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StatPhys 27 Main Conference

Non-equilibrium transport in junctions using bosonization

Nayana Shah, C. J. Bolech

Published Apr 17, 2019• 0 citations
OpenAlex

Abstract

We will present our attempts to assure that bosonization-based calculations of non-equilibrium transport are fully consistent with the pre-bosonization formulations of the problems. Our initial focus on the case of a tunneling junction out of equilibrium showed that the conventional approach to bosonize-transform-debosonize gives results that are not consistent with the exact solution of that problem. We identified the root of the discrepancies in missing conservation laws and introduced a procedure that we developed to preserve these via a new framework that should be widely applicable [1]. We further applied the updated procedure to another key theoretical prototype of immediate experimental relevance, the two-lead Kondo junction [2]. Follow up calculations are helping to contextually demarcate when the need for the new bosonization framework arises in different types of problems. References: [1] Nayana Shah and C. J. Bolech, Phys. Rev. B  93 , 085440 (2016). [2] C. J. Bolech and Nayana Shah, Phys. Rev. B  93 , 085441 (2016).

Related papers

Consistent bosonization-debosonization. II. The two-lead Kondo problem and the fate of its nonequilibrium Toulouse point

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Following the development of a scheme to bosonize and debosonize consistently [N. Shah and C. J. Bolech, Phys. Rev. B 93, 085440 (2016)], we present in detail the Toulouse-point analytic solution of the two-lead Kondo junction model. The existence and location of the solvable point is not modified, but the calculational methodology and the final expressions for observable quantities change markedly as compared to the existent results. This solvable point is one of the remarkably few exact results for nonequilibrium transport in correlated systems. It yields relatively simple analytical expressions for the current in the full range of temperature, magnetic field, and voltage. It also shows precisely, within the limitations of the Toulouse fine-tuning, how the transport evolves depending on the relative strengths of interlead and intralead Kondo exchange couplings ranging from weak to strong. Thus its improved understanding is an important stepping stone for future research.

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We critically reexamine the bosonization-debosonization procedure for systems including certain types of localized features (although more general scenarios are possible). By focusing on the case of a tunneling junction out of equilibrium, we show that the conventional approach gives results that are not consistent with the exact solution of the problem even at the qualitative level. We identify inconsistencies that can adversely affect the results of all types of calculations. We subsequently show a way to avoid these and proceed consistently. The extended framework that we develop here should be widely applicable.

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We consider the electron transport properties through fully interacting nanoscale junctions beyond the linear-response regime. We calculate the current flowing through an interacting region connected to two interacting leads, with interaction crossing at the left and right contacts, by using a non-equilibrium Green function technique. The total current at one interface (the left one for example) is made of several terms which can be regrouped into two sets. The first set corresponds to a very generalized Landauer-like current formula with physical quantities defined only in the interacting central region and with renormalized lead self-energies. The second set characterizes inelastic scattering events occurring in the left lead. We show how this term can be negligible or even vanish due to the pseudo-equilibrium statistical properties of the lead in the thermodynamic limit. The expressions for the different Green functions needed for practical calculations of the current are also provided. We determine the constraints imposed by the physical condition of current conservation. The corresponding equation imposed on the different self-energy quantities arising from the current conservation is derived. We discuss in detail its physical interpretation and its relation with previously derived expressions. Finally several important key features are discussed in relation to the implementation of our formalism for calculations of quantum transport in realistic systems.

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Noise and interactions in mesoscopic systems far from equilibrium

Artyom Borin

This thesis is devoted to developing of an universal description of strongly interacting mesoscopic systems out of equilibrium. The nature of universalities we are looking for is twofold. Firstly, our goal is to find novel and simple dependences of physical observables on the experimental parameters. Secondly, we are looking for an universal theoretical approach that can be applied to a class of seemingly different strongly interacting physical problems. To achieve this generality, we rely on the bosonization technique, which allows one to account for interactions exactly. However, it is not trivial to apply this technique to out-of-equilibrium systems, because an injection of non-equilibrium electrons is naturally described at the fermion level, whereas the interactions are very elegantly incorporated within the bosonic framework. In this thesis, we discuss an approach that treats out-of-equilibrium corrections as perturbations. This allows us to stay within the framework of bosonization and to study non-equilibrium systems.

