Single Mode Quantum Wire Research Articles

Conductance of fractional Luttinger liquids at finite temperatures

We study the electrical conductance in single-mode quantum wires with Rashba spin-orbit interaction subjected to externally applied magnetic fields in the regime in which the ratio of spin-orbit momentum to the Fermi momentum is close to an odd integer, so that a combined effect of multi-electron interaction and applied magnetic field leads to a partial gap in the spectrum. We study how this partial gap manifests itself in the temperature dependence of the fractional conductance of the quantum wire. We use two complementing techniques based on bosonization: refermionization of the model at a particular value of the interaction parameter and a semiclassical approach within a dilute soliton gas approximation of the functional integral. We show how the low-temperature fractional conductance can be affected by the finite length of the wire, by the properties of the contacts, and by a shift of the chemical potential, which takes the system away from the resonance condition. We also predict an internal resistivity caused by a dissipative coupling between gapped and gapless modes.

Three-particle collisions in quantum wires: Corrections to thermopower and conductance

We consider the effect of electron-electron interaction on the electron transport through a finite length single-mode quantum wire with reflectionless contacts. The two-particle scattering events cannot alter the electric current and therefore we study the effect of three-particle collisions. Within the Boltzmann equation framework, we calculate corrections to the thermopower and conductance to the leading order in the interaction and in the length of wire $L$. We check explicitly that the three-particle collision rate is identically zero in the case of several integrable interaction potentials. In the general (non-integrable) case, we find a positive contribution to the thermopower to leading order in $L$. The processes giving rise to the correction involve electron states deep in the Fermi sea. Therefore the correction follows an activation law with the characteristic energy of the order of the Fermi energy for the electrons in the wire.

Dynamical Transport Property through an Interacting QuantumWire

Using the equation of motion, we investigate theoretically thedynamical ac conductance of a clean Luttinger-liquid quantum wireadiabatically coupled to Fermi liquid electron reservoirs in thepresence of short-ranged electron-electron interactions. For aperfect single mode quantum wire, in the limit of zero-rangedinteraction we conclude that the static dc conductance ofω→0 is e2/h, which is independent of theelectron interactions. While in the dynamical case ofω≠0, the ac conductance oscillates with the amplitudee2/h and the period which depends on the interaction strengthand the driving frequency as well as the position in the wire.

Parameter regime of a resonance quantum switch

The design of a three-terminal resonance quantum switch is suggested in the form of a network consisting of a circular quantum well with four semi-infinite single-mode quantum wires attached to it. In the resonance case, when the Fermi level in the wires is close to an energy level in the well, the magnitude of the governing electric field on the well may be specified such that the switching effect is obtained; the quantum current across the switch from the incoming wire to the outgoing wires (terminals) is controlled via rotation of the orthogonal projection of the field onto the plane of the device. Using an approximate formula for the scattering matrix we define essential details of the design and the parameter regime of the switch depending on the desired working temperature, the Fermi level in the wires, and the effective mass of an electron.

Conductance of a quantum wire in the Wigner-crystal regime.

We study the effect of Coulomb interactions on the conductance of a single-mode quantum wire connecting two bulk leads. When the density of electrons in the wire is very low, they arrange in a finite-length Wigner crystal. In this regime the electron spins form an antiferromagnetic Heisenberg chain with an exponentially small coupling J. An electric current in the wire perturbs the spin chain and gives rise to a temperature-dependent contribution of the spin subsystem to the resistance. At low temperature T<<J this effect is small, and the conductance of the wire remains close to 2e2/h. At T>>J the spin effect reduces the conductance to e2/h.

Ladder approximation to spin velocities in quantum wires

The spin sector of charge-spin separated single mode quantum wires is studied, accounting for realistic microscopic electron-electron interactions. We utilize the ladder approximation (LA) to the interaction vertex and exploit thermodynamic relations to obtain spin velocities. Down to not too small carrier densities our results compare well with existing quantum Monte-Carlo (QMC) data. Analyzing second order diagrams we identify logarithmically divergent contributions as crucial which the LA includes but which are missed, for example, by the self-consistent Hartree-Fock approximation. Contrary to other approximations the LA yields a non-trivial spin conductance. Its considerably smaller computational effort compared to numerically exact methods, such as the QMC method, enables us to study overall dependences on interaction parameters. We identify the short distance part of the interaction to govern spin sector properties.

