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In this paper we consider two different geometry of quasi one-dimensional semiconductors and calculate their exchange-correlation induced bandgap renormalization (BGR) as a function of the electron-hole plasma density and quantum wire width. Based on different fabrication scheme, we define suitable external confinement potential and then leading-order GW dynamical screening approximation is used in the calculation by treating electron–electron Coulomb interaction and electron-optical phonon interaction. Using a numerical scheme, screened Coulomb potential, probability of different states, profile of charge density and the values of the renormalized gap energy are calculated and the effects of variation of confinement potential width and temperature are studied.

Chiral edge states of $(2+1)$-dimensional Abelian and non-Abelian topological phases can be represented by chiral conformal field theories with integer and noninteger values of central charge, respectively. In this work we describe certain edge states in terms of constrained fermionic fields that realize chiral coset CFT structures. This construction arises naturally in the so-called quantum wires approach for topological phases and allows for representing fractionalized edge states directly in terms of fermionic degrees of freedom. At the same time, the constrained fermions description introduces some subtleties concerning gauge anomalies since it involves the coupling of chiral fermions to gauge fields. We describe in this paper how to handle these issues.

The combined effects of Rashba spin-orbit interaction (SOI) strength and the length of SOI excited region, which can be controlled by the external gate voltage deposited on the heterostructure, and on the electron spin precession in quasi-one-dimensional quantum wires are investigated by evaluating the relative conductance change, i.e. the ratio of difference of the conductances of the spin-up and spin-down polarized electrons to the total conductance. It is found that for proper wire width, electron spin precession can be smoothly achieved by co-adjusting the SOI strength and the length of SOI excited region. However, for wide quantum wire and strong SOI, the electron spin precession is significantly reduced due to the appearance of inter-subband mixing.

The scattering intensity (SI) for an electron resonant Raman scattering (ERRS) process in a free-standing semiconductor quantum wire of cylindrical geometry associated with bulk longitudinal optical (LO) phonon modes or the surface optical (SO) phonon modes is calculated for T=0 K. The Fröhlich interaction is considered to illustrate the theory for a GaAs system. Electron states are confined within a free-standing quantum wire (FSW). Single parabolic conduction and valence bands are assumed. The selection rules are studied. Numerical results and a discussion are also presented for various radii of the cylindrical quantum wires.

We have investigated the transport properties of anisotropic disordered quantum wire by the method of energy level statistics and transfer matrix method. We have found a general average conductance relation in terms of the anisotropy parameter t, disorder strength W, and the cross-sectional area, A, of the wire. From the available numerical data, we have also shown that the anisotropic correlation length ξ_t can be related to the isotropic correlation length ξ as ξ_t ≃ t²ξ, for L ≃ A and ξ_t ≃ tξ, for L ≫ A. Here, L is the length of the wire. In addition, anisotropic dependence of conductance fluctuation and conductance distribution have been studied to a certain extent.

In this work we present a semi-classical transfer matrix method to study one-dimensional modified quantum transverse-field Ising model. Both average magnetization per spin along the z-direction 〈σ^z〉 and along the x-direction 〈σ^x〉 are calculated in this picture. It is predicted that the t > 1 case is the corresponding effective ferromagnetic phase at sufficiently high H_z whereas t < 1 case is an effective paramagnetic phase . Consequently, it is concluded that t = H_z/K = 1, here H_z is the transverse field along the z-axis and K is the coupling strength, which corresponds to quantum ferromagnetic-paramagnetic phase transition. In other words, the same result of the sophisticated quantum field theoretical calculation is predicted unexpectedly in the naive semiclassical picture.

Effects due to the proximity of a superconductor has motivated a lot of research work in the last several decades both from theoretical and experimental point of view. In this review, we are going to describe the physics of systems containing normal metal-superconductor interface. Mainly we discuss transport properties through such hybrid structures. In particular, we describe the effects of electron–electron interaction on transport through such superconducting junction of multiple one-dimensional quantum wires. The latter can be described in terms of a non-Fermi liquid theory called Luttinger liquid. In this review, from the application point of view, we also demonstrate the possible scenarios for production of pure spin current and large tunneling magnetoresistance in such hybrid junctions and analyze the influence of electron–electron interaction on the stability of the production of pure spin current.

By considering a suitable confinement potential, we calculate the exchange-correlation induced band gap renormalization (BGR) in a V-grooved quantum wire as a function of the electron-hole plasma density and quantum wire width. The leading-order GW dynamical screening approximation is used in the calculation by treating the electron-electron Coulomb interaction and electron-optical phonon interaction. A numerical scheme has been proposed, and the screened Coulomb potential, density of states (profile of charge distribution) and the value of the renormalized gap energy are calculated. We will show that the carrier concentration, the screened confinement potential and the relative band gap renormalization are functions of the ratio of the well width in the x and y directions.

