Electromagnetic wave refraction at an interface of a double wire medium

Plane-wave reflection and refraction at an interface with a double wire medium is considered. The problem of additional boundary conditions (ABC) in application to wire media is discussed and an ABC-free approach, known in the solid state physics, is used. Expressions for the fields and Poynting vectors of the refracted waves are derived. Directions and values of the power density flow of the refracted waves are found and the conservation of the power flow through the interface is checked. The difference between the results, given by the conventional model of wire media and the model, properly taking into account spatial dispersion, is discussed.Comment: 17 pages, 11 figure

A Variational Approach to Nonlocal Exciton-Phonon Coupling

In this paper we apply variational energy band theory to a form of the Holstein Hamiltonian in which the influence of lattice vibrations (optical phonons) on both local site energies (local coupling) and transfers of electronic excitations between neighboring sites (nonlocal coupling) is taken into account. A flexible spanning set of orthonormal eigenfunctions of the joint exciton-phonon crystal momentum is used to arrive at a variational estimate (bound) of the ground state energy for every value of the joint crystal momentum, yielding a variational estimate of the lowest polaron energy band across the entire Brillouin zone, as well as the complete set of polaron Bloch functions associated with this band. The variation is implemented numerically, avoiding restrictive assumptions that have limited the scope of previous assaults on the same and similar problems. Polaron energy bands and the structure of the associated Bloch states are studied at general points in the three-dimensional parameter space of the model Hamiltonian (electronic tunneling, local coupling, nonlocal coupling), though our principal emphasis lay in under-studied area of nonlocal coupling and its interplay with electronic tunneling; a phase diagram summarizing the latter is presented. The common notion of a "self-trapping transition" is addressed and generalized.Comment: 33 pages, 11 figure

Weak and strong coupling limits of the two-dimensional Fr\"ohlich polaron with spin-orbit Rashba interaction

The continuous progress in fabricating low-dimensional systems with large spin-orbit couplings has reached a point in which nowadays materials may display spin-orbit splitting energies ranging from a few to hundreds of meV. This situation calls for a better understanding of the interplay between the spin-orbit coupling and other interactions ubiquitously present in solids, in particular when the spin-orbit splitting is comparable in magnitude with characteristic energy scales such as the Fermi energy and the phonon frequency. In this article, the two-dimensional Fr\"ohlich electron-phonon problem is reformulated by introducing the coupling to a spin-orbit Rashba potential, allowing for a description of the spin-orbit effects on the electron-phonon interaction. The ground state of the resulting Fr\"ohlich-Rashba polaron is studied in the weak and strong coupling limits of the electron-phonon interaction for arbitrary values of the spin-orbit splitting. The weak coupling case is studied within the Rayleigh-Schr\"odinger perturbation theory, while the strong-coupling electron-phonon regime is investigated by means of variational polaron wave functions in the adiabatic limit. It is found that, for both weak and strong coupling polarons, the ground state energy is systematically lowered by the spin-orbit interaction, indicating that the polaronic character is strengthened by the Rashba coupling. It is also shown that, consistently with the lowering of the ground state, the polaron effective mass is enhanced compared to the zero spin-orbit limit. Finally, it is argued that the crossover between weakly and strongly coupled polarons can be shifted by the spin-orbit interaction.Comment: 11 pages, 5 figure

Electron-phonon interaction via Pekar mechanism in nanostructures

We consider an electron-acoustic phonon coupling mechanism associated with the dependence of crystal dielectric permittivity on the strain (the so-called Pekar mechanism) in nanostructures characterized by strong confining electric fields. The efficiency of Pekar coupling is a function of both the absolute value and the spatial distribution of the electric field. It is demonstrated that this mechanism exhibits a phonon wavevector dependence similar to that of piezoelectricity and must be taken into account for electron transport calculations in an extended field distribution. In particular, we analyze the role of Pekar coupling in energy relaxation in silicon inversion layers. Comparison with the recent experimental results is provided to illustrate its potential significance

