No Arabic abstract
In disordered metals, electron-electron interactions are the origin of a small correction to the conductivity, the Altshuler-Aronov correction. Here we investigate the Altshuler-Aronov correction of a conductor in which the electron motion is ballistic and chaotic. We consider the case of a double quantum dot, which is the simplest example of a ballistic conductor in which the Altshuler-Aronov correction is nonzero. The fact that the electron motion is ballistic leads to an exponential suppression of the correction if the Ehrenfest time is larger than the mean dwell time or the inverse temperature.
On a high mobility two-dimensional hole gas (2DHG) in a GaAs/GaAlAs heterostructure we study the interaction correction to the Drude conductivity in the ballistic regime, $k_BTtau /hbar $ $>1$. It is shown that the metallic behaviour of the resistivity ($drho /dT>0$) of the low-density 2DHG is caused by hole-hole interaction effect in this regime. We find that the temperature dependence of the conductivity and the parallel-field magnetoresistance are in agreement with this description, and determine the Fermi-liquid interaction constant $F_0^sigma $ which controls the sign of $drho /dT$.
We introduce a non-linear frequency dependent D+1 terminal conductance that characterizes a D dimensional Fermi gas, generalizing the Landauer conductance in D=1. For a ballistic conductor we show that this conductance is quantized and probes the Euler characteristic of the Fermi sea. We critically address the roles of electrical contacts and of Fermi liquid interactions, and we propose experiments on 2D Dirac materials such as graphene using a triple point contact geometry.
Electric-field effect control of two-dimensional electron gases (2-DEG) has enabled the exploration of nanoscale electron quantum transport in semiconductors. Beyond these classical materials, transition metal-oxide-based structures have d-electronic states favoring the emergence of novel quantum orders absent in conventional semiconductors. In this context, the LaAlO3/SrTiO3 interface that combines gate-tunable superconductivity and sizeable spin-orbit coupling is emerging as a promising platform to realize topological superconductivity. However, the fabrication of nanodevices in which the electronic properties of this oxide interface can be controlled at the nanoscale by field-effect remains a scientific and technological challenge. Here, we demonstrate the quantization of conductance in a ballistic quantum point contact (QPC), formed by electrostatic confinement of the LaAlO3/SrTiO3 2-DEG with a split-gate. Through finite source-drain voltage, we perform a comprehensive spectroscopic investigation of the 3d energy levels inside the QPC, which can be regarded as a spectrometer able to probe Majorana states in an oxide 2-DEG.
We consider a one-channel coherent conductor with a good transmission embedded into an ohmic environment whose impedance is equal to the quantum of resistance R_q=h/e^2 below the RC frequency. This choice is motivated by the mapping of this problem to a Tomonaga-Luttinger liquid with one impurity whose interaction parameter corresponds to the specific value K=1/2, allowing for a refermionization procedure. The new fermions have an energy-dependent transmission amplitude which incorporates the strong correlation effects and yields the exact dc current and zero-frequency noise through expressions similar to those of the scattering approach. We recall and discuss these results for our present purpose. Then we compute, for the first time, the finite-frequency differential conductance and the finite-frequency non-symmetrized noise. Contrary to intuitive expectation, both cannot be expressed within the scattering approach for the new fermions, even though they are still determined by the transmission amplitude. Even more, the finite-frequency conductance obeys an exact relation in terms of the dc current which is similar to that derived perturbatively with respect to weak tunneling within the Tien-Gordon theory, and extended recently to arbitrary strongly interacting systems coupled eventually to an environment or/and with a fractional charge. We also show that the emission excess noise vanishes exactly above eV, even though the underlying Tomonaga-Luttinger liquid model corresponds to a many-body correlated system. Our results apply for all ranges of temperature, voltages and frequencies below the RC frequency, and they allow to explore fully the quantum regime.
We demonstrate that branching of the electron flow in semiconductor nanostructures can strongly affect macroscopic transport quantities and can significantly change their dependence on external parameters compared to the ideal ballistic case even when the system size is much smaller than the mean free path. In a corner-shaped ballistic device based on a GaAs/AlGaAs two-dimensional electron gas we observe a splitting of the commensurability peaks in the magnetoresistance curve. We show that a model which includes a random disorder potential of the two-dimensional electron gas can account for the random splitting of the peaks that result from the collimation of the electron beam. The shape of the splitting depends on the particular realization of the disorder potential. At the same time magnetic focusing peaks are largely unaffected by the disorder potential.