Frequency-dependent Shot Noise Research Articles

Frequency-dependent transport properties in disordered systems: A generalized coherent potential approximation approach

To predict transport properties of disordered systems, especially ac transport properties, one has to calculate the disorder average of the correlation of the multiple Green's function at different energies. To avoid brute force calculation, diagrammatic perturbation expansion must be used along with the coherent potential approximation (CPA). In this paper, we develop a theoretical formalism based on the nonequilibrium Green's function that maps the average of the correlation of the multiple Green's function into an average over a single generalized Green's function. After the mapping, this formalism is structurally very similar to the CPA and completely eliminates the need to perform diagrammatic expansion. As a demonstration of our theory, the dynamic conductance, frequency-dependent shot noise under dc bias, and frequency-dependent noise spectrum under ac bias in the presence of Anderson disorder are calculated by directly taking the disorder average of the generating function of full counting statistics (FCS) within the CPA. Our numerical results on dynamic conductance, frequency-dependent shot noise under dc bias, and frequency-dependent noise spectrum under ac bias show remarkable agreement with that obtained by the brute force calculation. The phase diagram in the frequency versus disorder strength plane has been efficiently calculated using the generalized FCS-CPA method.

Noise in the Helical Edge Channel Anisotropically Coupled to a Local Spin

We calculate the frequency-dependent shot noise in the edge states of a two-dimensional topological insulator coupled to a magnetic impurity with spin $S=1/2$ of arbitrary anisotropy. If the anisotropy is absent, the noise is purely thermal at low frequencies, but tends to the Poissonian noise of the full current $I$ at high frequencies. If the interaction only flips the impurity spin but conserves those of electrons, the noise at high voltages $eV\gg T$ is frequency-independent. Both the noise and the backscattering current $I_{bs}$ saturate at voltage-independent values. Finally, if the Hamiltonian contains all types of non-spin-conserving scattering, the noise at high voltages becomes frequency-dependent again. At low frequencies, its ratio to $2eI_{bs}$ is larger than 1 and may reach 2 in the limit $I_{bs}\to 0$. At high frequencies it tends to 1.

Time-dependent shot noise in multi-level quantum dot-based single-electron devices

By means of three-dimensional self-consistent simulation, we investigate the time- and frequency-dependent shot noise in multi-level quantum dot (QD)-based double-tunnel junction by analyzing auto-correlation functions and distribution of waiting times between consecutive tunnel events through a given barrier. We derive analytic expressions for correlation and waiting time distributions (WTDs) in the case of a maximum of two electrons in the QD. We separate the contributions of the different evolution paths of the number of electrons in the dot between two consecutive current pulses, called ‘basic paths’. The close relation revealed between probabilities, WTDs and correlation functions associated to basic paths allows a good understanding of the specific dynamics in spectral densities. The analytic results show a perfect agreement with those obtained from numerical Monte-Carlo simulation.

Fano–Kondo shot noise in a quantum dot embedded interferometer irradiated with microwave fields

Abstract The shot noise of a quantum dot embedded Aharonov–Bohm (AB) interferometer under the perturbation of microwave fields is investigated by employing equation of motion method. The frequency-dependent shot noise formula is derived, and the photon-assisted Fano–Kondo resonance, the suppression of Kondo peak are presented with increasing the direct tunneling strength. The interference and correlation of electrons induce the asymmetric resonant peak–valley behavior of shot noise. The enhancement and suppression of shot noise are resulting from the competition of incoherent correlation and destructive interference effects, and super-Poissonian and sub-Poissonian noise can be adjusted by the applied photon irradiation, gate bias, and direct tunneling strength. The periodic oscillation versus AB phase with period 2 π appears to show plateaus and flat valleys.