Fabry-Perot interference and spin filtering in carbon nanotubes

We study the two-terminal transport properties of a metallic single-walled carbon nanotube with good contacts to electrodes, which have recently been shown [W. Liang et al., Nature (London) 441, 665 (2001)] to conduct ballistically with weak backscattering occurring mainly at the two contacts. The measured conductance, as a function of bias and gate voltages, shows an oscillating pattern of quantum interference. We show how such patterns can be understood and calculated, taking into account Luttinger liquid effects resulting from strong Coulomb interactions in the nanotube. We treat backscattering in the contacts perturbatively and use the Keldysh formalism to treat nonequilibrium effects due to the nonzero bias voltage. Going beyond current experiments, we include the effects of possible ferromagnetic polarization of the leads to describe spin transport in carbon nanotubes. We thereby describe both incoherent spin injection and coherent resonant spin transport between the two leads. Spin currents can be produced in both ways, but only the latter allow this spin current to be controlled using an external gate. In all cases, the spin currents, charge currents, and magnetization of the nanotube exhibit components varying quasiperiodically with bias voltage, approximately as a superposition of periodic interference oscillations of spin- and charge-carrying ``quasiparticles'' in the nanotube, each with its own period. The amplitude of the higher-period signal is largest in single-mode quantum wires, and is somewhat suppressed in metallic nanotubes due to their subband degeneracy.

Ballistic transport of electrons in a long single-mode 1-D channel

The dependence of coherent transport through a very long 1-D single-mode quantum wire on the influence of a remote doped layer is determined for three cases: (i) the donors in the layer are completely ionised, unscreened and randomly (Poisson) distributed; (ii) incomplete ionisation of the donors resulting in a more regular distribution of the ions; and (iii) the ionised layer is screened by a conducting layer in close proximity. In (i) the random potential in the wire is shown to behave like a marginal fractal with fluctuations increasing without limit as the length of the wire increases, resulting in strong scattering and short mean-free-paths. By contrast, for both cases (ii) and (iii) the charge distributions are approximated well by random dipoles giving rise to an outer scale in the potential fluctuations in the wire. This greatly reduces the scattering in long wires resulting in mean-free-paths which are consistent with experiment. In all cases, in contrast with metals, the Born approximation is not generally applicable for ballistic transport along the wire since potential fluctuations can be comparable with, or even exceed, the kinetic energy of the electrons. A more appropriate estimation of the mean-free-path is to determine the distance along the wire for which the r.m.s. fluctuation in potential is equal to the electron's kinetic energy. This results in conductance behaviour near threshold that is qualitatively different from that given by the usual localisation theory appropriate to metals.

Experimental evidence for resonant tunneling in a luttinger liquid

We have measured the low-temperature conductance of a one-dimensional island embedded in a single mode quantum wire. The quantum wire is fabricated using the cleaved edge overgrowth technique and the tunneling is through a single state of the island. Our results show that while the resonance line shape fits the derivative of the Fermi function the intrinsic linewidth decreases in a power law fashion as the temperature is reduced. This behavior agrees quantitatively with Furusaki's model for resonant tunneling in a Luttinger liquid.

Precursors of a Mott insulator in modulated quantum wires

We investigate the transport of interacting electrons through single-mode quantum wires whose parameters are periodically modulated on the scale of the electronic Fermi wave length. The Umklapp and backscattering of electrons can be described in terms of non-uniform quantum sine-Gordon-like models which also incorporate the effects of electronic reservoirs (electrodes) adiabatically coupled to the wire. We concentrate on weak Umklapp scattering and analyze the precursors of the Mott transition. At half-filling the temperature dependence of the extra resistance $\Delta R = R - \pi \hbar/e^2$ of a modulated quantum wire of length $L$ changes from the interaction-dependent "bulk" power-law $\Delta R \propto T^{4K_\rho-3}$ at high temperatures, $T \gg v_\rho/L$, to the universal $\Delta R \propto T^2$ behavior at low temperatures, $T \ll v_\rho/L$. Away from half-filling the "bulk" results are qualitatively incorrect even at high temperatures $v_\rho/L \ll T \ll T^{*}$ despite the electron coherence in the wire is absent in this regime.

