Interacting Quantum Wire Research Articles

Minimal model of quantized conductance in interacting ballistic quantum wires

We review what we consider to be the minimal model of quantized conductance in a finite interacting quantum wire. Our approach utilizes the simplicity of the equation of motion description to both deal with general spatially dependent interactions and finite wire geometry. We emphasize the role of two different kinds of boundary conditions, one associated with local "chemical" equilibrium in the sense of Landauer, the other associated with screening in the proximity of the Fermi liquid metallic leads. The relation of our analysis to other approaches to this problem is clarified. We then use our formalism to derive a Drude type expression for the low frequency AC-conductance of the finite wire with general interaction profile.

Spin-orbit interaction induced anisotropic property in interacting quantum wires.

We investigate theoretically the ground state and transport property of electrons in interacting quantum wires (QWs) oriented along different crystallographic directions in (001) and (110) planes in the presence of the Rashba spin-orbit interaction (RSOI) and Dresselhaus SOI (DSOI). The electron ground state can cross over different phases, e.g., spin density wave, charge density wave, singlet superconductivity, and metamagnetism, by changing the strengths of the SOIs and the crystallographic orientation of the QW. The interplay between the SOIs and Coulomb interaction leads to the anisotropic dc transport property of QW which provides us a possible way to detect the strengths of the RSOI and DSOI.PACS numbers: 73.63.Nm, 71.10.Pm, 73.23.-b, 71.70.Ej

Anisotropic property in interacting quantum wires embedded in (110) plane

We investigate the theoretically combined effect of spin–orbit interactions and Coulomb interaction on the ground state and transport property of a quantum wire oriented along different crystallographic directions in the (110) plane. We find that the electron’s ground state exhibits phase transition among spin density wave, charge density wave, singlet superconductivity and metamagnetism, which can be controlled by changing the crystallographic orientation, the strengths of the spin–orbit interactions and the Coulomb interaction. The ac conductance exhibits a significant anisotropic behavior and a out-of-plane spin polarization which can be tuned by an in-plane electric field.

How to Find Conductance Tensors of Quantum Multiwire Junctions through Static Calculations: Application to an InteractingYJunction

Conductance is related to dynamical correlation functions which can be calculated with time-dependent methods. Using boundary conformal field theory, we relate the conductance tensors of quantum junctions of multiple wires to static correlation functions in a finite system. We then propose a general method for determining the conductance through time-independent calculations alone. Applying the method to a Y junction of interacting quantum wires, we numerically verify the theoretical prediction for the conductance of the chiral fixed point of the Y junction and then calculate the thus far unknown conductance of its M fixed point with the time-independent density matrix renormalization group method.

Nearly Universal $\hbox{1}/f^{2}$ Spectrum of Mobility Fluctuation Noise in a Quantum Wire at Radio and Microwave Frequencies

We have studied the noise power spectrum associated with mobility fluctuations of hot carriers in a GaAs quantum wire in the frequency range of 20 MHz-50 GHz using ensemble Monte Carlo simulation. This frequency range is outside the regime where a noise peak occurs in quantum wires due to well-known streaming oscillations in the carrier drift velocity. In this frequency range, the noise power spectrum is found to exhibit a nearly universal 1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> dependence, where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> is the frequency. The exponent α remains remarkably constant over a wide range of electric field and temperature, and varies between 1.96 and 1.98 as the driving electric field is varied from 500 V/cm to 10 kV/cm at two different temperatures of 30 and 77 K. The constancy of α and its value of ~ 2 may be related to the nature of electron-phonon interactions in quantum wires.

Interference in transport through double barriers in interacting quantum wires

We investigate interference effects of the backscattering current through a double-barrier structure in an interacting quantum wire attached to noninteracting leads. Depending on the interaction strength and the location of the barriers, the backscattering current exhibits different oscillation and scaling characteristics with the applied voltage in the strong and weak interaction cases. However, in both cases, the oscillation behaviors of the backscattering current are mainly determined by the quantum mechanical interference due to the existence of the double barriers.

Bosonization of one-dimensional fermions out of equilibrium

Bosonization technique for one-dimensional fermions out of equilibrium is developed in the framework of the Keldysh action formalism. We first demonstrate how this approach is implemented for free fermions and for the problem of non-equilibrium Fermi edge singularity. We then employ the technique to study an interacting quantum wire attached to two electrodes with arbitrary energy distributions. The non-equilibrium electron Green functions, which can be measured via tunneling spectroscopy technique and carry the information about energy distribution, zero-bias anomaly, and dephasing, are expressed in terms of functional determinants of single-particle "counting" operators. The corresponding time-dependent scattering phase is found to be intrinsically related to "fractionalization" of electron-hole excitations in the tunneling process and at boundaries with leads. Results are generalized to the case of spinful particles as well to Green functions at different spatial points (relevant to the problem of dephasing in Luttinger liquid interferometers). For double-step distributions, the dephasing rates are oscillatory functions of the interaction strength.

