We study interaction-induced localization of electrons in an inhomogeneous quasi-one-dimensional system--a wire with two regions, one at low density and the other high. Quantum Monte Carlo techniques are used to treat the strong Coulomb interactions in the low density region, where localization of electrons occurs. The nature of the transition from high to low density depends on the density gradient--if it is steep, a barrier develops between the two regions, causing Coulomb blockade effects. Ferromagnetic spin polarization does not appear for any parameters studied. The picture emerging here is in good agreement with measurements of tunneling between two wires.
We study the effect of electron-electron interactions on the transport in an inhomogeneous quantum wire. We show that contrary to the well-known Luttinger liquid result, non-uniform interactions contribute substantially to the resistance of the wire. In the regime of weakly interacting electrons and moderately low temperatures we find a linear in T resistivity induced by the interactions. We then use the bosonization technique to generalize this result to the case of arbitrarily strong interactions.
We study transport properties of weakly interacting one-dimensional electron systems including on an equal footing thermal equilibration due to three-particle collisions and the effects of large-scale inhomogeneities. We show that equilibration in an inhomogeneous quantum wire is characterized by the competition of interaction processes which reduce the electrons total momentum and such which change the number of right- and left-moving electrons. We find that the combined effect of interactions and inhomogeneities can dramatically increase the resistance of the wire. In addition, we find that …
We study electron and spin transport in interacting quantum wires contacted by noninteracting leads. We theoretically model the wire and junctions as an inhomogeneous chain where the parameters at the junction change on the scale of the lattice spacing. We study such systems analytically in the appropriate limits based on Luttinger liquid theory and compare the results to quantum Monte Carlo calculations of the conductances and local densities near the junction. We first consider an inhomogeneous spinless fermion model with a nearest-neighbor interaction and then generalize our results to a sp…
We consider scattering and transport in interacting quantum wires that are connected to leads. Such a setup can be represented by a minimal model of interacting fermions with inhomogeneities in the form of sudden changes in interaction strength and/or velocity. The inhomogeneities generally cause relevant backscattering, so it is a priori unclear if a perfectly ballistic quantum wire can exist in the low temperature limit. We are able to identify such a perfectly conducting fixed point even for large abrupt changes, which in the considered model corresponds to a velocity matching condition. Th…
Inhomogeneities and junctions in wires are natural sources of scattering, and hence resistance. A conducting fixed point usually requires an adiabatically smooth system. One notable exception is "healing", which has been predicted in systems with special symmetries, where the system is driven to the homogeneous fixed point. Here we present theoretical results for a different type of conducting fixed point which occurs in inhomogeneous wires with an abrupt jump in hopping and interaction strength. We show that it is always possible to tune the system to an unstable conducting fixed point which …
We use the Hartree-Fock method to study an interacting one-dimensional electron system on a finite wire, partially depleted at the center by a smooth potential barrier. A uniform one-Tesla Zeeman field is applied throughout the system. We find that with the increase in the potential barrier, the low density electrons under it go from a non-magnetic state to an antiferromagnetic state, and then to a state with a well-localized spin-aligned region isolated by two antiferromagnetic regions from the high density leads. At this final stage, in response to a continuously increasing barrier potential…
We explore the theory of electrons confined by one dimensional power law potentials. We calculate the density profile in the high density electron gas, the low density Wigner crystal, and the intermediate regime. We extract the momentum space wavefunction of the electron at the Fermi surface, which can be measured in experiments on tunneling between parallel wires. The onset of localization leads to a dramatic broadening of the momentum space wavefunction together with pronounced sharpening (in energy) of the tunneling spectrum.
