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Topological thermal Hall effect for topological excitations in spin liquid: Emergent Lorentz force on the spinons
by Yong Hao Gao, Gang Chen
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|As Contributors:||Gang Chen|
|Arxiv Link:||https://arxiv.org/abs/1901.01522v1 (pdf)|
|Date submitted:||2019-07-23 02:00|
|Submitted by:||Chen, Gang|
|Submitted to:||SciPost Physics|
We study the origin of Lorentz force on the spinons in a U(1) spin liquid. We are inspired by the previous observation of gauge field correlation in the pairwise spin correlation using the neutron scattering measurement when the Dzyaloshinskii-Moriya interaction intertwines with the lattice geometry. We extend this observation to the Lorentz force that exerts on the (neutral) spinons. The external magnetic field, that polarizes the spins, effectively generates an internal U(1) gauge flux for the spinons and twists the spinon motion through the Dzyaloshinskii-Moriya interaction. Such a mechanism for the emergent Lorentz force differs fundamentally from the induction of the internal U(1) gauge flux in the weak Mott insulating regime from the charge fluctuations. We apply this understanding to the specific case of spinon metals on the kagome lattice. Our suggestion of emergent Lorentz force generation and the resulting topological thermal Hall effect may apply broadly to other non-centrosymmetric spin liquids with Dzyaloshinskii-Moriya interaction. We discuss the relevance with the thermal Hall transport in kagome materials volborthite and kapellasite.
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Anonymous Report 2 on 2019-11-10 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1901.01522v1, delivered 2019-11-10, doi: 10.21468/SciPost.Report.1308
Paper is well written
Introduces a novel mechanism to get linear in T thermal Hall effect
The mean field spinon tight binding model is derived somewhat hand-wavily.
This paper introduces an interesting idea for how to get a thermal Hall effect that is linear in T at small T in the spinon Fermi surface spin liquids with U(1) gauge fields. The idea follows naturally from a few previous works, that are acknowledged in the paper, but I still find it important to highlight their mechanism as an interesting way to get substantial thermal Hall effect that scales linearly with T even in the strongly insulating regime.
My main concern is not the quality and novelty of their essential ideas, but rather with the specifics of the example that they chose to illustrate such general ideas. They consider a Hamiltonian given by Eq(1). I suspect that they are correct to assume that such Hamiltonian has a stable Spinon Fermi surface state at least at the level of Slave Fermion Mean Field neglecting the gauge field fluctuations. The pattern of fluxes that they conjecture in the presence of the Zeeman field does not increase the unit cell, so it should be easy to derive this pattern of fluxes as the one that minimises the mean field energy because their Hamiltonian is a spin bilinear. The work would be more complete if they did so and demonstrate explicitly that the pattern of fluxes is the one that minizes the mean field energy. But more than completeness, there are certain issues of consistency with their stated mean field Hamiltonian. For example, their tight binding model, Eq.(6), has conservation of total Sz. This is strange because their original Hamiltonian has DM interactions which break conservation of Sz in general. Are they assuming a restricted form of DM to get such conservation?
Their description of the Berry curvature is also rather limited. It seems they are dealing with a band structure with 3 different bands, and the bands have no touchings at finite B. What are their separate Chern numbers of each band? This is particularly important because the fully occupied bands could be contributing to the Hall effect.
When plotting Figure 3 they don't specify the value of B/t (Zeeman over kinetic energy), but only the value of the flux. These are independent parameters. What is this value?
Also I find very peculiar that their Thermal Hall conductivity reaches a value of order 1 at a temperature scale of the order of the band-width, even for very weak values of flux in their Fig. 3. For temperatures above the Zeeman scale their effect should be washed out by temperature and the system should resemble the case of no Zeeman, which should have zero Hall conductivity, because the Zeeman scale is what self-consistently determines the flux. The ban-width could be huge in comparison to Zeeman since it ie determined by J. But they never specify the value of the Zeeman scale for this plot so it is hard to tell. This is could also be an artefact of their not solving the mean field self-consistently since the value of the effective magnetic field itself should decrease with temperature because the system should have an Sz spin susceptibility that itself decreases with temperature.
I hope that the authors address my concerns in the Report before recommending publication.
Anonymous Report 1 on 2019-8-1 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1901.01522v1, delivered 2019-08-01, doi: 10.21468/SciPost.Report.1090
1. Very readable paper, nicely written on the whole.
2. Makes a contribution to the literature.
3. No technical faults
1. Major weakness is whether the work is of high enough significance to warrant publication in scipost
2. Use of the word "Topological" for this thermal hall effect (despite other papers doing similarthings) seems deceptive and should be avoided.
3. Citation should be added into abstract.
Overall I liked this paper -- it is clear and well written. My concern, however, is that it is not a sufficient advance to warrant publication in SciPost (which requires a somewhat higher level of work than, for example, PRB, in my understanding). The problem is that the results seems hardly surprising. (a) it is hardly surprising (based on symmetry) that once you add a zeeman field you will generate a chiral order parameter (b) once you have a nonzero chiral order parameter it is hardly surprising that you will have a thermal hall effect roughly proportional linear in the order parameter at least for small values. If either (a) or (b) is surprising, it is not clear to me why, and it is not explained in the manuscript. If the authors can explain this convincingly I would be happy to recommend it for publication. Otherwise, I'm not sure it is interesting enough. So although I will label the paper as "minor revision", unless the authors convince me it is interesting enough, I'm hesitant to recommend publication.
I have two further comments. First, I don't think using the word "topological" is really acceptable here. What is topological in this calculation? You use berry curvature, but this is not topological -- it is a geometric curvature, and unless you integrate over the whole zone to get a chern band, which you don't, it is not topological. There are no topological invariants, and no topological objects. The word topological is simply out of place and it seems like people just insert the word "topological" randomly in order to attract attention. I know the word has been used similarly in other publications, but this does not make it correct.
My final point is very minor. The abstract states that this work is based on prior work (second and third sentences of the abstract). These works should be cited within the abstract to clarify. With abstract citation, the entire publication information should be within the abstract itself. The way it stands it is quite hard for the reader to figure out what reference the authors mean until half-way through the paper.
1. Clarify why this is important/interesting enough to be in SciPost
2. Remove use of word "topological" where it is not appropriate (including the title)
3. Include appropriate citation in abstract.