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Transient Features in Charge Fractionalization, Local Equilibration and Nonequilibrium Bosonization
by Alexander Schneider, Mirco Milletari, Bernd Rosenow
 Published as SciPost Phys. 2, 007 (2017)
Submission summary
As Contributors:  Mirco Milletari 
Arxiv Link:  http://arxiv.org/abs/1610.02036v3 (pdf) 
Date accepted:  20170208 
Date submitted:  20161214 01:00 
Submitted by:  Milletari, Mirco 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
In quantum Hall edge states and in other onedimensional interacting systems, charge fractionalization can occur due to the fact that an injected charge pulse decomposes into eigenmodes propagating at different velocities. If the original charge pulse has some spatial width due to injection with a given sourcedrain voltage, a finite time is needed until the separation between the fractionalized pulses is larger than their width. In the formalism of nonequilibrium bosonization, the above physics is reflected in the separation of initially overlapping square pulses in the effective scattering phase. When expressing the single particle Green's function as a functional determinant of counting operators containing the scattering phase, the time evolution of charge fractionalization is mathematically described by functional determinants with overlapping pulses. We develop a framework for the evaluation of such determinants, describe the system's equilibration dynamics, and compare our theoretical results with recent experimental findings.
Ontology / Topics
See full Ontology or Topics database.Published as SciPost Phys. 2, 007 (2017)
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 1 on 2017114 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1610.02036v3, delivered 20170114, doi: 10.21468/SciPost.Report.63
Strengths

Weaknesses

Report
The analysis presented in this work is, to a large extent, of technical nature. I would like to commend the authors for being able to get their message(s) through, even for those readers who may not follow in detail each and every step of the derivation.
The authors’ two main thrusts are: (i) extend previous analyses of nonequilibrium bosonization. Specifically, the time evolution of injected charge is formally described by functional determinants with overlapping square pulses which describe the effective scattering phase. Unlike in the “semiclassical limit”, where those pulses are nonoverlapping, here a fullfledged quantum mechanical treatment is required, and is developed by the authors. (ii) apply nonequilibrium bosonization (in this fully quantum limit) to the problem of electron fractionalization. Specifically, the authors address the transient behavior of fractionalization at the edge of \nu=2 integer QHE system, and compare their analysis to experimental data.
These are clearly significant contributions in this important field of nonequilibrium quantum electronic matter. As a further added value of this work, I would mention its clarity and the fact that the analysis is well embedded in a broad context of earlier works (on bosonization and on fractionaliation). I could easily see how the introduction of this paper is extended into a review of the field…
I therefore strongly recommend this work for publication.
Requested changes
Two items the authors ** may** want to consider (but should not constitute a condition for publication): First, in the introduction the authors refer to “recently developed nonequilibrium bosonization” and provide a list of references. In fac, nonequilibrium bosonization was first developed in Ref. 16 (and to some extent also in D.B. Gutman, et al, Phys. Rev.Lett. 2008) before the other references mentioned in the Introduction. Second, it would be intriguing to think how the results presented here should apply to more complex edges, e.g., the edge of a fractional bulk filling fraction (e.g., the $\nu=2/3$ FQHE), which has been recently studied experimentally.
Author: Mirco Milletari on 20170224 [id 104]
(in reply to Report 1 on 20170114)We would like to thank the referee for his/her valuable comments and for recommending our paper for publication in SciPost. We are pleased to learn that the referee found our contribution “clearly significant”. Below we address the referee’s comments.
As for the First comment, we thank the referee for pointing to us the missing reference. We have modified the manuscript accordingly.
Concerning the Second comment, it would be indeed intriguing to think how our results generalise to more complex edges, e.g., the edge of a fractional bulk filling fraction (e.g., the ν=2/3 FQHE). Although the interferometer setup with edges at fractional filling fractions bear similarities with the problem considered in our paper, there are few important differences:
In our problem, we used the fact that the system before the first quantum point contact was noninteracting. Although this point seems crucial for the Quantum Quench model to work, it is possible to get around this restriction by using the original functional Keldysh approach developed in Ref. 16. We believe that this would allow to generalise our results to the case of Fractional filling fractions.
For the composite fractional edge, one would expect the existence of additional constraints on the dynamics of the system coming from its nontrivial topology. It would be certainly intriguing to understand the interplay of topology and strong nonequilibrium in this setup.