We study the transport properties of a long non-uniform quantum wire where the electron-electron interactions and the density vary smoothly at large length scales. We show that these inhomogeneities lead to a finite resistivity of the wire, due to a weak violation of momentum conservation in the collisions between electrons. Estimating the rate of change of momentum associated with non-momentum-conserving scattering processes, we derive the expression for the resistivity of the wire in the regime of weakly interacting electrons and find a contribution linear in temperature for a broad range of…
The bound state energies of L-shaped or T-shaped quantum wires in inhomogeous magnetic fields are found to depend strongly on the asymmetric parameter $α=W_{2}/W_{1}$, i.e. the ratio of the arm widths. Two effects of magnetic field on bound state energies of the electron are obtained. One is the depletion effect which purges the electron out of the OQD system. The other is to create an effective potential due to quantized Landau levels of the magnetic field. The bound state energies of the electron in L-shaped or T-shaped quantum wires are found to depend quadratically (linearly) on the magnet…
We show that quasi-bound electron states are formed in a quantum wire as a result of electron backscattering in the transition regions between the wire and the electron reservoirs, to which the wire is coupled. The backscattering mechanism is caused by electron density oscillations arising even in smooth transitions due to the reflection of electrons not transmitting through the wire. The quasi-bound states reveal themselves in resonances of the electron transmission probability through the wire. The calculations were carried out within the Hartree-Fock approximation using quasiclassic wavefun…
We study the level repulsion and its relationship with the localization length in a disordered one-dimensional quantum wire excited with monochromatic linearly polarized light and described by the Anderson-Floquet model. In the high frequency regime, the linear scaling between the localization length divided by the length of the system and the spectral repulsion is the same as in the one-dimensional Anderson model without driving, although both quantities depend on the parameters of the external field. In the low frequency regime the level repulsion depends mainly on the value of the amplitude…
We investigate electron quantum transport through nano-wires with one-sided surface roughness in the presence of a perpendicular magnetic field. Exponentially diverging localization lengths are found in the quantum-to-classical crossover regime, controlled by tunneling between regular and chaotic regions of the underlying mixed classical phase space. We show that each regular mode possesses a well-defined mode-specific localization length. We present analytic estimates of these mode localization lengths which agree well with the numerical data. The coupling between regular and chaotic regions …
The Friedel oscillations caused due to an impurity located at one edge of a disordered interacting quantum wire are calculated numerically. The electron density in the system's ground state is determined using the DMRG method, and the Friedel oscillations data is extracted using the density difference between the case in which the wire is coupled to an impurity and the case where the impurity is uncoupled. We show that the power law decay of the oscillations occurring for an interacting clean 1D samples described by Luttinger liquid theory, is multiplied by an exponential decay term due to the…
A self-consistent treatment of exchange and correlation interactions in a quantum wire (QW) subject to a strong perpendicular magnetic field is presented using a modified local-density approximation (MLDA). The influence of many-body interactions on the spin-splitting between the two lowest Landau levels (LLs) is calculated within the screened Hartree-Fock approximation (SHFA), for filling factor ν=1, and the strong spatial dependence of the screening properties of electrons is taken into account. In comparison with the Hartree-Fock result, the spatial behavior of the occupied LL in a QW is st…
We study the quantum transport through networks of diffusive wires connected to reservoirs in the Landauer-Büttiker formalism. The elements of the conductance matrix are computed by the diagrammatic method. We recover the combination of classical resistances and obtain the weak localization corrections. For arbitrary networks, we show how the cooperon must be properly weighted over the different wires. Its nonlocality is clearly analyzed. We predict a new geometrical effect that may change the sign of the weak localization correction in multiterminal geometries.
We discuss a model of random segmented wire, with linear segments of 2D wires joined by circular bends. The joining vertices act as scatterers on the propagating electron waves. The model leads to resonant Anderson localization when all segments are of similar length. The resonant behavior is present with one and also with several propagating modes. The probability distributions evolve from diffusive to localized regimes when increasing the number of segments in a similar way for long and short localization lengths. As a function of the energy a finite segmented wire typically evolves from loc…
Finite size effects in the localization properties of disordered quantum wires are analyzed through conductance calculations. Disorder is induced by introducing vacancies at random positions in the wire and thus preserving the chiral symmetry. For quasi one-dimensional geometries and low concentration of vacancies, an exponential decay of the mean conductance with the wire length is obtained even at the center of the energy band. For wide wires, finite size effects cause the conductance to decay following a non-pure exponential law. We propose an analytical formula for the mean conductance tha…
We show that electron transport in disordered quantum wires can be described by a modified Cooperon equation, which coincides in form with the Dirac equation for the massive fermions in a 1+1 dimensional system. In this new formalism, we calculate the DC electric current induced by electromagnetic fields in quasi-one-dimensional rings. This current changes sign, from diamagnetic to paramagnetic, depending on the amplitude and frequency of the time-dependent external electromagnetic field.
