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Register a new userHierarchical quantum master equation approach to current fluctuations in nonequilibrium charge transport through nanosystems
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Christian Schinabeck
Publication date
2019
fields
Physics
and research's language is
English
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We present a hierarchical quantum master equation (HQME) approach, which allows the numerically exact evaluation of higher-order current cumulants in the framework of full counting statistics for nonequilibrium charge transport in nanosystems. The novel methodology is exemplarily applied to a model of vibrationally coupled electron transport in a molecular nanojunction. We investigate the influence of cotunneling on avalanche-like transport, in particular in the nonresonant transport regime, where we find that inelastic cotunneling acts as trigger process for resonant avalanches. In this regime, we also demonstrate that the correction to the elastic noise upon opening of the inelastic transport channel is strongly affected by the nonequilibrium excitation of the vibration as well as the polaron shift.
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Within the hierarchical quantum master equation (HQME) framework, an approach is presented, which allows a numerically exact description of nonequilibrium charge transport in nanosystems with strong electronic-vibrational coupling. The method is applied to a generic model of vibrationally coupled transport considering a broad spectrum of parameters ranging from the nonadiabatic to the adiabatic regime and including both resonant and off-resonant transport. We show that nonequilibrium effects are important in all these regimes. In particular in the off-resonant transport regime, the inelastic co-tunneling signal is analyzed for a vibrational mode in full nonequilibrium, revealing a complex interplay of different transport processes and deviations from the commonly used $G_0/2$-thumb-rule. In addition, the HQME-approach is used to benchmark approximate master equation and nonequilibrium Greens function methods.
We present a novel hierarchical quantum master equation (HQME) approach which provides a numerically exact description of nonequilibrium charge transport in nanosystems with electronic-vibrational coupling. In contrast to previous work [Phys. Rev. B $bf{94}$, 201407 (2016)], the active vibrational degrees of freedom are treated in the reservoir subspace and are integrated out. This facilitates applications to systems with very high excitation levels, for example due to current-induced heating, while properties of the vibrational degrees of freedom, such as the excitation level and other moments of the vibrational distribution function, are still accessible. The method is applied to a generic model of a nanosystem, which comprises a single electronic level that is coupled to fermionic leads and a vibrational degree of freedom. Converged results are obtained in a broad spectrum of parameters, ranging from the nonadiabatic to the adiabatic transport regime. We specifically investigate the phenomenon of vibrational instability, that is, the increase of current-induced vibrational excitation for decreasing electronic-vibrational coupling. The novel HQME approach allows us to analyze the influence of level broadening due to both molecule-lead coupling and thermal effects. Results obtained for the first two moments suggest that the vibrational excitation is always described by a geometric distribution in the weak electronic-vibrational coupling limit.
We study shot noise in tunneling current through a double quantum dot connected to two electric leads. We derive two master equations in the occupation-state basis and the eigenstate basis to describe the electron dynamics. The approach based on the occupation-state basis, despite widely used in many previous studies, is valid only when the interdot coupling strength is much smaller than the energy difference between the two dots. In contrast, the calculations using the eigenstate basis are valid for an arbitrary interdot coupling. We show that the master equation in the occupation-state basis includes only the low-order terms with respect to the interdot coupling compared with the more accurate master equation in the eigenstate basis. Using realistic model parameters, we demonstrate that the predicted currents and shot-noise properties from the two approaches are significantly different when the interdot coupling is not small. Furthermore, properties of the shot noise predicted using the eigenstate basis successfully reproduce qualitative features found in a recent experiment.
In this paper, the exact transient quantum transport of non-interacting nanostructures is investigated in the presence of initial system-lead correlations and initial lead-lead correlations for a device system coupled to general electronic leads. The exact master equation incorporating with initial correlations is derived through the extended quantum Langevin equation. The effects of the initial correlations are manifested through the time-dependent fluctuations contained explicitly in the exact master equation. The transient transport current incorporating with initial correlations is obtained from the exact master equation. The resulting transient transport current can be expressed in terms of the single-particle propagating and correlation Green functions of the device system. We show that the initial correlations can affect quantum transport not only in the transient regime, but also in the steady-state limit when system-lead couplings are strong enough so that electron localized bound states occur in the device system.
We report on charge transport and current fluctuations in a single bacteriorhodpsin protein in a wide range of applied voltages covering direct and injection tunnelling regimes. The satisfactory agreement between theory and available experiments validates the physical plausibility of the model developed here. In particular, we predict a rather abrupt increase of the variance of current fluctuations in concomitance with that of the I-V characteristic. The sharp increase, for about five orders of magnitude of current variance is associated with the opening of low resistance paths responsible for the sharp increase of the I-V characteristics. A strong non-Gaussian behavior of the associated probability distribution function is further detected by numerical calculations.
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