The method of two variational wavefunctions has been used to calculate theoretically the impurity binding energy in a GaAs/Ga_1-xAl_xAs quantum wire. The effective potential in the quantum wire consists of a parabolic well potential in the x-direction and a square well potential in the z-direction with an applied electric field. We can obtain the results which are in good agreement with previous theoretical results. Furthermore, the impurity binding energy in the quantum wire is sensitive to the geometrical effects and the applied electric field strength F.

This paper reviews the method of bosonization for one-dimensional interacting fermions. Example of its application to mesoscopic systems is presented with an explicit calculation of the spin and charge currents in an interacting quantum wire subject to a uniform magnetic field and alternating voltage source. Special emphasis is given to the details of the calculation using bosonization and Keldysh techniques.

This paper reviews the fundamental issues associated with the magnetoplasmon excitations investigated in a semiconducting quantum wire characterized by a harmonic confining potential and subjected to an applied (perpendicular) magnetic field. We embark on the charge–density excitations in a two-subband model within the framework of Bohm–Pines's random-phase approximation. The problem involves two length scales: and , which characterize the strengths of the confinement and the magnetic field (B). Essentially, we focus on the device aspects of the intersubband collective (magnetoroton) excitation, which observes a negative group velocity between maxon and roton. Consequently, it leads to tachyon-like (superluminal) behavior without one's having to introduce the negative energies. Existence of the negative group velocity is a clear manifestation of a medium with population inversion brought about due to a metastable state caused by the magnetic field that satisfies the condition B > B_th; B_th being the threshold value below which the magnetoroton does not exist. The interest in negative group velocity is based on anomalous dispersion in a medium with inverted population, so that gain instead of absorption occurs at the frequencies of interest. A medium with an inverted population has the remarkable ability of amplifying a small optical signal of definite wavelength, i.e. it can serve as an active laser medium. An extensive scrutiny of the gain coefficient suggests an interesting and important application: The electronic device designed on the basis of such magnetoroton modes can act as an optical amplifier. Examining the magnetic field dependence of the life-time of magnetorotons leads us to infer that relatively smaller magnetic fields are optimal.

Those who measure success with culmination do not seem to be aware that life is a journey not a destination. This spirit is best reflected in the unceasing failures in efforts for solving the problem of controlled thermonuclear fusion for even the simplest pinches for over decades; and the nature keeps us challenging with examples. However, these efforts have permitted researchers the obtention of a dense plasma with a lifetime that, albeit short, is sufficient to study the physics of the pinch effect, to create methods of plasma diagnostics, and to develop a modern theory of plasma processes. Most importantly, they have impregnated the solid state plasmas, particularly the electron–hole plasmas in semiconductors, which do not suffer from the issues related with the confinement and which have demonstrated their potential not only for the fundamental physics but also for the device physics. Here, we report on a two-component, cylindrical, quasi-one-dimensional quantum plasma subjected to a radial confining harmonic potential and an applied magnetic field in the symmetric gauge. It is demonstrated that such a system, as can be realized in semiconducting quantum wires, offers an excellent medium for observing the quantum pinch effect at low temperatures. An exact analytical solution of the problem allows us to make significant observations: Surprisingly, in contrast to the classical pinch effect, the particle density as well as the current density display a determinable maximum before attaining a minimum at the surface of the quantum wire. The effect will persist as long as the equilibrium pair density is sustained. Therefore, the technological promise that emerges is the route to the precise electronic devices that will control the particle beams at the nanoscale.

Quantum wires occupy a unique status among the semiconducting nanostructures with reduced dimensionality, no other system seems to have engaged researchers with as many appealing features to pursue. This paper aims at a core issue related with the magnetoplasmon excitations in the quantum wires characterized by the confining harmonic potential and subjected to a longitudinal electric field and a perpendicular magnetic field in the symmetric gauge. Despite the substantive complexity, we obtain the exact analytical expressions for the eigenfunction and eigenenergy, using the scheme of ladder operators, which fundamentally characterize the quantal system. Crucial to this inquiry is an intersubband collective excitation that evolves into a magnetoroton — above a threshold value of magnetic field — which observes a negative group velocity between the maxon and the roton. The evidence of negative group velocity implies anomalous dispersion in a gain medium with the population inversion that forms the basis for the lasing action of lasers. Thus, the technological pathway that unfolds is the route to devices exploiting the magnetoroton features for designing the novel optical amplifiers at nanoscale and hence paving the way to a new generation of lasers.