We study the diffusive and localization properties of wavepackets in disordered wires in a magnetic field. In contrast to a recent supersymmetry approach our numerical results show that the decay rate of the steady state changes {\em smoothly} at the crossover from preserved to broken time-reversal symmetry. Scaling and fluctuation properties are also analyzed and a formula, which was derived analytically only in the pure symmetry cases is shown to describe also the steady state wavefunction at the crossover regime. Finally, we present a scaling for the variance of the packet which shows again…
The magnetic field dependent localization in a disordered quantum wire is considered nonperturbatively. An increase of an averaged localization length with the magnetic field is found, saturating at twice its value without magnetic field. The crossover behavior is shown to be governed both in the weak and strong localization regime by the magnetic diffusion length L_B. This function is derived analytically in closed form as a function of the ratio of the mean free path l, the wire thickness W, and the magnetic length l_B for a two-dimensional wire with specular boundary conditions, as well as …
We study effects of disorder on the low energy single particle transport in a normal wire surrounded by a superconductor. We show that the heat conductance includes the Andreev diffusion decreasing with increase in the mean free path $\ell $ and the diffusive drift produced by a small particle-hole asymmetry, which increases with increasing $\ell$. The conductance thus has a minimum as a function of $\ell$ which leads to a peculiar re-entrant localization as a function of the mean free path.
We report transport measurements on superconducting wire networks which provide the first experimental evidence of a new localization phenomenon induced by magnetic field on a 2D periodic structure. In the case of a superconducting wave function this phenomenon manifests itself as a depression of the network critical current and of the superconducting transition temperature at a half magnetic flux quantum per tile. In addition, the strong broadening of the resistive transition observed at this field is consistent with enhanced phase fluctuations due to this localization mechanism.
We investigate electronic quantum transport through nano-wires with one-sided surface roughness. A magnetic field perpendicular to the scattering region is shown to lead to exponentially diverging localization lengths in the quantum-to-classical crossover regime. This effect can be quantitatively accounted for by tunneling between the regular and the chaotic components of the underlying mixed classical phase space.
The crossover in energy level statistics of a quasi-1-dimensional disordered wire as a function of its length L is used, in order to derive its averaged localization length, without magnetic field, in a magnetic field and for moderate spin orbit scattering strength. An analytical function of the magnetic field for the local level spacing is obtained, and found to be in excellent agreement with the magnetic field dependent activation energy, recently measured in low-mobility quasi-one-dimensional wires\cite{khavin}. This formula can be used to extract directly and accurately the localization le…
We study the signatures of disorder in the production of orbital electron entanglement in quantum wires. Disordered entanglers suffer the effects of localization of the electron wave function and random fluctuations in the entanglement production. This manifests in the statistics of the concurrence, a measure of the produced two-qubit entanglement. We calculate the concurrence distribution as a function of the disorder strength within a random-matrix approach. We also identify significant constraints on the entanglement production as a consequence of the breaking/preservation of time-reversal …
We derive exact quantum expressions for the localization length $L_c$ for weak disorder in two- and three chain tight-binding systems coupled by random nearest-neighbour interchain hopping terms and including random energies of the atomic sites. These quasi-1D systems are the two- and three channel versions of Dorokhov's model of localization in a wire of $N$ periodically arranged atomic chains. We find that $L^{-1}_c=N.ξ^{-1}$ for the considered systems with $N=(1,2,3)$, where $ξ$ is Thouless' quantum expression for the inverse localization length in a single 1D Anderson chain, for weak disor…
The supersymmetry technique [A. V. Kolesnikov and K. B. Efetov, Phys. Rev. Lett. 83, 3689 (1999)] predicts a two-scale behavior of wavefunction decay in disordered wires in the crossover regime from preserved to broken time-reversal symmetry. We have tested this prediction by a transmission approach, relying on the Borland conjecture that relates the decay length of the transmittance to the decay length of the wavefunctions. Our numerical simulations show no indication of two-scale behavior.
