A. C. Sharma

Electron?electron scattering rate in presence of random impurity potential in low-dimensional systems

The electron–electron scattering rate (1/τee) in the presence of a random disorder potential has been computed, within the random phase approximation, as a function of excitation energy (e) for a quantum well (QWL), a quantum wire (QWR) and a periodic quantum wire structure (QWS). It is found that: (i) 1/τee goes to zero when and (ii) the e dependence as well as the magnitude of 1/τee are determined by the value of the inverse electron–impurity collision time (1/τ), the carrier density and the width of a QWR. The computed 1/τee exhibits its maximum value for and it decreases thereafter on increasing 1/τ, for all values of e and other parameters. The computed 1/τee of a QWR declines monotonically with the width of the QWR and it reduces to 1/τee of a QWL at larger wire widths, for a given value of e and the other intrinsic parameters. The 1/τee of a QWS differs from that of a QWR because of the added contribution from inter-wire electron–electron interactions in a QWS. For the given values of e, 1/τ, carrier density and the width of a QWR, the 1/τee of a QWS is found to be smaller than that of a QWR and larger than that of a QWL. This suggests that the electron–electron scattering rate is enhanced on the reduction in the effective dimensionality of a system. Our theoretical study of 1/τee and its dependence on various intrinsic parameters of QWL, QWR and QWS suggests, in conclusion, that a quasi-particle Fermi liquid description can be applied to electron–electron scattering in the presence of an electron-disorder potential scattering, at zero temperature, in low-dimensional systems.

Many particle aspects of a semiconductor quantum wire within an improved random phase approximation

The structure factor, pair distribution function, screened impurity potential, density of screening charge, and exchange and screened exchange energies have been theoretically investigated for a semiconductor quantum wire using an improved random phase approximation that takes into account the local field corrections within the Hubbard approximation. Our approach enabled us to obtain approximate analytical results on some of the aspects and to greatly simplify the computation task on others. However, computed results from our simple approach show very good agreement with those obtained by performing cumbersome numerical solutions for the structure factor, density–density response function and the static local field corrections, within the Singwi–Tosi–Land–Sjolander approximation. Our investigations suggest that: (i) the magnitude of the screened impurity potential and the average distribution of electrons about an electron at larger distances are enhanced on reducing the width of quantum wire, and (ii) the exchange interactions strengthen on narrowing the quantum wire and on increasing the carrier density. Friedel oscillations are seen in both our computed screened potential and the density of screening charge.

Dynamical conductivity of high-Tc superconductors below Tc

Abstract In this paper, we present a model calculation of frequency- and temperature-dependent conductivity for temperatures below T c . Calculation has been performed for cuprate superconductors with one and two conducting Cu–O layers per unit cell. However, our results are mainly discussed for YBa 2 Cu 3 O 7− δ , which consists of two conducting layers per unit cell. To make a comparison between our calculation and experimental results, we introduced frequency and temperature dependent transport relaxation time and frequency dependent effective mass of electron in our calculation. Our computed macroscopic conductivity as a function of temperature in microwave frequency regime shows a very good agreement with experimental data. A good agreement between our calculated macroscopic conductivity as a function of frequency and experimental results has also been obtained. It is found that the peak in temperature dependent conductivity, in microwave regime, is the manifestation of temperature and frequency dependent, transport relaxation time. Our calculation of microscopic conductivity gives the frequency of longitudinal collective excitation modes whose frequency, for an arbitrary value of wave vector, lies below the frequency gap. These observations are very similar to that reported earlier by Fertig and Das Sarma.

Collective excitations and their lineshapes for a modulation-doped GaAs/AlAs superlattice

The density-density correlation function has been calculated for a modulation-doped GaAs/AlAs superlattice. The superlattice is modelled to be an infinite periodic sequence of layers which consists of two dissimilar layers, one of GaAs and the other of AlAs, per unit cell. The conduction electrons are assumed to be confined to GaAs layers. Our calculation shows that although the electron gas is confined in the GaAs layers, the plasma oscillations can interact with the lattice vibrations of both GaAs and AlAs. The interaction between AlAs lattice vibrations and the plasmons significantly contributes to the light-scattering spectrum. It is therefore argued that the experimentally measured frequencies of the coupled plasmon-phonon modes and their lineshapes for a modulation-doped GaAs/AlAs superlattice cannot correctly be described by the previous theoretical calculations which have been performed for a layered electron gas embedded in a homogeneous dielectric background. For the special case of a homogeneous dielectric background, our results, however, agree with the previously reported calculations.

Temperature dependent screened electronic transport in gapped graphene

We report our theoretical calculations on the temperature and energy dependent electrical conductivity of gapped graphene within the framework of Boltzmann transport formalism. Since screening effects have known to be of vital importance in explaining the conductivity of gapless graphene therefore we first worked out the behavior of the temperature dependent polarization function for gapped graphene as a function of wave vector and band gap, respectively. Polarization of gapped graphene has been compared with that of gapless graphene, bilayer graphene, and 2DEG to see the effects of gap. It is found that the gapped graphene polarization function exhibits a strong dependence on temperature, wave vector and band gap and the effect translates to the conductivity of gapped graphene. The nature of conductivity in gapped graphene is observed to be non-monotonic ranging from good to poor to semiconducting. We also find that the conductivity computed as a function of temperature by averaging over quasi-particle energy significantly differs from that computed at Fermi energy, suggesting that a notable contribution to temperature dependent conductivity is made by electrons close to the Fermi level.

