Transport in quantum wires

Physical Review Letters, 2001

We model one-dimensional transport through each open channel of a quantum wire by a Luttinger liquid with three different interaction parameters for the leads, the contact regions and the wire, and with two barriers at the contacts. We show that this model explains several features of recent experiments, such as the flat conductance plateaux observed even at finite temperatures and for different lengths, and universal conductance corrections in different channels. We discuss the possibility of seeing resonance-like structures of a fully open channel at very low temperatures.

Physical Review B, 2007

We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. Two alternative approaches to the problem are developed, both combining fermionic and bosonic treatment of the underlying physics. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit. Our approach provides a framework for a systematic study of mesoscopic effects in strongly correlated electron systems.

European Physical Journal B, 2005

We discuss the effects of a strong magnetic field in quantum wires. We show how the presence of a magnetic field modifies the role played by electron electron interaction producing a strong reduction of the backward scattering corresponding to the Coulomb repulsion. We discuss the consequences of this and other effects of magnetic field on the Tomonaga-Luttinger liquids and especially on their power-law behaviour in all correlation functions. The focal point is the rescaling of all the repulsive terms of the interaction between electrons with opposite momenta, due to the edge localization of the electrons and to the reduction of the length scale. Because of the same two reasons there are some interesting effects of the magnetic field concerning the backward scattering due to the presence of one impurity and the corresponding conductance. As an effect of the magnetic field we find also a spin polarization induced by a combination of electrostatic forces and the Pauli principle, quite similar to the one observed in large Quntum Dots.

Entropy

Europhysics Letters (EPL), 2001

We studied the conductance of quantum wires (QWRs) with rigid confinement potential in different configurations, including single QWRs, QWRs with restricted access to the 2D reservoirs, and serially connected QWRs. We explain the deviations of quantized conductance values from 2e 2 /h as coming from the lack of 1D/2D coupling. The role of intersubband scattering in establishing contact between the QWR and 2D reservoirs is demonstrated. The achievement of conductance step values close to 2e 2 /h in these wires depends on establishing strong intersubband scattering without significant backscattering. Introduction. -Electron transport in one-dimensional (1D) systems has drawn considerable attention over the last decade since it exhibits new physics related both to the quantum confinement and to the modified electron interaction resulting from the reduced dimensionality. In a non-interacting 1D electron system, the conductance is quantized in units of G 0 ≡ 2e 2 /h, corresponding to perfect electron transmission via 1D channels [1-3]. Such quantized conductance has been observed in quantum point contact (QPC) devices in which extremely narrow conducting channels are defined in a high-mobility 2D electron gas (2DEG) using a negatively biased split gate . In these structures, there is an adiabatic transition from the few, well-separated 1D channels between the gates, through a multitude of closely spaced 1D states, to the continuum of 2D electron states away from the constriction, which act as an effective reservoir. However, all attempts to observe the same conductance values in wires with "rigid" confining potential (CP), such as etched-and-regrown [6], cleavededge-overgrown [7] and V-groove [8] quantum wires (QWRs) failed, showing conductance step values that are lower than G 0 with non-universal deviations . The major difference between QWRs and QPCs is the coupling between the 1D and 2D states, the latter ones being so far the only means to contact experimentally 1D states. In an ideal QWR with rigid CP, and in the absence of scattering, the 1D states are very weakly coupled to the 2D states and through them to the external contacts. Therefore, a scattering-free QWR system, which shows the universal values of conductance steps n • G 0 , would be impossible to contact through 2D states. In such wires, one could thus only attempt to approach the ideal conductance values by searching for a compromise between strong 1D/2D coupling and small backscattering. The momentum transfer required by a 1D/2D scattering is on the order of k F , since the entire

2000

We describe the transport properties of a 5 µm long one-dimensional (1D) quantum wire. Reduction of conductance plateaux due to the introduction of weakly disorder scattering are observed. In an in-plane magnetic field, we observe spin-splitting of the reduced conductance steps. Our experimental results provide evidence that deviation from conductance quantisation is very small for electrons with spin parallel and is about 1/3 for electrons with spin anti-parallel. Moreover, in a high in-plane magnetic field, a spin-polarised 1D channel shows a plateau-like structure close to 0.3 × e 2 /h which strengthens with increasing temperatures. It is suggested that these results arise from the combination of disorder and the electron-electron interactions in the 1D electron gas.

Physica B: Condensed Matter, 2009

We investigate an effective one-dimensional conducting channel considering both the contact umklapp and the Coulomb electron-electron interaction. We show that, at low electronic density, the proximity to the Wigner crystal reproduces the anomaly in conductance at 0:7G 0 . The crucial ingredient of our theory is the fact that the gate voltage acts as a bias controlling the intensity of the umklapp term. At large gate voltages, the umklapp vanishes and we obtain a conducting quantum wire with a perfect conductance. At low gate voltages, the Wigner crystal is pinned by the umklapp term, giving rise to an insulating behavior with vanishing conductance. This crossover pattern has a transition point which can be identified with the anomalous conductance around 0:7G 0 . This picture is obtained within the framework of a renormalization group calculation. The conductance static regime is achieved by taking first the limit of finite length and then the limit of zero frequency.

Physical Review B, 1997

Recent experiments have revealed that the temperature dependence of the conductance of quasiballistic quantum wires bears clear features of the Luttinger-liquid state. In this paper, the conductance of an N-channel quantum wire is calculated within the model of N coupled Luttinger liquids and under the assumption of weak disorder. It is shown that as the number of channels increases, a crossover from the Luttinger-liquid to the Fermi-liquid behavior occurs. This crossover manifests itself in the 1/N decrease of the scaling exponent of the temperature dependence. An exact expression for the scaling exponent for the case of N coupled Luttinger chains is obtained, and the large N limit is studied for the case of a quantum wire. The case of N = 2 for electrons with spin is analyzed in detail, and a qualitative agreement with the experiment is achieved.

The European Physical Journal B, 2012

We investigate magneto-transport properties of a θ shaped three-arm mesoscopic ring where the upper and lower sub-rings are threaded by Aharonov-Bohm fluxes φ1 and φ2, respectively, within a non-interacting electron picture. A discrete lattice model is used to describe the quantum network in which two outer arms are subjected to binary alloy lattices while the middle arm contains identical atomic sites. It is observed that the presence of the middle arm provides localized states within the band of extended regions and lead to the possibility of switching action from a high conducting state to a low conducting one and vice versa. This behavior is justified by studying persistent current in the network. Both the total current and individual currents in three separate branches are computed by using second-quantized formalism and our idea can be utilized to study magnetic response in any complicated quantum network. The nature of localized eigenstates are also investigated from probability amplitudes at different sites of the quantum device.

We observe a small but definite decrease in quantized conductance at low temperatures in 2 to 10 pm-long single-mode quantum wires. The temperature dependence is stronger in the longer wires. The conductance of the 2 urn-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 pm-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.