Spin Filtering by Field-Dependent Resonant Tunneling

We consider theoretically transport in a spinful one-channel interacting quantum wire placed in an external magnetic field. For the case of two pointlike impurities embedded in the wire, under a small voltage bias the spin-polarized current occurs at special points in the parameter space, tunable by a single parameter. At sufficiently low temperatures complete spin polarization may be achieved, provided repulsive interaction between electrons is not too strong.

Effects of decoherence on the shot noise in carbon nanotubes

We study the zero frequency noise in an interacting quantum wire connected to leads, in the presence of an impurity. In the absence of quasiparticle decoherence the zero-frequency noise is that of a non-interacting wire. However, if the collective, fractionally-charged modes have a finite lifetime, we find that the zero-frequency noise may still exhibit signatures of charge fractionalization, such as a small but detectable reduction of the ratio between the noise and the backscattered current (Fano factor). We argue that this small reduction of the Fano factor is consistent with recent observations of a large reduction in the experimentally-inferred Fano factor in nanotubes (calculated assuming that the backscattered current is the difference between the ideal current in a multiple-channel non-interacting wire and the measured current.

Screening of a Luttinger liquid wire by a scanning tunneling microscope tip. I. Spectral properties

The screening effect due to a scanning tunneling microscope tip which is placed in the vicinity of an interacting quantum wire is considered. With the help of a bosonization procedure, we are able to determine nonperturbatively the Green's functions of the quantum wire in the presence of both electrostatic screening by the tip and Coulomb interactions in the wire. In our approach we justify that the working Hamiltonian of the whole system is quadratic when ${K}_{c}&gt;1/2$ and can be solved by integration over the degrees of freedom of the tip. Once the Green's functions are known, we calculate the spectral properties. We show that the spectral function, as well as the tunneling density of states, is affected by the screening and that the local density of states strongly deviates from its unscreened value when the tip gets close to the wire. Moreover, we observe that the spatial extension of the deviation of the local density of states is related to both the Coulomb interactions parameter and the screening strength.

Low-energy theory and RKKY interaction for interacting quantum wires with Rashba spin-orbit coupling

We present the effective low-energy theory for interacting 1D quantum wires subject to Rashba spin-orbit coupling. Under a one-loop renormalization group scheme including all allowed interaction processes for not too weak Rashba coupling, we show that electron-electron backscattering is an irrelevant perturbation. Therefore no gap arises and electronic transport is described by a modified Luttinger liquid theory. As an application of the theory, we discuss the RKKY interaction between two magnetic impurities. Interactions are shown to induce a slower power-law decay of the RKKY range function than the usual 1D noninteracting cos(2kF x)/|x| law. Moreover, in the noninteracting Rashba wire, the spin-orbit coupling causes a twisted (anisotropic) range function with several different spatial oscillation periods. In the interacting case, we show that one special oscillation period leads to the slowest decay, and therefore dominates the RKKY interaction for large separation.

Spin-polarized currents through interacting quantum wires with nonmagnetic leads

We study the performance of a quantum wire spin filter that is based on the Rashba spin-orbit interaction in the presence of the electron-electron interaction. The finite-length wire is attached to two semi-infinite nonmagnetic leads. Analyzing the spin polarization of the linear conductance at zero temperature, we show that spin filtering is possible by adequate tuning of the system parameters first considering noninteracting electrons. Next, the functional renormalization-group method is used to capture correlation effects induced by the Coulomb interaction. For short wires we show that the energy regime in which spin polarization is found is strongly affected by the Coulomb interaction. For long wires we find the power-law suppression of the total conductance on low-energy scales typical for inhomogeneous Luttinger liquids while the degree of spin polarization stays constant.

All-Electrical Detection of the Relative Strength of Rashba and Dresselhaus Spin-Orbit Interaction in Quantum Wires

We propose a method to determine the relative strength of Rashba and Dresselhaus spin-orbit interaction from transport measurements without the need of fitting parameters. To this end, we make use of the conductance anisotropy in narrow quantum wires with respect to the directions of an in-plane magnetic field, the quantum wire, and the crystal orientation. We support our proposal by numerical calculations of the conductance of quantum wires based on the Landauer formalism which show the applicability of the method to a wide range of parameters.