Static structure factor and pair correlation function of graphene

We report our theoretical investigations on the static structure factor and pair correlation function using both the density-density and spin-density response functions of a doped single graphene sheet based on the random phase approximation and on graphenes massless Dirac fermions concept. The static structure factor and pair correlation function are obtained by regularizing the dynamical polarization function, which otherwise is clearly divergent due to the interaction energy of the infinite Dirac sea of negative energy states. The local field effects have been considered in the simplistic Hubbard approximation. We find the structure factor to be dependent on the dimensionless coupling constant α, and for high values of coupling constant the magnetic structure factor indicates paramagnetic instability which is also corroborated from other theoretical investigations. The spin symmetric pair correlation function computed in the simplistic Hubbard approximation begins from zero at zero separation only at very high densities but the results for parallel spin and anti-parallel spin pair correlation functions expose the shortcoming of this local field approximation. This work should stimulate more investigations testing various other local field schemes and also quantum Monte Carlo based simulations.

Finite temperature dynamical polarization and plasmons in gapped graphene

In this study, we report our numerical results on finite temperature non-interacting dynamical polarization function, plasmon modes, and electron energy loss function of doped single layer gapped graphene (SLGG) within the random phase approximation. We find that the interplay of linear energy band dispersion, chirality, bandgap, and temperature endow SLGG with strange polarizability behavior, which is a mixture of 2DEG, single layer and bilayer graphene and as a result the plasmon spectrum also manifests strikingly peculiar behavior. The plasmon dispersion is observed to be suppressed till temperatures up to ∼0.5Tf, similar to the gapless graphene case but beyond 0.5Tf a reversal in trend is seen in gapped graphene, for all values of band gap. This behavior is also corroborated by the density plots of electron energy loss function. The opening of a small gap also generates a new undamped plasmon mode, which is found to disappear at high temperatures. The plasmonic behavior of gapped graphene is further found to be hugely influenced by the substrate on which the gapped graphene sheet rests, which signifies the need for a careful substrate selection in the making of desirable graphene-based plasmonics devices.

Collective excitations and their lineshapes for a compositional superlattice of type II

The dielectric function and the density - density correlation function are calculated for a compositional superlattice of type II, which consists of alternate electron and hole layers (a two-component plasma) in an inhomogeneous dielectric background. The dielectric background of the electron gas is considered to be different from that of holes and the finite width of an electron (hole) layer is considered to allow both intrasubband and intersubband transitions. Our model superlattice consists of electron plasma, hole plasma, lattice vibrations of the background of the electron gas and lattice vibrations of the background of the hole gas. Electron - electron, electron - hole, hole - hole, electron - phonon, hole - phonon and phonon - phonon interactions take place in our model superlattice. Our calculation is applied to the superlattice. Variation of plasmon - phonon coupled modes and their lineshapes with (x, y) and unit cell width has been investigated in order to study the effects of semiconductor to semimetal or vice versa phase transitions. It is found that phase transition prominently affects the plasmon modes, while phonon modes remain almost unaffected. The inhomogeneity in the background of the electron - hole gas also produces a significant change in plasma frequencies. Lineshapes of coupled plasmon - phonon modes for both semimetal and semiconductor phases are calculated and are computed with those of the homogeneous background. Significant changes in peak height and half width are observed due to inhomogeneity in the dielectric background and the semiconductor to semimetal phase transition.

Effective interaction potential for copper oxide superconductors

Abstract We calculate the effective interaction potential for copper oxide superconductors which consist of one and two CuO planes per unit cell, respectively. It is shown that for small angle scattering of charge carriers at the Fermi surface, a single polarization term shows well-behaved acoustic as well as optic plasmon modes supported by a CuO layer and can give rise to a reasonable value of T c for copper oxide superconductors consisting of one Cuz.sbnd;Olayers per unit cell. The calculation of T c for copper oxide superconductors consisting of one CuO layer per unit cell is reported here. The calculated effective interaction potentials are also compared with the effective interaction potential for an isolated two-dimensional free electron layer. Our calculation shows that the coupling between CuO conducting layers makes the effective potential more attractive and less repulsive.

Magnetic structure factor and pair correlation function for a semiconductor quantum wire

In this paper we report the spin correlation and its effects on the many-body properties of a quantum wire whose width is given practical consideration. The single-pole approximation, which is of much relevance in studying the many-body properties of an interacting one-dimensional electron gas (1DEG) because of the severe constraints imposed on the phase space of plasma–hole excitations, has been used to obtain analytical results. The local-field corrections are incorporated within the Hubbard approximation (HA). We find the results obtained for low electron densities under the single-pole approximation on the paramagnon dispersion relation, magnetic structure factor and the symmetric and anti-symmetric pair correlation function to be in good quantitative agreement with those obtained under heavily computational self-consistent field calculations. Unlike prior reported work on the magnetic structure factor and pair correlation function, our calculation is applicable to quantum wires of width less than 10 nm, where interesting quantum size effects are observed.