Electrons In Quantum Wires Research Articles

Characteristic features of strong correlation: lessons from a 3-fermion one-dimensional harmonic trap

Abstract Many quantum phenomena responsible for key applications in material science and quantum chemistry arise in the strongly correlated regime. This is at the same time, a costly regime for computer simulations. In the limit of strong correlation analytic solutions exist, but as we move away from this limit numerical simulation are needed, and accurate quantum solutions do not scale well with the number of interacting particles. In this work we propose to use few-particle harmonic traps in combination with twisted light as a quantum emulator to investigate the transition into a strongly-correlated regime. Using both analytic derivations and numerical simulations we generalize previous findings on 2 Coulomb interacting fermions trapped in a one-dimensional harmonic trap to the case of 3 fermions. The 4 signatures of strong correlation we have identified in the one-dimensional harmonic trap are: (i) the ground state density is highly localized around N equilibrium positions, where N is the number of particles, (ii) the symmetric and antisymmetric ground state wavefunctions become degenerate, (iii) the von Neumann entropy grows, (iv) the energy spectrum is fully characterized by N normal modes or less. Our findings describe the low-energy behavior of electrons in quantum wires and ions in Paul traps. Similar features have also been reported for cold atoms in optical lattices.

Dynamic correlation and polaronic effects on the correlational properties of finite-temperature electron quantum wire

We study the role of dynamic correlation and polaronic effects on the correlational properties of a GaAs-based electron quantum wire at finite-temperature T. The dynamics of electron correlations is incorporated through the self-consistent mean-field approximation of Hasegawa and Shimizu (the qSTLS theory) and the polaronic effects via the Fröhlich interactions. Results are presented for the static correlation functions, dynamic structure factor and electron’s contact probability over a wide range of T and electron number density r s . We find that for a fixed wire width b and T, electrons undergo a transition from the quantum liquid to Wigner crystal state due to the dynamics of severely correlated electrons at a critical . The inclusion of polaronic effects along with the conventional electron-electron interactions tends to increase r s c significantly at each T ultimately improving the quantum phase diagram. The electron’s contact probability exhibits a non-monotonic T-dependence which remains positive over a broader range of r s owing to the inclusion of polaronic effects. Besides, we explore the effect of phonon contribution on the plasmon energy of the quantum wire at non-zero T and find that there is splitting in the energy into two branches namely, plasmonlike and phononlike with former having energy lower than the latter. Both of the energy modes show consistent blue shift with rise in T, get damp at a critical wave vector q c , and q c decreases with T. Finally, we calculate the finite-T polaronic contribution to the free energy whose magnitude increases with T as r s → 0 and it becomes almost constant at sufficiently high r s .

Impact of electron-phonon interactions on Wigner crystallization in an electron quantum wire

In this paper, we explore the impact of electron-phonon (e-ph) coupling on the Wigner crystallization occurring due to strong electron-electron (e-e) interactions in a semiconductor-based electron quantum wire. The e-ph coupling is represented by the Fröhlich interaction potential and electron correlations are included within the dynamic version of self-consistent mean-field approximation of Hasegawa and Shimizu. Numerical results are reported for the static structure factor and pair-correlation function for fixed wire width and some selected values of electron number density parameter rs . A strong peak in the static structure factor and pronounced periodic oscillations in pair-correlation function indicate the formation of Wigner crystal in the quantum wire at a critical electron number density rs c . We find that the inclusion of e-ph interactions in addition to the usual e-e interactions significantly enhance rs c , at a fixed wire width.

Electronic States in a Doubly Eccentric Cylindrical Quantum Wire

Electronic states of a single electron in doubly eccentric cylindrical quantum wire are theoretically investigated in this paper. The motion of electron in quantum wire is free along axial direction in a cylindrical quantum wire and restricted in annular regions by three different parallel finite cylindrical barriers as soft wall confinement. The effective mass Schrödinger equation with effective mass boundary conditions is used to find energy eigenvalues and corresponding wavefunctions. Addition theorem for cylindrical Bessel functions is used to shift the origin for applying boundary conditions at different circular boundaries. Fourier expansion is applied after addition theorem to get wavefunctions in analytical form. A determinant equation is obtained as a result of applications of effective mass boundary conditions which roots gives energy of various electronic states. The lowest root gives ground state energy. The variation in ground state energy with eccentricity is obtained numerically and presented graphically. Electronic states in massive wall confinement and hard wall confinement is further obtained as limiting behavior of the states obtained in soft wall confinement. The knowledge of electronic states in such cylindrical hetrostructures semiconductor material can lead to improve the efficiency of many quantum devices.