Fractal and chaotic solutions of the discrete nonlinear Schr\"odinger equation in classical and quantum systems

We discuss stationary solutions of the discrete nonlinear Schr\"odinger equation (DNSE) with a potential of the $\phi^{4}$ type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a $1D$ chain of atoms --- the (Rashba)--Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another relevant example is that of superconducting states in layered superconductors described by the same DNSE. Amongst many other applications the typical example for a classical lattice is a system of coupled nonlinear oscillators. We present the exact energy spectrum of this model in the strong coupling limit and the corresponding wave function. Using this as a starting point we go on to calculate the wave function for moderate coupling and find that the energy eigenvalue of these structures of the wave function is in exquisite agreement with the exact strong coupling result. This procedure allows us to obtain (numerically) exact solutions of the DNSE directly. When applied to our typical example we find that the wave function of an electron on a deformable lattice (and other quantum or classical discrete systems) may exhibit incommensurate and irregular structures. These states are analogous to the periodic, quasiperiodic and chaotic structures found in classical chaotic dynamics

Optical Properties of Crystals with Spatial Dispersion: Josephson Plasma Resonance in Layered Superconductors

We derive the transmission coefficient, $T(\omega)$, for grazing incidence of crystals with spatial dispersion accounting for the excitation of multiple modes with different wave vectors ${\bf k}$ for a given frequency $\omega$. The generalization of the Fresnel formulas contains the refraction indices of these modes as determined by the dielectric function $\epsilon(\omega,{\bf k})$. Near frequencies $\omega_e$, where the group velocity vanishes, $T(\omega)$ depends also on an additional parameter determined by the crystal microstructure. The transmission $T$ is significantly suppressed, if one of the excited modes is decaying into the crystal. We derive these features microscopically for the Josephson plasma resonance in layered superconductors.Comment: 4 pages, 2 figures, epl.cls style file, minor change

Electron locking in semiconductor superlattices

We describe a novel state of electrons and phonons arising in semiconductor superlattices (SSL) due to strong electron-phonon interactions. These states are characterized by a localization of phonons and a self-trapping or locking of electrons in one or several quantum wells due to an additional, deformational potential arising around these locking wells in SSL. The effect is enhanced in a longitudinal magnetic field. Using the tight-binding and adiabatic approximations the whole energy spectrum of the self-trapped states is found and accurate, analytic expressions are included for strong electron-phonon coupling. Finally, we discuss possible experiments which may detect these predicted self-trapped states.Comment: 8 pages, 2 figures. Please note that the published article has the title 'Electron locking in layered structures by a longitudinal magnetic field

Spin singlet small bipolarons in Nb-doped BaTiO3

The magnetic susceptibility and electrical resistivity of n-type BaTi{1-x}Nb{x}O3 have been measured over a wide temperature range. It is found that, for 0 < x < 0.2, dopant electrons form immobile spin singlet small bipolarons with binding energy around 110 meV. For x = 0.2, a maximum in the electrical resistivity around 15 K indicates a crossover from band to hopping transport of the charge carriers, a phenomenon expected but rarely observed in real polaronic systems.Comment: 5 pages, 4 figure

Disorder-induced tail states in a gapped bilayer graphene

The instanton approach to the in-gap fluctuation states is applied to the spectrum of biased bilayer graphene. It is shown that the density of states falls off with energy measured from the band-edge as $\nu(\epsilon)\propto \exp(-|\epsilon/\epsilon_t|^{3/2})$, where the characteristic tail energy, $\epsilon_t$, scales with the concentration of impurities, $n_i$, as $n_i^{2/3}$. While the bare energy spectrum is characterized by two energies: the bias-induced gap, $V$, and interlayer tunneling, $t_{\perp}$, the tail, $\epsilon_t$, contains a {\it single} combination $V^{1/3}t_{\perp}^{2/3}$. We show that the above expression for $\nu(\epsilon)$ in the tail actually applies all the way down to the mid-gap.Comment: 7 pages, 4 figure