Electronic transport in inhomogeneous quantum wires
J. Rech, K. A. Matveev
备注：
18 pages, 2 figures. Invited paper for special issue of Journal of Physics: Condensed Matter on "The 0.7 Feature and Interactions in One-dimensional Systems"
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 temperatures below the Fermi energy. By estimating the energy dissipated throughout the wire by low-energy excitations, we then develop a different method for deriving the resistivity of the wire, which can be combined with the bosonization formalism. This allows us to compare our results with previous works relying on an extension of the Tomonaga-Luttinger model to inhomogeneous systems.
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 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.
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 microscopically derive transport equations for the conduction electrons in ferromagnetic materials with an inhomogeneous magnetization profile. Our quantum kinetic approach includes elastic scattering and anisotropic spin-flip scattering at magnetic impurities. In the diffusive limit, we calculate the resistance through a domain wall and find that the domain-wall resistance can be positive or negative. In the limit of long domain walls we derive analytical expressions and compare them with existing works, which used less general models or different theoretical frameworks.
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 …
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 theoretically investigate the effect of inhomogeneous light beams with (twisted light) and without (plane-wave light) orbital angular momentum on semiconductor-based nanostructures, when the symmetry axes of the beam and the nanostructure are displaced parallel to each other. Exact analytical results are obtained by expanding the off-centered light field in terms of the appropriate light modes centered around the nanostructure. We demonstrate how electronic transitions involving the transfer of different amounts of orbital angular momentum are switched on and off as a function of the separa…
The density functional theory is used to study the electronic structure of a quantum wire in a magnetic field. In a GaAs quantum wire, a critical density has been found, below which the electron density has a strong spatial inhomogeneity. The effect of the disorder potential on the electron density profile in a two-dimensional electron gas is estimated.
Monoatomic chains of molybdenum encapsulated in single walled carbon nanotubes of different chiralities are investigated using density functional theory. We determine the optimal size of the carbon nanotube for encapsulating a single atomic wire, as well as the most stable atomic arrangement adopted by the wire. We also study the transport properties in the ballistic regime by computing the transmission coefficients and tracing them back to electronic conduction channels of the wire and the host. We predict that carbon nanotubes of appropriate radii encapsulating a Mo wire have metallic behavi…
Despite the importance of Si:P delta-doped wires for modern nanoelectronics, there are currently no computational models of electron transport in these devices. In this paper we present a nonequilibrium Green's function model for electronic transport in a delta-doped wire, which is described by a tight-binding Hamiltonian matrix within a single-band effective-mass approximation. We use this transport model to calculate the current-voltage characteristics of a number of delta-doped wires, achieving good agreement with experiment. To motivate our transport model we have performed density-functio…
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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…
A strict method is used to calculate the current-voltage characteristics of a double-stranded DNA. A more reliable model considering the electrostatic potential drop along an individual DNA molecular wire between the contacts is considered and the corresponding Green's Function is obtained analytically using Generating Function method, which avoids difficult numerical evaluations. The obtained results indicate that the electrostatic drop along the wire always increases the conductor beyond the threshold than without considering it, which is in agreement with recent experiments. The present met…
Magnetic barriers in graphene are not easily tunable. However, introducing both electric and magnetic fields, provides tunable and far more controllable electronic states in graphene. Here we study such systems. A one-dimensional channel can be formed in graphene using perpendicular electric and magnetic fields. This channel (quantum wire) supports localized electron-hole states, with parameters that can be controlled by an electric field. Such quantum wire offers peculiar conducting properties, like unidirectional conductivity and robustness to disorder. Two separate quantum wires comprise a …
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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…
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Electronic transmission in bent quantum wires modeled by the tight binding Hamiltonian, and clamped between ideal, semi-infinite leads is studied. The effect of `bending' the chain is simulated by introducing a non-zero hopping between the extremities of the wire. It is seen that the proximity of the two ends gives rise to Falo line shapes in the transmission spectrum. Transmission properties for both an ordered lattice and a Fibonacci quantum wire are discussed. In the quasi-periodic Fibonacci chain, the proximity of the two ends of the chain closes all the gaps in the spectrum and the spectr…
Inhomogeneous superconductivity in (001), (110), and (111) KTaO$_3$ two-dimensional electronic gases: effect of electronic confinement on the transition temperature
Physics Department “E.R. Caianiello”, Università degli Studi di Salerno（萨莱诺大学 E.R. Caianiello 物理系）；INFN - Sezione collegata di Salerno（意大利国家核物理研究所萨莱诺分部）；CNR-SPIN（国家研究委员会自旋科学研究所）；Physics Department “Ettore Pancini”, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学 Ettore Pancini 物理系）
We derive an explicit expression for the quantum conductivity of a molecular wire containing a redox center, which is embedded in an electrochemical environment. The redox center interacts with the solvent, and the average over the solvent configurations is performed numerically. Explicit calculations have been performed for a chain of three atoms. When the redox center interacts strongly with neighboring electronic levels, the current-potential curves show interesting features like rectification, current plateaus and negative differential resistance. Electronic spectroscopy of intermediate st…
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We study nonequilibrium quantum transport through a mesoscopic wire coupled via local exchange to a ferromagnetic spin chain. Using the Keldysh formalism in the self-consistent Born approximation, we identify fingerprints of the magnetic polaron state formed by hybridization of electronic and magnon states. Because of its low decoherence rate, we find coherent transport signals. Both elastic and inelastic peaks of the differential conductance are discussed as a function of external magnetic fields, the polarization of the leads and the electronic level spacing of the wire.