•Jan 1, 2019•0 citations
We will present our attempts to assure that bosonization-based calculations of non-equilibrium transport are fully consistent with the pre-bosonization formulations of the problems. Our initial focus on the case of a tunneling junction out of equilibrium showed that the conventional approach to bosonize-transform-debosonize gives results that are not consistent with the exact solution of that problem. We identified the root of the discrepancies in missing conservation laws and introduced a procedure that we developed to preserve these via a new framework that should be widely applicable [1]. We further applied the updated procedure to another key theoretical prototype of immediate experimental relevance, the two-lead Kondo junction [2]. Follow up calculations are helping to contextually demarcate when the need for the new bosonization framework arises in different types of problems. References: [1] Nayana Shah and C. J. Bolech, Phys. Rev. B  93 , 085440 (2016). [2] C. J. Bolech and Nayana Shah, Phys. Rev. B  93 , 085441 (2016).
Following the development of a scheme to bosonize and debosonize consistently [N. Shah and C. J. Bolech, Phys. Rev. B 93, 085440 (2016)], we present in detail the Toulouse-point analytic solution of the two-lead Kondo junction model. The existence and location of the solvable point is not modified, but the calculational methodology and the final expressions for observable quantities change markedly as compared to the existent results. This solvable point is one of the remarkably few exact results for nonequilibrium transport in correlated systems. It yields relatively simple analytical expressions for the current in the full range of temperature, magnetic field, and voltage. It also shows precisely, within the limitations of the Toulouse fine-tuning, how the transport evolves depending on the relative strengths of interlead and intralead Kondo exchange couplings ranging from weak to strong. Thus its improved understanding is an important stepping stone for future research.
We critically reexamine the bosonization-debosonization procedure for systems including certain types of localized features (although more general scenarios are possible). By focusing on the case of a tunneling junction out of equilibrium, we show that the conventional approach gives results that are not consistent with the exact solution of the problem even at the qualitative level. We identify inconsistencies that can adversely affect the results of all types of calculations. We subsequently show a way to avoid these and proceed consistently. The extended framework that we develop here should be widely applicable.
Capitalizing on recent work, which clarifies the consistent use of bosonization-debosonization methods to study Kondo-type quantum impurity models even in nonequilibrium settings, we revisit the compactification procedure of the two-channel Kondo model (by which it is rewritten more ``compactly'' using the single-channel version of the model and exploiting separation and duality between spin and charge) and uncover some hidden approximations that could limit its range of validity. This complements and extends, for two or any even number of channels, beyond previous work on the Toulouse limit of these models, and reinforces the need for the use of an extended framework in these calculations. We carry out a number of exact comparisons between the different models and show that keeping track of the so-called consistency factors leads to full agreement between the compactified and original versions of the model.
We consider the electron transport properties through fully interacting nanoscale junctions beyond the linear-response regime. We calculate the current flowing through an interacting region connected to two interacting leads, with interaction crossing at the left and right contacts, by using a non-equilibrium Green function technique. The total current at one interface (the left one for example) is made of several terms which can be regrouped into two sets. The first set corresponds to a very generalized Landauer-like current formula with physical quantities defined only in the interacting central region and with renormalized lead self-energies. The second set characterizes inelastic scattering events occurring in the left lead. We show how this term can be negligible or even vanish due to the pseudo-equilibrium statistical properties of the lead in the thermodynamic limit. The expressions for the different Green functions needed for practical calculations of the current are also provided. We determine the constraints imposed by the physical condition of current conservation. The corresponding equation imposed on the different self-energy quantities arising from the current conservation is derived. We discuss in detail its physical interpretation and its relation with previously derived expressions. Finally several important key features are discussed in relation to the implementation of our formalism for calculations of quantum transport in realistic systems.
This thesis is devoted to developing of an universal description of strongly interacting mesoscopic systems out of equilibrium. The nature of universalities we are looking for is twofold. Firstly, our goal is to find novel and simple dependences of physical observables on the experimental parameters. Secondly, we are looking for an universal theoretical approach that can be applied to a class of seemingly different strongly interacting physical problems. To achieve this generality, we rely on the bosonization technique, which allows one to account for interactions exactly. However, it is not trivial to apply this technique to out-of-equilibrium systems, because an injection of non-equilibrium electrons is naturally described at the fermion level, whereas the interactions are very elegantly incorporated within the bosonic framework. In this thesis, we discuss an approach that treats out-of-equilibrium corrections as perturbations. This allows us to stay within the framework of bosonization and to study non-equilibrium systems.