In the paper the dynamic localization of charged particle (electron) in a quantum wire under the external non-uniform time-dependent electric field is considered. The electrons are trapped in a deep 'dynamic' quantum wells which are the result of specific features of the potential imposed on 2D electron gas: the scale of spatial nonuniformity is much smaller then the electron mean free path (L_1 << \bar{l}) and the frequency is much greater then τ^{-1}, where τis the electron free flight time. As a result, the effect of this field on the charged particle is in a sense equivalent to the effect …
We consider the dynamics of an electron in an infinite disordered metallic wire. We derive exact expressions for the probability of diffusive return to the starting point in a given time. The result is valid for wires with or without time-reversal symmetry and allows for the possibility of topologically protected conducting channels. In the absence of protected channels, Anderson localization leads to a nonzero limiting value of the return probability at long times, which is approached as a negative power of time with an exponent depending on the symmetry class. When topologically protected ch…
In a recent work Schomerus and Beenakker [Phys. Rev. Lett. 84, 3927 (2000)] tried to check numerically our prediction about a two-scale localization in disordered wires in a weak magnetic field. According to our theory an exponential decay of wave functions with the localization length of the orthogonal ensemble is followed at larger distances by another exponential decay with the length of the unitary ensemble. Studying the transmittance, Schomerus and Beenakker did not confirm our theory. The most probable explanation they suggested is that only rare states could have the two scales while ``…
We present Fokker-Planck equations that describe transport of heat and spin in dirty unconventional superconducting quantum wires. Four symmetry classes are distinguished, depending on the presence or absence of time-reversal and spin rotation invariance. In the absence of spin-rotation symmetry, heat transport is anomalous in that the mean conductance decays like $1/\sqrt{L}$ instead of exponentially fast for large enough length $L$ of the wire. The Fokker-Planck equations in the presence of time-reversal symmetry are solved exactly and the mean conductance for quasiparticle transport is calc…
Calculating the density-density correlation function for disordered wires, we study localization properties of wave functions in a magnetic field. The supersymmetry technique combined with the transfer matrix method is used. It is demonstrated that at arbitrarily weak magnetic field the far tail of the wave functions decays with the length $L_{\rm cu}=2L_{\rm co}$, where $L_{\rm co}$ and $L_{\rm cu}$ are the localization lengths in the absence of a magnetic field and in a strong magnetic field, respectively. At shorter distances, the decay of the wave functions is characterized by the length $…
We study an interaction of 2D quasiparticles with linear dispersion (graphene) with impurity potentials. It is shown that in 1D potential well (quantum wire) there are discrete levels, corresponding to localized states, whereas in 2D well (quantum dot) there are no such states. Scattering cross-section of electrons (holes) of graphene by an axially symmetric potential well is found and it is shown that for infinetily large energy of incoming particles the cross-section tends to a constant. The effective Hamiltonian for a curved quantum wire of graphene is derived and it is shown that the corre…
The quantum correction to the conductivity in disordered quantum wires with linear Rashba spin-orbit coupling is obtained. For quantum wires with spin-conserving boundary conditions, we find a crossover from weak anti- to weak localization as the wire width W is reduced using exact diagonalization of the Cooperon equation. This crossover is due to the dimensional dependence of the spin relaxation rate of conduction electrons, which becomes diminished, when the wire width is smaller than the bulk spin precession length $L_{SO}$. We thus confirm previous results for small wire width, $W/L_{SO}<=…
Using the supersymmetry technique combined with the transfer matrix method we calculate different physical quantities characterizing localization in disordered wires. In particular, we analyze the density-density correlation function and study effects of an external magnetic field $H$ on tails of wave functions. At zero and very strong magnetic fields, we obtain explicit expressions, valid at arbitrary distances, for all moments and for the entire distribution function of the density-density correlations. A two-scale decay is shown to be a typical feature of infinitely long wires at weak magne…
Carrier relaxation processes have been investigated in GaAs/AlGaAs v-groove quantum wires (QWRs) with a large subband separation (46 meV). Signatures of inhibited carrier relaxation mechanisms are seen in temperature-dependent photoluminescence (PL) and photoluminescence-excitation (PLE) measurements; we observe strong emission from the first excited state of the QWR below ~50 K. This is attributed to reduced inter-subband relaxation via phonon scattering between localized states. Theoretical calculations and experimental results indicate that the pinch-off regions, which provide additional tw…
Isolated Majorana fermion states can be produced at the boundary of a topological superconductor in a quasi-one-dimensional geometry. If such a superconductor is connected to a disordered quantum wire, the Majorana fermion is spread into the wire, subject to Anderson localization. We study this effect in the limit of a thick wire with broken time-reversal and spin-rotational symmetries. With the use of a supersymmetric nonlinear sigma model, we calculate the average local density of states in the wire as a function of energy and of the distance from the interface with the superconductor. Our r…
We study the quantum transport in multiterminal networks of quasi-one-dimensional diffusive wires. When calculating the weak localization correction to the conductances, we show that the Cooperon must be properly weighted over each wire. This can even change the sign of the weak localization correction in certain geometries.
The conductance of a quantum wire with off-diagonal disorder that preserves a sublattice symmetry (the random hopping problem with chiral symmetry) is considered. Transport at the band center is anomalous relative to the standard problem of Anderson localization both in the diffusive and localized regimes. In the diffusive regime, there is no weak-localization correction to the conductance and universal conductance fluctuations are twice as large as in the standard cases. Exponential localization occurs only for an even number of transmission channels in which case the localization length does…
