillator results in nonlinearity of the current-voltage characteristics. The effects of mechanical vacuum fluctuations are also discussed.

We present a microscopic analysis of electron spin dynamics in the presence of an external magnetic field for non-centrosymmetric semiconductors in which the D'yakonov-Perel' spin-orbit interaction is the dominant spin relaxation mechanism. We implement a fully microscopic two-step calculation, in which the relaxation of orbital motion due to electron-bath coupling is the first step and spin relaxation due to spin-orbit coupling is the second step. On this basis, we derive a set of Bloch equations for spin with the relaxation times T_1 and T_2 obtained microscopically. We show that in bulk semiconductors without magnetic field, T_1 = T_2, whereas for a quantum well with a magnetic field applied along the growth direction T_1 = T_2/2 for any magnetic field strength., Comment: to appear in Proceedings of Mesoscopic Superconductivity and Spintronics (MS+S2002)

The phenomenon of transparency in two-dimensional and three-dimensional superlattices is analyzed on the basis of the Boltzmann equation with a collision term encompassing three distinct scattering mechanisms (elastic, inelastic and electron-electron) in terms of three corresponding distinct relaxation times. On this basis, we show that electron heating in the plane perpendicular to the current direction drastically changes the conditions for the occurrence of self-induced transparency in the superlattice. In particular, it leads to an additional modulation of the current amplitudes excited by an applied biharmonic electric field with harmonic components polarized in orthogonal directions. Furthermore, we show that self-induced transparency and dynamic localization are different phenomena with different physical origins, displaced in time from each other, and, in general, they arise at different electric fields., Comment: to appear in Physical Review B

We employ the method of the theory of open quantum systems to analyze spin relaxation and decoherence in semiconductors in the presence of a magnetic field. We derive a set of Bloch equations for electron spin with a fully microscopic determination of longitudinal and transverse relaxation times. Electron scattering from optical and acoustic phonons and random impurities is taken into account. We obtain explicit expressions for the spin relaxation times in terms of material constants and coupling strengths, exhibiting formal agreement with earlier treatments in the zero magnetic field limit with microscopic specification of their phenomenological parameters., Comment: to appear in Problems of Modern Statistical Physics, Nizhny Novgorod, Russia