Effect of donor layer ordering on the formation of single mode quantum wires

We calculate the self-consistent electronic structure of GaAs-AlGaAs split gate quantum wires taking into account the ordering in the donor layer which occurs when the ionization fraction F is less than unity. Ordered ion distributions are generated via a Metropolis-like algorithm Monte Carlo simulation which finds a local minimum of the interacting Coulomb energy. We study the structure of the wire modes and show that ordering substantially reduces the standard deviation of mode energies, making single mode quantum wires possible.

Reduction of quantized conductance at low temperatures observed in 2 to 10 μm-long quantum wires

We observe a small but definite decrease in quantized conductance at low temperatures in 2 to 10 μm-long single-mode quantum wires. The temperature dependence is stronger in the longer wires. The conductance of the 2 μm-long wire is nearly constant below a critical temperature, at which the thermal length becomes longer than the wire length, while that of the 5 and 10 μm-long wires decreases fairly monotonically with decreasing temperature. We will discuss the effect of mutual Coulomb interaction that is responsible for the change in quantized conductance observed as a function of temperature and wire length.

Triple electron scattering rates in a single mode quantum wire

In quantum limit when only lower subband in a quasi-one dimensional system such as the electron gas confined in the quantum wire is occupied by electrons, pair electron collisions do not cause momentum and energy exchange between electrons. In this case more complex scattering events will determine electron momentum, energy, and phase relaxation. We calculated electron-electron scattering rates associated with triple scattering events with participation of two electrons and one charged impurity. The electron temperature relaxation time in triple collisions is estimated. We show that this time can be comparable with momentum relaxation time.

Prediction of Spin-Polarization Effects in Quantum Wire Transport

We predict a new effect for transport in quantum wires: spontaneous spin polarization. Most work on transport in mesoscopic devices has assumed a model of non interacting, spin-free electrons. We introduce spin, electron pair scattering and microscopic crystal properties into the design of mesoscopic devices. The new spin polarization effect results from the fact that in a single mode quantum wire, electron and hole bands still have two spin subbands. In general, these two spin subbands are expected to be split even in zero magnetic field. At sufficiently low temperatures the electron pair scattering rates for one spin subband ( e.g., the spin-down) can be much larger than for the other spin subband. This effect can be used for an active spin polarizer device: hot electrons in one subband ( e.g., `spin up') pass with weak pair scattering, while electrons in the opposite subband ( e.g., `spin down'), have high probability of scattering into the `spin-up' subband, resulting in spin polarization of a hot electron beam.

Electron-electron scattering in quantum wires and its possible suppression due to spin effects.

A microscopic picture of electron-electron pair scattering in single mode quantum wires is introduced which includes electron spin. A new source of excess noise for hot carriers is presented. We show that zero magnetic field spin splitting in quantum wires can lead to a dramatic spin-subband dependence of electron-electron scattering, including the possibility of strong suppression. As a consequence extremely long electron coherence lengths and new spin-related phenomena are predicted. Since electron bands in III-V semiconductor quantum wires are in general spin split in zero applied magnetic field, these new transport effects are of general importance.

Absence of low temperature saturation of electron–electron scattering in a single mode quantum wire

At helium temperatures electron–electron scattering determines the phase breaking and therefore limits the size of quantum interference devices. The electron–electron scattering times and scattering lengths are calculated numerically for ideal single mode quantum wires. The striking result of the present work is that there is no saturation of the electron–electron scattering time at low temperatures in an ideal single mode quantum wire without impurity scattering, in contrast to the two- and three-dimensional cases. Phase coherence lengths up to 10 mm are predicted for mK temperatures and up to 50 μm around 4 K. Conditions to observe such long coherence lengths are discussed.