Ac conductance and nonsymmetrized noise at finite frequency in quantum wires and carbon nanotubes

We calculate the AC conductance and the finite-frequency non-symmetrized noise in interacting quantum wires and single-wall carbon nanotubes in the presence of an impurity. We observe a strong asymmetry in the frequency spectrum of the non-symmetrized excess noise, even in the presence of the metallic leads. We find that this asymmetry is proportional to the differential AC conductance of the system. The asymmetry disappears for a linear system (in the absence of interactions). In the quantum regime, for temperatures much smaller than the frequency and the applied voltage, we find that the emission noise is exactly equal to the impurity partition noise. Moreover the noise exhibits oscillations with respect to frequency, whose period is inversely proportional to the value of the interaction parameter g, and whose envelope is given by the noise in an infinite Luttinger liquid with the same value of g.

EFFECT OF STRONG CORRELATION ON THE STUDY OF RENORMALIZATION GROUP FLOW DIAGRAM FOR KONDO EFFECT IN AN INTERACTING QUANTUM WIRE

We present the study of Kondo effect in an interacting quantum wire. We mainly emphasize the effect of strong electronic correlations in the study of renormalization group flow diagram and the stability analysis of fixed points for both magnetic and nonmagnetic impurities. We observe that the behavior of the system is either in the single channel or in the two channel Kondo effect, depending on the initial values of coupling constants and strong correlations.

Spin-orbital effects in magnetized quantum wires and spin chains

We present analysis of the interacting quantum wire problem in the presence of magnetic field and spin-orbital interaction. We show that an interesting interplay of Zeeman and spin-orbit terms, facilitated by the electron-electron interaction, results in the spin-density wave (SDW) state when the magnetic-field and spin-orbit axes are orthogonal. We show that this instability is enhanced in a closely related problem of Heisenberg spin chain with asymmetric uniform Dzyaloshinskii-Moriya (DM) interaction. Magnetic field in the direction perpendicular to the DM anisotropy axis results in staggered long-range magnetic order along the orthogonal to the applied field direction. We explore consequences of the uniform DM interaction for the electron-spin-resonance (ESR) measurements, and point out that they provide way to probe right- and left-moving excitations of the spin chain separately.

Voltage profile and four-terminal resistance of an interacting quantum wire

We investigate the behavior of the four-terminal resistance ${R}_{4\text{pt}}$ in a quantum wire described by a Luttinger liquid in two relevant situations: (i) in the presence of a single impurity within the wire and (ii) under the effect of asymmetries introduced by disordered voltage probes. In the first case, interactions leave a signature in a power-law behavior of ${R}_{4\text{pt}}$ as a function of the voltage $V$ and the temperature $T$. In the second case interactions tend to mask the effect of the asymmetries. In both scenarios the occurrence of negative values of ${R}_{4\text{pt}}$ is explained in simple terms.

Nonequilibrium Functional Renormalization Group for Interacting Quantum Systems

We propose a nonequilibrium version of functional renormalization within the Keldysh formalism by introducing a complex-valued flow parameter in the Fermi or Bose functions of each reservoir. Our cutoff scheme provides a unified approach to equilibrium and nonequilibrium situations. We apply it to nonequilibrium transport through an interacting quantum wire coupled to two reservoirs and show that the nonequilibrium occupation induces new power law exponents for the conductance.

Rashba quantum wire: exact solution and ballistic transport

The effect of Rashba spin–orbit interaction in quantum wires with hard-wall boundaries isdiscussed. The exact wavefunction and eigenvalue equation are worked out, pointing outthe mixing between the spin and spatial parts. The spectral properties are also studiedwithin perturbation theory with respect to the strength of the spin–orbit interaction anddiagonalization procedure. A comparison is made with the results of a simple model,the two-band model, that takes account only of the first two sub-bands of thewire. Finally, the transport properties within the ballistic regime are analyticallycalculated for the two-band model and through a tight-binding Green function forthe entire system. Single and double interfaces separating regions with differentstrengths of spin–orbit interaction are analysed by injecting carriers into the first andthe second sub-band. It is shown that in the case of a single interface the spinpolarization in the Rashba region is different from zero, and in the case of twointerfaces the spin polarization shows oscillations due to spin-selective bound states.

Spin-Orbit-Induced Spin-Density Wave in a Quantum Wire

We present analysis of the interacting quantum wire problem in the presence of magnetic field and spin-orbit interaction. We show that an interesting interplay of Zeeman and spin-orbit terms, facilitated by the electron-electron interaction, results in the spin-density wave state when the magnetic field and spin-orbit axes are orthogonal. This strongly affects charge transport through the wire: With the spin-density wave stabilized, single-particle backscattering off a nonmagnetic impurity becomes irrelevant. The sensitivity of the effect to the direction of the magnetic field can be used for experimental verification of this proposal.