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Modulation induced transport signatures in correlatedelectron waveguides
by Gal Shavit, Yuval Oreg
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Submission summary
| Authors (as registered SciPost users): | Gal Shavit |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202008_00012v1 (pdf) |
| Date submitted: | 2020-08-20 10:27 |
| Submitted by: | Shavit, Gal |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Phenomenological |
Abstract
Recent transport experiments in spatially modulated quasi-1D structures created on top of LaAlO$_3$/SrTiO$_3$ interfaces have revealed some interesting features, including phenomena conspicuously absent without the modulation. In this work, we focus on two of these remarkable features and provide theoretical analysis allowing their interpretation. The first one is the appearance of two-terminal conductance plateaus at rational fractions of $e^2/h$. We explain how this phenomenon, previously believed to be possible only in systems with strong repulsive interactions, can be stabilized in a system with attraction in the presence of the modulation. Using our theoretical framework we find the plateau amplitude and shape, and characterize the correlated phase which develops in the system due to the partial gap, namely a Luttinger liquid of electronic trions. The second observation is a sharp conductance dip below a conductance of $1\times e^2/h$, which changes its value over a wide range when tuning the system. We theorize that it is due to resonant backscattering caused by a periodic spin-orbit field. The behavior of this dip can be reliably accounted for by considering the finite length of the electronic waveguides, as well as the interactions therein. The phenomena discussed in this work exemplify the intricate interplay of strong interactions and spatial modulations, and reveal the potential for novel strongly correlated phases of matter in system which prominently feature both.
Author comments upon resubmission
We would like to thank all three referees for their thoughtful and careful reading of the manuscript. We are glad they all found our work interesting, original, and appropriate for publication in SciPost. The comments provided by the referees mostly concern the presentation and clarifications needed to make the manuscript more accessible to the readers. We have fully implemented their comments and suggestions in the revised manuscript, which is now improved as a consequence. We have detailed the changes made to the manuscript in the response to each referee below. With this, we trust the manuscript is ready for publication in SciPost.
Sincerely yours,
Gal Shavit and Yuval Oreg.
List of changes
The changes made in the revised manuscript detailed in the responses to the referees.
Additionally, we have changed the formatting to conform with the SciPost format.
Current status:
Reports on this Submission
Anonymous Report 2 on 2020-8-27 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202008_00012v1, delivered 2020-08-27, doi: 10.21468/SciPost.Report.1944
Report
I much appreciate the improvements the authors have made to the paper and their answers to my questions. A few final issues remain to be cleared up:
p. 14 In the revision (and their reply) the authors write:
"Notice that at $\mu=\mu_Q$, $\tilde{\mu} \to 0$, which gives the resonance condition"
I cannot follow why $\tilde{\mu}$ must vanish: starting from the relations that I can extract from the paper on p. 12 (I eliminate $v=k_F/m$),
$k_F^2 = 2m(\mu +V_Z) + k_{SO}^2$
and
$\mu_Q = k_F Q/2$,
it is not obvious how this gives the condition $Q=2k_F$ to nullify
$\tilde{\mu}=k_F (2k_F-Q)/2=0$ as defined on p. 12.
Please clarify which clue I am missing.
p. 13, after Eq. (33)
The definition of $\Delta_Q$ seems to have changed. If it is now correct (it seems so), then
$\Delta_Q$ coincides with $V_Q$ which appears in discussion after Eq. (36) alongside $\Delta_Q$ which is very confusing. Please replace throughout Sec. 3.2 $V_Q \to \Delta_Q$ or clarify the use of different symbols for the same thing.
p. 12 bottom:
The authors have indicated that they corrected a typo in the unitary transformation. It seems that the phrase "and once more neglecting spatially oscillating terms" needs to be removed: Unless I misunderstood, Eq. (32) seems to imply Eq. (33) by working out the corrected unitary transformation.
Please clarify.
p. 4: Equation (4) seems to has changed (not indicated by the authors) but leaves me confused:
I understood $g_{bs}$ is just a number ("coupling coefficient"), how can there be there be a $\delta_{k_{1F},k_{2F}}$ on the right hand side?
Please clarify (4) or adjust Eq. (3).
----------------------
Minor typographic issues/suggestions that I noted:
Abstract, last line: "s" missing
"of matter in systemS which prominently feature both."
p. 3: ".. we explain how can this feature be used"
-> " we explain how this feature can be used"
p. 7 : Skip the paragraph break at (dangling remark)
"..spin-degenerate electrons in a quantum wire. We emphasize that .."
Fig. 2 on p. 7 is discussed only on p. 9.
Perhaps move the figure to p. 8?
p. 14: Skip the paragraph break at
..regions of the system. In contrast to our discussion.."
Requested changes
see report
Anonymous Report 1 on 2020-8-26 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202008_00012v1, delivered 2020-08-26, doi: 10.21468/SciPost.Report.1939
Report
The authors have addressed all referees' concerns and suggestions in an impressively careful and constructive way. The adopted changes make the paper even more outstanding.
Author: Gal Shavit on 2020-09-08 [id 948]
(in reply to Report 1 on 2020-08-26)We would like to thank the referee for reading the revised manuscript, reviewing our comments and corrections and describing the paper as outstanding.
Author: Gal Shavit on 2020-09-08 [id 950]
(in reply to Report 2 on 2020-08-27)We would like to thank the referee for carefully reading the revised manuscript and reviewing our comments and corrections.
We address the issues he raise below.
1)
Regarding the comment about $\mu$ and $\tilde{\mu}$ in page 14:
The resonance condition for the backscattering is given by $vk_F=\mu_Q$. In a linearized Dirac Hamiltonian, e.g., Eq. (33), the Fermi energy, or the chemical potential is measured relatively to the Dirac crossing point is just $\mu=vk_F$, which is why we claim that when $\mu=\mu_Q$ the backscattering is resonant.
However, the referee's point seems to be that this $\mu$ should not be the same as the one in Eq. (29) (which we have replaced by $\epsilon_0$ in the revised manuscript). This is a valid point. Although $\epsilon_0$ determines $\mu$ (via the definition of $k_F$), it is not equal to it.
To correct this point, and avoid using confusing notation, we have changed $\mu\to\epsilon_0$ in Eq. (29).
Additionally, we clarify the point of chemical potential being defined with respect to the linear model below Eq. (35).
2)
Regarding the redundancy between $\Delta_Q$ and $V_Q$.
Indeed, as the referee points out, these two coincide.
Thus, we replace $V_Q$ by $\Delta_Q$ everywhere in the amended manuscript.
3)
Regarding the unitary transformation at the bottom of page 12.
The sentence the referee refers to should indeed be removed, and is removed in the revised manuscript.
4)
Regarding $g_{\rm bs}$ in Eq. (4).
The meaning of the Kronecker delta previously used in Eq. (4) is to clarify that $g_{\rm bs}$ plays a role only when the two Fermi momenta are approximately the same. Otherwise, the corresponding term will oscillate rapidly along the waveguide.
For the sake of clarity, we omit the Kronecker delta in Eq. (4), and clarify this condition following Eq. (4).
The other typos and suggestions of the referee have been fully implemented in the revised manuscript.