Roughness scattering induced insulator-metal-insulator transition in a quantum wire

We have theoretically investigated the influence of interface roughness scattering on the low temperature mobility of electrons in quantum wires when electrons fill one or many subbands. We find the Drude conductance of the wire with length $\mathcal{L}$ first increases with increasing linear concentration of electrons $\eta$ and then decreases at larger concentrations. For small radius $R$ of the wire with length $\mathcal{L}$ the peak of the conductance $G_{max}$ is below $e^2/h$ so that electrons are localized. The height of this peak grows as a large power of $R$, so that at large $R$ the conductance $G_{max}$ exceeds $e^2/h$ and a window of concentrations with delocalized states (which we call the metallic window) opens around the peak. Thus, we predict an insulator-metal-insulator transition with increasing concentration for large enough $R$. Furthermore, we show that the metallic domain can be sub-divided into three smaller domains: 1) single-subband ballistic conductor, 2) many-subband ballistic conductor 3) diffusive metal, and use our results to estimate the conductance in these domains. Finally we estimate the critical value of $R_c(\mathcal{L})$ at which the metallic window opens for a given length $\mathcal{L}$ and find it to be in reasonable agreement with experiment.

Conduction of Electrons in Quantum Wires of Circular Cross-Section

Objectives: Quantum wires are one-dimensional (1-D) material that exhibit length to width ratios of about 1000 or more. The properties of quantum wire are due to the electrons in them have quantized energy levels perpendicular to their lengths. Such quantum confinement effect exhibits discrete values of electrical conductance which are integral multiples of (e2/h). Methods/ Analysis: In this paper we present a quantum mechanical analysis of evaluation of the electron energy eigen states and their corresponding eigen functions in a quantum wire of circular cross-section. Findings: The energy eigen values of quantum wires of different radii are calculated. Applications: On the basis of our preliminary analysis it has been observed that quantum wires can also be used as electronic energy filters.

Spin dynamics of hopping electrons in quantum wires: Algebraic decay and noise

We study theoretically spin decoherence and intrinsic spin noise in semiconductor quantum wires caused by an interplay of electron hopping between the localized states and the hyperfine interaction of electron and nuclear spins. At a sufficiently low density of localization sites the hopping rates have an exponentially broad distribution. It allows the description of the spin dynamics in terms of closely-situated "pairs" of sites and single "reaching" states, from which the series of hops result in the electron localized inside a "pair". The developed analytical model and numerical simulations demonstrate disorder-dependent algebraic tails in the spin decay and power-law singularity-like features in the low-frequency part of the spin noise spectrum.

Thermal Transport of Weakly Interacting Electrons in Quantum Wires

Thermal Transport of Weakly Interacting Electrons in Quantum Wires

Phase diagram of a quantum Coulomb wire

We report the quantum phase diagram of a one-dimensional Coulomb wire obtained using the path integral Monte Carlo (PIMC) method. The exact knowledge of the nodal points of this system permits us to find the energy in an exact way, solving the sign problem which spoils fermionic calculations in higher dimensions. The results obtained allow for the determination of the stability domain, in terms of density and temperature, of the one-dimensional Wigner crystal. At low temperatures, the quantum wire reaches the quantum-degenerate regime, which is also described by the diffusion Monte Carlo method. Increasing the temperature the system transforms to a classical Boltzmann gas which we simulate using classical Monte Carlo. At large enough density, we identify a one-dimensional ideal Fermi gas which remains quantum up to higher temperatures than in two- and three-dimensional electron gases. The obtained phase diagram as well as the energetic and structural properties of this system are relevant to experiments with electrons in quantum wires and to Coulomb ions in one-dimensional confinement.

Quantum Mechanical Tunneling of Electrons in Quantum Wire p–n Junctions

Quantum Mechanical Tunneling of Electrons in Quantum Wire <i>p</i>–<i>n</i> Junctions

Zigzag phase transition in quantum wires.

We study the quantum phase transition of interacting electrons in quantum wires from a one-dimensional (1D) linear configuration to a quasi-1D zigzag arrangement using quantum Monte Carlo methods. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal, then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase, and, finally, the electrons form a disordered liquidlike phase. We show that the linear to zigzag phase transition is not destroyed by the strong quantum fluctuations present in narrow wires; it has characteristics which are qualitatively different from the classical transition.

A non-adiabatically driven electron in a quantum wire with spin–orbit interaction

An exact solution is derived for the wavefunction of an electron in a semiconductor quantum wire with spin–orbit interaction and driven by external time-dependent harmonic confining potential. The formalism allows analytical expressions for various quantities to be derived, for example spin and pseudo-spin rotations, energy and occupation probabilities for excited states. It is demonstrated how perfect spin and pseudo-spin flips can be achieved at high frequencies of the order of ω, the confining potential level spacing. By an appropriately chosen driving term, spin manipulation can be exactly performed far into the non-adiabatic regime. The implications for spin-polarized emission and spin-dependent transport are also discussed.

