Transport In Mesoscopic Conductors Research Articles

Light emission in delta- T -driven mesoscopic conductors

The scattering picture of electron transport in mesoscopic conductors shows that fluctuations of the current reveal additional information on the scattering mechanism not available through the conductance alone. The electronic fluctuations are coupled to the electromagnetic field and a junction at finite bias or temperature will emit radiation. The nonsymmetrized current-current correlators characterize the emission and absorption spectrum. Recent interest is focused on the so-called delta-$T$ noise, which is the nonequilibrium noise caused by a temperature difference between the terminals. Here, we generalize the notion of delta-$T$ noise to the nonsymmetrized current-current correlator at finite frequencies. We investigate the spectral density for energy-independent scattering and for a resonant level as an example of energy-dependent scattering. We find that a temperature difference $\mathrm{\ensuremath{\Delta}}T$ leads to a partial reduction of the noise for certain frequency ranges. This is a consequence of temperature broadening in combination with a frequency shift of the involved Fermi distributions. In the case of energy-independent scattering, the lowest order is a quadratic $\ensuremath{\propto}{(\mathrm{\ensuremath{\Delta}}T)}^{2}$ correction of the thermallike noise spectrum. For the resonance, an additional contribution to the delta-$T$ noise spectrum arises that is $\ensuremath{\propto}\mathrm{\ensuremath{\Delta}}T$ to the lowest order.

Electron Waiting Times in a Strongly Interacting Quantum Dot: Interaction Effects and Higher-Order Tunneling Processes.

Distributions of electron waiting times have been measured in several recent experiments and have been shown to provide complementary information compared with what can be learned from the electric current fluctuations. Existing theories, however, are restricted to either weakly coupled nanostructures or phase-coherent transport in mesoscopic conductors. Here, we consider an interacting quantum dot and develop a real-time diagrammatic theory of waiting time distributions that can treat the interesting regime, in which both interaction effects and higher-order tunneling processes are important. Specifically, we find that our quantum-mechanical theory captures higher-order tunneling processes at low temperatures, which are not included in a classical description, and which dramatically affect the waiting times by allowing fast tunneling processes inside the Coulomb blockade region. Our work paves the way for systematic investigations of temporal fluctuations in interacting quantum systems, for example close to a Kondo resonance or in a Luttinger liquid.

Detector's quantum backaction effects on a mesoscopic conductor and fluctuation‐dissipation relation

When measuring quantum mechanical properties of charge transport in mesoscopic conductors, backaction effects occur. We consider a measurement setup with an elementary quantum circuit, composed of an inductance and a capacitor, as detector of the current flowing in a nearby quantum point contact. A quantum Langevin equation for the detector variable including backaction effects is derived. Differences with the quantum Langevin equation obtained in linear response are pointed out. In this last case, a relation between fluctuations and dissipation is obtained, provided that an effective temperature of the quantum point contact is defined.

Nonlinear heat transport in mesoscopic conductors: Rectification, Peltier effect, and Wiedemann-Franz law

We investigate nonlinear heat properties in mesoscopic conductors using a scattering theory of transport. Our approach is based on a leading-order expansion in both the electrical and thermal driving forces. Beyond linear response, the transport coefficients are functions of the nonequilibrium screening potential that builds up in the system due to interactions. Within a mean-field approximation, we self-consistently calculate the heat rectification properties of a quantum dot attached to two terminals. We discuss nonlinear contributions to the Peltier effect and find departures from the Wiedemann-Franz law in the nonlinear regime of transport.

Electron Waiting Times in Mesoscopic Conductors

Electron transport in mesoscopic conductors has traditionally involved investigations of the mean current and the fluctuations of the current. A complementary view on charge transport is provided by the distribution of waiting times between charge carriers, but a proper theoretical framework for coherent electronic systems has so far been lacking. Here we develop a quantum theory of electron waiting times in mesoscopic conductors expressed by a compact determinant formula. We illustrate our methodology by calculating the waiting time distribution for a quantum point contact and find a crossover from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off. Even when the low-frequency transport is noiseless, the electrons are not equally spaced in time due to their inherent wave nature. We discuss the implications for renewal theory in mesoscopic systems and point out several analogies with level spacing statistics and random matrix theory.

