Fractional Conductances of Wires: The S-Matrix Approach
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsComments can be found in the attachment!
Comments for author File: 
Comments.pdf
Author Response
Comment 1: Outline the main fixes for large but finite gaps. The analysis ultimately takes ρ→∞ for gapped sectors. How does g(T,V) approach the projector value and which operators establish the first non-zero power laws? pg. 5
Response 1: we have added the following text at the top of page 5:
The limit $\rho\to\infty$ must be associated with $L\Delta/v\to\infty$ limit. The non-universal corrections of order $v/(L\Delta) \ll 1$ require an instanton analysis and lie beyond the scope of our approximation. In this work we focus on the universal values of the fractional conductance at intermediate temperatures, where strong backscattering fully suppresses certain fluctuations. We also do not consider the extreme low-temperature regime, where renormalization group analysis shows that backscattering becomes irrelevant and the ideal conductance is restored.
Comment 2: How imperfect contacts enter the formalism? (do they act as additional backscatter channels living outside of G or modify the t-projection?) eqs 1,2
Response 2: we have added this text after the Eq.(2):
Nonideal contacts would result in additional terms similar to ${\cal H}_{bs}$ with amplitudes $\Delat(x)$ being nonzero only in the vicinity of the wire ends. This effect would lead to a non-universal conductance and will not be considered in this paper.
Comment 3: It would help to explicitly map “channels” to spin-resolved right/left movers and restate the minimality claims with and without spin degeneracy side-by-side
Response 3: the text added at the top of page 9:
The channels in the experiment are modes with both right- and left-moving chiralities. Whether spin is counted as a separate channel depends whether spin degeneracy is present or absent. These are all very important issues but we would like to focus on the possible values of fractional conductances without getting in the specifics of the system.
Comment 4: The symbol r is used both for reflection amplitudes (Sec. 2.1, one-channel example) and for rightmover blocks/vectors ra in multi-channel formulas (Eqs. (14)–(16)). Consider renaming one of them (e.g., use R for reflection matrix) to avoid confusion
Response 4: The symbol r used for reflection coefficient is a scalar whereas ${\bf r}_a$ are vectors typed in a boldface. We believe that the confusion can be avoided.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe manuscript shows a theoretical study of transport in wires with multiple conduction channels.
It was analysed the scattering matrix of such model system, and it was derived the formula for
the conductance (Eq. (20)). This formula was applied to the single backscattering case and
single gapless case, and the results (Eqs. (22), (24), (25), and (27)), agree and generalize the ones of Refs. [15] and [23]. Finally, the authors proposed a minimal coupled wire model that reproduces the fractional conductance plateau with even denominators, as recently observed in experiments (Refs. [10], [24]).
Overall, I consider the manuscript interesting and useful, and I recommend its publication.
I have some minor points to be addressed:
- it is not clear why the conductances of systems with three and four channels can
have only odd denominators. Which mathematical theorem is at the base of this
statement?
- the derivation of Eq. (27) can be better explained
- in the section "2.1. Scattering and transfer matrices", there are cited only few references. I think the main results of this section should be better connected with the published results.
Author Response
Comment 1: it is not clear why the conductances of systems with three and four channels can have only odd denominators. Which mathematical theorem is at the base of this
statement?
Response 1: we have added subsection ‘Generic analysis’ on page 9 where we provide a proof of the statement.
Comment 2: the derivation of Eq. (27) can be better explained
Response 2: we have added another equation (it is now Eq. (27)) and expanded the former Eq. (27) (which is now Eq. (28)) to provide a detailed calculation leading to the result.
Comment 3: in the section "2.1. Scattering and transfer matrices", there are cited only few references. I think the main results of this section should be better connected with the published results.
Response 3: that section contained five references, and I am afraid there are no more references that can be added because the approach is our main result, and it is original. Another relevant reference [26] which was cited later has now been added to that section.