Spin-resolved correlations at arbitrary spin polarization and ground state of a quasi-one-dimensional electron gas

We study the spin-resolved correlations at arbitrary spin polarization ζ and the ground state of a quasi-one-dimensional electron gas by using the dynamical self-consistent mean-field theory of Singwi et al. Numerical results are presented for the spin-resolved pair-correlation functions, correlation energies, and ground-state energy at selected ζ and a range of electron density rs. Our results agree nicely with the recent lattice regularized diffusion Monte Carlo simulation data at small rs and ζ. With increasing rs and/or ζ, the spin-resolved correlations become less satisfactory, but the spin-summed quantities show a reasonable agreement, thus implying a cancellation among discrepancies in the components. Interestingly, theory predicts that the like-spin correlation energy becomes little positive for rs>1.5. A comparison between the ground-state energies of the unpolarized and fully polarized spin phases reveals that the exchange–correlations may induce a phase transition to the latter above a critical rs, rsc. Importantly, the transition is in agreement with recent experiments on low density electron quantum wires. However, the stability of partially spin-polarized states could not be ascertained due to difficulty in obtaining the self-consistent density response function beyond a certain rs, preceding rsc. Using the static mean-field theory, we find that the spin-polarization transition is abrupt (i.e., the partially spin-polarized states are energetically unstable) and it occurs at nearly the same rs as in the dynamical approach.

One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm

For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. We review the recent progress in understanding 1D quantum fluids beyond the low-energy limit, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi edge singularity and the Fermi liquid theory, perturbation theory in the interaction strength, and a new way of treating finite-size integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined to a 1D trap. We review existing results for various dynamic correlation functions, in particular the density structure factor and the spectral function. Moreover, we show how a dispersion nonlinearity leads to finite particle lifetimes, and discuss its impact on the transport properties of 1D systems at finite temperatures. The conventional Luttinger liquid theory is a special limit of the new theory, and we explain the relation between the two.

Spectral function of few electrons in quantum wires and carbon nanotubes as a signature of Wigner localization

We demonstrate that the profile of the space-resolved spectral function at finite temperature provides a signature of Wigner localization for electrons in quantum wires and semiconducting carbon nanotubes. Our numerical evidence is based on the exact diagonalization of the microscopic Hamiltonian of few particles interacting in gate-defined quantum dots. The minimal temperature required to suppress residual exchange effects in the spectral function image of (nanotubes) quantum wires lies in the (sub-) Kelvin range.

Interaction effects on thermal transport in quantum wires

We develop a theory of thermal transport of weakly interacting electrons in quantum wires. Unlike higher-dimensional systems, a one-dimensional electron gas requires three-particle collisions for energy relaxation. The fastest relaxation is provided by the intrabranch scattering of comoving electrons which establishes a partially equilibrated form of the distribution function. The thermal conductance is governed by the slower interbranch processes which enable energy exchange between counterpropagating particles. We derive an analytic expression for the thermal conductance of interacting electrons valid for arbitrary relation between the wire length and electron thermalization length. We find that in sufficiently long wires the interaction-induced correction to the thermal conductance saturates to an interaction-independent value.

A new approach for modeling of dark current characteristics of quantum wire infrared photodetectors

In order to study the dark current characteristics in a quantum wire infrared photodetector (QRIP), the average number of electrons in quantum wires (QRs) must be got, which is mostly too complicated. In this paper we give a simple formula to calculate the average number of carriers in a quantum wire (QR) that can be easily evaluated by mathematical softwares, and then we use this formula to study dark current characteristics of a quantum wire infrared photodetector (QRIP).

Thermalization of Nonequilibrium Electrons in Quantum Wires

We study the problem of energy relaxation in a one-dimensional electron system. The leading thermalization mechanism is due to three-particle collisions. We show that for the case of spinless electrons in a single channel quantum wire the corresponding collision integral can be transformed into an exactly solvable problem. The latter is known as the Schrödinger equation for a quantum particle moving in a Pöschl-Teller potential. The spectrum for the resulting eigenvalue problem allows for bound-state solutions, which can be identified with the zero modes of the collision integral, and a continuum of propagating modes, which are separated by a gap from the bound states. The inverse gap gives the time scale at which counterpropagating electrons thermalize.

Energy Relaxation and Thermalization of Hot Electrons in Quantum Wires

We develop a theory of energy relaxation and thermalization of hot carriers in clean quantum wires. Our theory is based on a controlled perturbative approach for large excitation energies and emphasizes the important roles of the electron spin and finite temperature. Unlike in higher dimensions, relaxation in one-dimensional electron liquids requires three-body collisions and is much faster for particles than holes which relax at nonzero temperatures only. Moreover, comoving carriers thermalize more rapidly than counterpropagating carriers. Our results are quantitatively consistent with a recent experiment.

Calculation of the nonlinear absorption coefficient of a strong electromagnetic wave by confined electrons in quantum wires

General analytic expressions for the absorption coefficient (ACF) of a strong electromagnetic wave (SEM) caused by confined electrons in cylindrical quantum wires (CQW) are obtained by using the quantum kinetic equation for electrons in the case of electron–optical phonon scattering. Second-order multiphoton process is included into the result. The dependence of ACF on the amplitude E 0 and the energy ℏ Ω of a SEM, the temperature T of the system, and radius R of CQW for a specific CQW GaAs/AlAs is achieved due to numerical method. The computational results show that the dependence of ACF on ℏ Ω and R can be applied to optically detect the electric subbands in a CQW.