We investigate how two-particle interactions affect the electronic transport through meso- and nanoscopic systems of two different types: quantum dots with local Coulomb correlations and quasi one-dimensional quantum wires of interacting electrons. A recently developed functional renormalization group scheme is used that allows to investigate systems of complex geometry. Considering simple setups we show that the method includes the essential aspects of Luttinger liquid physics (one-dimensional wires) as well as of the physics of local correlations, with the Kondo effect being an important exa…
Quantum descriptions of many complex systems are formulated most naturally in bases of states that are not mutually orthogonal. We introduce a general and powerful yet simple approach that facilitates solving such models exactly by embedding the non-orthogonal states in a new Hilbert space in which they are by definition mutually orthogonal. This novel approach is applied to electronic transport in molecular quantum wires and is used to predict conductance antiresonances of a new type that arise solely out of the non-orthogonality of the local orbitals on different sites of the wire.
This article presents an overview of results pertaining to electronic structure, transport properties, and interaction effects in ballistic quantum wires with Rashba spin splitting. Limits of weak and strong spin--orbit coupling are distinguished, and spin properties of the electronic states elucidated. The case of strong Rashba spin splitting where the spin--precession length is comparable to the wire width turns out to be particularly interesting. Hybridization of spin--split quantum--wire subbands leads to an unusual spin structure where the direction of motion for electrons can fix their s…
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We investigate in atomic scale the electronic phase separation occurring in the well known quasi 1D charge-density wave (CDW) phase of the In atomic wire array on a Si(111) surface. The characteristic atomic scale defects, originated from excess In atoms, are found to be actively involved in the formation of the phase boundary between the metallic and the CDW phases by extensive analysis of scanning tunneling microscopy images at various temperatures. These particular defects flip the phase of the quasi 1D CDW to impose strong local constraints in the CDW correlation. We show that such local c…
We develop a simple model of surface states for topological insulators, developing matching relations for states on surfaces of different orientations. The model allows one to write simple Dirac Hamiltonians for each surface, and to determine how perturbations that couple to electron spin impact them. We then study two specific realizations of such systems: quantum wires of rectangular cross-section and a rectangular slab in a magnetic field. In the former case we find a gap at zero energy due to the finite size of the system. This can be removed by application of exchange fields on the top an…
Using DFT calculations, we present a thorough study of the quantum size effects on the stability of freestanding metal atom wires. Our systems include Na, Ag, Au, In, Ga and Pb atom wires, i.e. $s$, $sd$, and $sp$ electron prototypes. We found that the total energy always oscillates with the wire length, which clearly indicates the existence of preferred lengths. Increasing the length, the s-system exhibits even-odd oscillations following a $a/x +b/x^2$ decay law in the stability, which can be attributed to electron band filling and quantum confinement along the wire. The $sd$-system exhibits …
The dephasing effect of metallic gates on electrons moving in one quasi--one--dimensional diffusive wires is analyzed. The incomplete screening in this geometry implies that the effect of the gate can be described, at high energies or temperatures, as an electric field fluctuating in time. The resulting system can be considered a realization of the Caldeira-Leggett model of an environment coupled to many particles. Within the range of temperatures where this approximation is valid, a simple estimation of the inverse dephasing time gives $τ_{\rm G}^{-1} \propto T^{1/2}$.
Coherent electron transport through a quantum channel in the presence of a general extended scattering potential is investigated using a T-matrix Lippmann-Schwinger approach. The formalism is applied to a quantum wire with Gaussian type scattering potentials, which can be used to model a single impurity, a quantum dot or more complicated structures in the wire. The well known dips in the conductance in the presence of attractive impurities is reproduced. A resonant transmission peak in the conductance is seen as the energy of the incident electron coincides with an energy level in the quantum …
Novel bis(biphenyl)-capped polyynes have been synthesized to investigate the modulation of the electronic and optical properties of sp-hybridized carbon-atom wires (CAWs) capped with π-conjugated $sp^{2}$ endgroups. Raman and Surface Enhanced Raman spectroscopy (SERS) investigation of these systems and Density Functional Theory (DFT) calculations reveal structural changes from polyyne-like with alternating single-triple bonds towards cumulene-like with more equalized bonds as a consequence of the charge transfer occurring when wires interact with metallic nanoparticles. While polyynes have sem…
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We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially large in the ratio of bandwidth of excitations and temperature. Here we focus on shorter wires in which full equilibration is not accomplished. Signatures of relaxation then are due to backscattering of hole excitations close to the band bottom which perform a diffusive motion in momentum space while scattering from excitations at the Fermi level. This is remini…
The transport through a quantum wire with a side coupled quantum dot is studied. We use the X-boson treatment for the Anderson single impurity model in the limit of $U=\infty $. The conductance presents a minimum for values of T=0 in the crossover from mixed-valence to Kondo regime due to a destructive interference between the ballistic channel associated with the quantum wire and the quantum dot channel. We obtain the experimentally studied Fano behavior of the resonance. The conductance as a function of temperature exhibits a logarithmic and universal behavior, that agrees with recent experi…
Study on the electronic transport of a large scale two dimensional system by the transfer matrix method (TMM) based on the Schördinger equation suffers from the numerical instability. To address this problem, we propose a renormalized transfer matrix method (RTMM) by setting up a set of linear equations from U times of multiplication of traditional transfer matrix (U=N/S}with N and S being the atom number of length and the transfer step), and smaller S is required for wider systems. Then we solve the above linear equations by Gauss elimination method and further optimize to reduce the computat…
