Abstract: Based on the metastable electron-pair energy band in a two-dimensional (2D) periodic potential obtained previously by Hai and Castelano [J. Phys.: Condens. Matter 26, 115502 (2014)], we present in this work a Hamiltonian of many electrons consisting of single electrons and electron pairs in the 2D system. The electron-pair states are metastable of energies higher than those of the single-electron states at low electron density. We assume two different scenarios for the single-electron band. When it is considered as the lowest conduction band of a crystal, we compare the obtained Hamiltonian with the phenomenological model Hamiltonian of a boson-fermion mixture proposed by Friedberg and Lee [Phys. Rev. B 40, 6745 (1989)]. Single-electron-electron-pair and electron-pair-electron-pair interaction terms appear in our Hamiltonian and the interaction potentials can be determined from the electron-electron Coulomb interactions. When we consider the single-electron band as the highest valence band of a crystal, we show that holes in this valence band are important for stabilization of the electron-pair states in the system.

Abstract: The thermal expansion alpha(T) in layered crystals is of fundamental and technological interest. As suggested by I. M. Lifshitz in 1952, in thin solid films (crystalline membranes) a negative contribution to alpha(T) is due to anharmonic couplings between in-plane stretching modes and out-of-plane bending (flexural modes). Genuine in-plane anharmonicities give a positive contribution to alpha(T). The competition between these two effects can lead to a change of sign (crossover) from a negative value of alpha(T) in a temperature (T) range T <= T-alpha to a positive value of alpha(T) for T > T-alpha in layered crystals. Here, we present an analytical lattice dynamical theory of these phenomena for a two-dimensional (2D) hexagonal crystal. We start from a Hamiltonian that comprises anharmonic terms of third and fourth order in the lattice displacements. The in-plane and out-of-plane contributions to the thermal expansion are studied as functions of T for crystals of different sizes. Besides, renormalization of the flexural mode frequencies plays a crucial role in determining the crossover temperature T-alpha. Numerical examples are given for graphene where the anharmonic couplings are determined from experiments. The theory is applicable to other layer crystals wherever the anharmonic couplings are known. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Abstract: Piezo- and flexoelectricity are manifestations of electromechanical coupling in solids with potential applications in nanoscale materials. Naumov etal. [Phys. Rev. Lett. 102, 217601 (2009)] have shown by first principles calculations that a monolayer BN sheet becomes macroscopically polarized in-plane when in a corrugated state. Here, we investigate the interplay of layer corrugation and in-plane polarization by atomistic lattice dynamics. We treat the coupling between static flexural modes and in-plane atomic ion displacements as an anharmonic effect, similar to the membrane effect that is at the origin of negative thermal expansion in layered crystals. We have derived analytical expressions for the corrugation-induced static in-plane strains and the optical displacements with the resulting polarization response functions. Beyond h-BN, the theory applies to transition metal dichalcogenides and dioxides. Numerical calculations show that the effects are considerably stronger for 2D h-BN than for 2H-MoS2.

Abstract: Cyclotron resonance (CR) of the electrons accumulated at sheets with heavy Si doping in InSb were observed using far infrared radiation. The angular dependence of the CR follows closely the 1/cos theta behaviour with some small deviations at high angles attributed to coupling between subbands. From the effective mass of the lowest subband, which is found to be 0.027m(o), the bottom of the lowest subband was determined to lie 125 meV below the Fermi level.