A theoretical investigation has been made of the magnetoplasmon excitations in a quasi-one-dimensional electron system composed of vertically stacked, self-assembled InAs/GaAs quantum dots. The smaller length scales involved in the experiments impel us to consider a perfectly periodic system of two-dimensionally confined InAs quantum dot layers separated by GaAs spacers. Subsequent system is subjected to a two-dimensional confining (harmonic) potential in the $x$–$y$ plane and an applied magnetic field (B) in the symmetric gauge. This scheme defines virtually a system of quantum wire comprised of vertically stacked quantum dots (VSQD). We derive and discuss the Dyson equation, the generalized (nonlocal and dynamic) dielectric function, and the inverse dielectric function for investigating the single-particle and collective (magnetoplasmon) excitations within the framework of (full) random-phase approximation (RPA). As an application, we study the influence of the confinement potential and the magnetic field on the component eigenfunctions, the density of states (DOS), the Fermi energy, the collective excitations, and the inverse dielectric functions. How the B-dependence of DOS validate the VSQD mimicking the realistic quantum wires, the Fermi energy oscillates as a function of the Bloch vector, the intersubband single-particle continuum bifurcates at the origin, a collective excitation emerges and propagates within the gap of the split single-particle continuum, and the alteration in the well- and barrier-widths allows to customize the excitation spectrum in the desired energy range are some of the remarkable features of this investigation. These findings demonstrate, for the very first time, the significance of investigating the system of VSQD subjected to a quantizing magnetic field. Given the edge over the planar quantum dots and the foreseen applications in the single-electron devices and quantum computation, investigating the system of VSQD is deemed vital. The results suggest exploiting magnetoplasmon qubits to be a potential option for implementing the solemn idea of quantum state transfer in devising quantum gates for the quantum computation and quantum communication networks.

Using ab initio total energy calculations, we have studied the formation of indium (In) wires on flat and stepped Si(100)-(2×1) surfaces at low coverage. On flat Si(100), two possible orientations of In wires are examined: (i) the wire is perpendicular to the underlying Si dimer rows, and (ii) the wire is parallel to the underlying Si dimer rows. Total energy optimization shows that the energetically favored orientation is where the In wire is perpendicular to the underlying Si dimer rows, i.e. the wire is oriented along the direction. We have also considered two neighboring wires and determined the repulsive force between the two wires. On stepped Si(100) surfaces, the influence of S_A and S_B steps on In wire formation is investigated. The calculations suggest that In wires are likely to form at positions away from S_A steps but close to S_B steps.

This work focuses on understanding the nonlinear-optical response of a 1-D quantum wire embedded in 2-D space when quantum-size effects in the transverse direction are minimized using an extremely weighted delta function potential. Our aim is to establish the fundamental basis for understanding the effect of geometry on the nonlinear-optical response of quantum loops that are formed into a network of quantum wires. It is shown that in the limit of full confinement, the sum rules are obeyed when the transverse infinite-energy continuum states are included. While the continuum states associated with the transverse wavefunction do not contribute to the nonlinear optical response, they are essential to preserving the validity of the sum rules. This work is a building block for future studies of nonlinear-optical enhancement of quantum graphs (which include loops and bent wires) based on their geometry. These properties are important in quantum mechanical modeling of any response function of quantum-confined systems, including the nonlinear-optical response of any system in which there is confinement in at least one dimension, such as nanowires, which provide confinement in two dimensions.

Quasi-1D quantum structures with spectra scaling faster than the square of the eigenmode number (superscaling) can generate intrinsic, off-resonant optical nonlinearities near the fundamental physical limits, independent of the details of the potential energy along the structure. The scaling of spectra is determined by the topology of the structure, while the magnitudes of the transition moments are set by the geometry of the structure. This paper presents a comprehensive study of the geometrical optimization of superscaling quasi-1D structures and provides heuristics for designing molecules to maximize intrinsic response. A main result is that designers of conjugated structures should attach short side groups at least a third of the way along the bridge, not near its end as is conventionally done. A second result is that once a side group is properly placed, additional side groups do not further enhance the response.

We report the correlated charge and spin density distributions in a quantum wire coupled to electron reservoirs. It is found that charging the wire because of the electron density redistribution between the wire and reservoirs results in the increase of the critical electron density, below which the spontaneous spin polarization appears. The distributions of the electron densities with spin up and spin down along the wire have components oscillating in opposite phases with the wave vector 2k_F, k_F being the Fermi wave vector. As a result the antiferromagnetic spin order appears, with one of the spin components spontaneously predominating. The charge density distribution is close to the Wigner order with the small amplitude of the 4k_F charge-density waves.

This paper reviews the method of bosonization for one-dimensional interacting fermions. Example of its application to mesoscopic systems is presented with an explicit calculation of the spin and charge currents in an interacting quantum wire subject to a uniform magnetic field and alternating voltage source. Special emphasis is given to the details of the calculation using bosonization and Keldysh techniques.