Models of mesoscopic time-resolved current detection

Quantum transport in mesoscopic conductors is essentially governed by the laws of quantum mechanics. One of the major open questions of quantum mechanics is what happens if non-commuting observables are measured simultaneously. Since current operators at different times do not commute, the high-frequency correlation functions of the current are realization of this fundamental quantum question. We formulate this problem in the context of measurements of finite-frequency current cumulants in a general quantum point contact, which are the subject to ongoing experimental effort. To this end, we present two models of detectors that correspond to a weak time-resolved measurement of the electronic current in a mesoscopic junction. In both cases, the backaction of the detector leads to observable corrections to the current correlations functions involving the so-called noise susceptibilities. As a result, we propose a reinterpretation of environmental corrections to the finite-frequency cumulants as inevitable effect resulting from basic quantum mechanical principles. Finally we make concrete predictions for the temperature-, voltage-, and frequency-dependence of the third cumulant, which could be verified directly using current experimental techniques.

SPIN RELATED TRANSPORT IN RASHBA 2DEG SYSTEMS

Transport in mesoscopic conductors is determined not only by orbital motion of carriers but also by quantum interference effect. However, it is well known that the quantum interference such as weak localization is much modified in the presence of spin-orbit interaction (SOI), leading to weak anti-localization. We discuss the origin of the Rashba SOI and spin related mesoscopic transport in InGaAs based two dimensional electron gases (2DEG) affected by the Rashba SOI. It is experimentally shown that the strength of the Rashba SOI in InGaAs 2DEG systems can be controlled by the gate voltage.1 The spin dynamics in solid systems is commonly determined by the competition between Zeeman effect and SOI. The spin relaxation time and dephasing time are studied from weak anti-localization analysis as a function of the relative strength of the Zeeman energy (EZ) and the Rashba SOI energy (E SOI ). The (EZ) was introduced by applying magnetic field parallel to the 2DEG plane. This in-pane magnetic field does not affect the orbital motion of electrons. The spin relaxation time increases with the Zeeman energy. The dephasing time associated with the spin-induced time reversal symmetry (TRS) breaking saturates when EZ becomes comparable to E SOI . Moreover, we show that the spin-induced TRS breaking mechanism is a universal function of the ratio EZ/E SOI within the experimental accuracy.2 Note from Publisher: This article contains the abstract only.

Formalism of nonlinear transport in mesoscopic conductors

We study nonlinear transport in mesoscopic conductors using the scattering approach. Extended multiterminal Landauer-B\"uttiker formulas are presented in conditions such as at zero/finite temperatures and in the weakly/strongly nonlinear regimes and are shown to be gauge invariant. As an example, we model the ballistic rectification effect recently observed in a symmetry-breaking microjunction. We are then able to provide an analytical description of the rectification effect, which is in remarkably good agreement with the experimental observations.

Applying voltage sources to a Luttinger liquid with arbitrary transmission

The Landauer approach to transport in mesoscopic conductors has been generalized to allow for strong electronic correlations in a single-channel quantum wire. We describe in detail how to account for external voltage sources in adiabatic contact with a quantum wire containing a backscatterer of arbitrary strength. Assuming that the quantum wire is in the Luttinger liquid state, voltage sources lead to radiative boundary conditions applied to the displacement field employed in the bosonization scheme. We present the exact solution of the transport problem for arbitrary backscattering strength at the special Coulomb interaction parameter g=1/2.

Mesoscopic superconductor-semiconductor heterostructures

A summary is given of recent results on carrier transport in mesoscopic conductors with superconducting electrodes. Three-dimensional transport in the diffusive limit is studied with crystalline silicon membranes sandwiched between two niobium electrodes or between one electrode superconducting and one normal. At low temperatures, inelastic scattering is negligible in the intermediate silicon layer. At finite voltages the distribution of electrons over the energies in the silicon is found to be strongly nonthermal, with details depending on the interplay between Andreev scattering and elastic scattering at the interfaces. At small voltages, well below the gap-voltage, transport is phase-coherent. A supercurrent is found if both electrodes are superconducting, provided the membrane is thin enough. If only one electrode is superconducting or for thick membranes an enhanced conductance is observed, which decreases with increasing voltage and magnetic field. Two-dimensional transport and the ballistic regime are being studied by using InAs- and GaAs-based heterostructures. Various interesting theoretical predictions have been made and some novel phenomena have been discovered experimentally. Interesting new phenomena have also been found in mesoscopic normal metals with superconducting electrodes.

Electron transport in mesoscopic conductors with superconducting contacts

As the dimensions of a normal (N) metallic conductor are reduced, the resistance of the conductor begins to increase when the contacts go into the superconducting (S) state. Likewise, the amplitude of the Aharonov-Bohm effect is strongly enhanced in mesoscopic wires and rings with superconducting contacts. We propose an explanation based on a quantization of electron energies resulting from Andreev reflections at N/S interfaces.