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arXiv:1105.0136

Noise spectrum of quantum transport through quantum dots: a combined effect of non-Markovian and cotunneling processes

Jinshuang Jin, Wei-Min Zhang, Xin-Qi Li, YiJing Yan

Published May 1, 2011• 1 citation
arXivHTMLPDF

Abstract

Based on our recently developed quantum transport theory in term of an exact master equation, the corresponding particle-number resolved ($n$-resolved) master equation and the related shot noise spectrum formalism covering the full frequency range are constructed. We demonstrate that the noise spectra of transport current through single quantum dot and double quantum dots show characteristic steps and/or peak-dips in different tunneling frequency regimes through tuning the applied bias voltage and/or gate voltage at low temperatures. The peak-dips crossing the tunneling resonant frequencies is a combination effect of non-Markovian and cotunneling processes. These voltage-dependent tunneling resonance characteristics can be utilized to effectively modulate the internal Rabi resonance signature in the noise spectrum.

DOI
10.48550/arxiv.1105.0136

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Based on our recently developed quantum transport theory in term of an exact master equation, the corresponding particle-number resolved (nnn-resolved) master equation and the related shot noise spectrum formalism covering the full frequency range are constructed. We demonstrate that the noise spectra of transport current through single quantum dot and double quantum dots show characteristic steps and/or peak-dips in different tunneling frequency regimes through tuning the applied bias voltage and/or gate voltage at low temperatures. The peak-dips crossing the tunneling resonant frequencies is a combination effect of non-Markovian and cotunneling processes. These voltage-dependent tunneling resonance characteristics can be utilized to effectively modulate the internal Rabi resonance signature in the noise spectrum.
In this thesis, I study quantum transport of electron (e.g., current and noise) in quantum dots exploring microscopic processes responsible for spin-relaxation in double quantum dots in Pauli spin blockade regime. This is a regime where current is blocked due to the spin configuration of electrons in the dot. The Pauli \nspin blockade provides a means for preparation, manipulation and readout in spin qubits. Hence, understanding the underlying mechanism which lifts this blockade is extremely important. \n \nFirst, I have developed a theory of spin-flip cotunneling (higher order tunneling) processes in double quantum dots in the Pauli spin blockade regime. Utilizing this \ntheory, I have calculated the full analytical dependence of the stationary current on applied magnetic fields, gate voltages, and an inter-dot tunnel coupling in Pauli \nspin blockade. This work is important for understanding the nature of leakage, especially in systems where other spin-flip mechanisms (due, e.g., hyperfine coupling \nto nuclear spins or spin-orbit coupling) are weak, including silicon and carbon nanotube or graphene quantum dots. This theory explains recent experiments on \ncarbon nanotubes and silicon double quantum dot. \n \nIn addition, I propose a new scheme based on the current noise to probe spin relaxation mechanisms in double quantum dot in the Pauli spin blockade regime, where spin-selection rule applies. As a result, I provide a simple closed-form expression which can be used to fit experimental data to extract multiple spin-relaxation \nrates, even at very low energy splitting. This method allows for the characterization of different aspects of decay process in these systems.
We construct a real time current-conserving functional renormalization group (RG) scheme on the Keldysh contour to study frequency-dependent transport and noise through a quantum dot in the local moment regime. We find that the current vertex develops a nontrivial nonlocal structure in time that is governed by a new set of RG equations. Solving these RG equations, we compute the complete frequency and temperature dependence of the noise spectrum. For voltages that are large compared to the Kondo temperature (i.e., $\mathit{eV}\ensuremath{\gg}{k}_{B}{T}_{K}$), two sharp antiresonances are found in the noise spectrum at frequencies $\ensuremath{\hbar}\ensuremath{\omega}=\ifmmode\pm\else\textpm\fi{}eV$ and, correspondingly, two Kondo-assisted peaks appear in the ac conductance through the dot.
We calculate the finite-frequency current noise of a nonequilibrium resonance-level quantum dot close to a dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a de-localized phase for weak dissipation and a localized phase for strong dissipation. The resonance-level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic boson bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. To compute the finite-frequency noise, we combine two recently developed Functional Renormalization Group (FRG) approaches in Refs.[17,22] and in Ref.[23]. The nonequilibrium current noise at zero-temperature and finite frequencies shows a singular dip in the de-localized phase for the magnitude of frequencies equal to the bias voltage; while the dip is smeared out as the system moves to the localized phase. The corresponding peak-to-dip crossover is found in the AC conductance for the magnitude of frequencies equal to the bias voltage. The relevance and applications of our results for the experiments and for tunnelings between Fractional Quantum Hall Edge (FQHE) states and chiral Luttinger liquids are discussed.
A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime.
We exploit the pumped spin-current and current noise spectra under equilibrium conditions in a single quantum dot connected to two normal leads as an electrical scheme for detection of the electron spin resonance (ESR) and decoherence. We propose spin-resolved quantum rate equations with correlation functions in Laplace space for the analytical derivation of the zero-frequency auto- and cross-shot noise spectra of charge and spin current. Our results show that in the strong Coulomb blockade regime, ESR-induced spin flip generates a finite spin current and quantum partition noises in the absence of net charge transport. Moreover, spin shot noise is closely related to the magnetic Rabi frequency and decoherence and would be a sensitive tool to measure them.