Quantum bistability and spin current shot noise of a single quantum dot coupled to an optical microcavity

Here we explore the quantum-mechanical limit of bistability that appears in the spin-dependent transport through a single quantum dot coupled to an optical microcavity. The spin current is generated by electron tunneling between a single doped reservoir and the dot combined with intradot spin-flip transitions induced by a quantized cavity mode. Earlier research has shown that in the classical limit where a large number of such dots interacts with the cavity so that quantum effects were ignorable, the average spin current exhibits bistability as a function of the laser that drives the cavity. We show that in the limit of a single quantum dot this bistability continues to be present in the intracavity photon statistics. Signatures of the bistable photon statistics manifest themselves in the frequency-dependent shot noise of the spin current despite the fact that the quantum-mechanical average spin current no longer exhibits bistability. Besides having significance for future quantum-dot-based optoelectronic devices, our results shed light on the relation between bistability, which is traditionally viewed as a classical effect, and quantum mechanics.

Effects of non-Abelian statistics on two-terminal shot noise in a quantum Hall liquid in the Pfaffian state

We study non-equilibrium noise in the tunnelling current between the edges of a quantum Hall liquid in the Pfaffian state, which is a strong candidate for the plateau at $\nu=5/2$. To first non-vanishing order in perturbation theory (in the tunneling amplitude) we find that one can extract the value of the fractional charge of the tunnelling quasiparticles. We note however that no direct information about non-abelian statistics can be retrieved at this level. If we go to higher-order in the perturbative calculation of the non-equilibrium shot noise, we find effects due to non-Abelian statistics. They are subtle, but eventually may have an experimental signature on the frequency dependent shot noise. We suggest how multi-terminal noise measurements might yield a more dramatic signature of non-Abelian statistics and develop some of the relevant formalism.

Electron transport through interacting quantum dots in the metallic regime

We present a detailed theoretical investigation of the effect of Coulomb interactions on electron transport through quantum dots and double-barrier structures connected to a voltage source via an arbitrary linear impedance. Combining real time path integral techniques with the scattering matrix approach, we derive the effective action and evaluate the current-voltage characteristics of quantum dots at sufficiently large conductances. Our analysis reveals a rich variety of different regimes, which we specify in detail for the case of chaotic quantum dots. At sufficiently low energies the interaction correction to the current depends logarithmically on temperature and voltage. We identify two different logarithmic regimes with the crossover between them occurring at energies of order of the inverse dwell time of electrons in the dot. We also analyze the frequency-dependent shot noise in chaotic quantum dots and elucidate its direct relation to interaction effects in mesoscopic electron transport.

Spin detection in quantum dots by electric currents

We develop a theoretical description of transport through quantum dots connected to reservoirs via spin-polarized ballistic contacts. Rate equations account for spin accumulation inside the dot, electron-electron interactions, and stochastic fluctuations. It is shown that both the ac response (admittance) and the frequency-dependent shot noise are governed by spin-flip scattering, which can be used to detect spin polarization and spin-flip processes in the dot.

Nonthermal mixing mechanism in a diffusion-cooled hot-electron detector

We present an analysis of a diffusion-cooled hot-electron detector fabricated from clean superconducting material with low transition temperature. The distinctive feature of a clean material, i.e., material with large electron mean free path, is a relatively weak inelastic electron scattering that is not sufficient for the establishment of an elevated thermodynamic electron temperature when the detector is subjected to irradiation. We propose an athermal model of a diffusion-cooled detector that relies on suppression of the superconducting energy gap by the actual dynamic distribution of excess quasiparticles. The resistive state of the device is caused by the electric field penetrating into the superconducting bridge from metal contacts. The dependence of the penetration length on the energy gap delivers the detection mechanism. The sources of the electric noise are equilibrium fluctuations of the number of thermal quasiparticles and frequency dependent shot noise. Using material parameters typical for A1, we evaluate performance of the device in the heterodyne regime at terahertz frequencies. Estimates show that the mixer may have a noise temperature of a few quantum limits and a bandwidth of a few tens of GHz, while the required local oscillator power is in the μW range due to ineffective suppression of the energy gap by quasiparticles with high energies.

Frequency-dependent shot noise as a probe of electron-electron interaction in mesoscopic diffusive contacts

The frequency-dependent shot noise in long and narrow mesoscopic diffusive contacts is numerically calculated. The case of arbitrarily strong electron-electron scattering and zero temperature of electrodes is considered. For all voltages, the noise increases with frequency and tends to finite values. These limiting values are larger than the Poissonian noise and increase with voltage nearly as ${V}^{4/3}.$ This allows one to experimentally determine the parameters of electron-electron interaction.