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Hydrodynamics with triangular point group
by Aaron J. Friedman, Caleb Q. Cook, Andrew Lucas
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Submission summary
| Authors (as registered SciPost users): | Aaron Friedman · Andrew Lucas |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2202.08269v2 (pdf) |
| Date submitted: | 2022-02-22 03:31 |
| Submitted by: | Lucas, Andrew |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
When continuous rotational invariance of a two-dimensional fluid is broken to the discrete, dihedral subgroup $D_6$ - the point group of an equilateral triangle - the resulting anisotropic hydrodynamics breaks both spatial-inversion and time-reversal symmetries, while preserving their combination. In this work, we present the hydrodynamics of such $D_6$ fluids, identifying new symmetry-allowed dissipative terms in the hydrodynamic equations of motion. We propose two experiments - both involving high-purity solid-state materials with $D_6$-invariant Fermi surfaces - that are sensitive to these new coefficients in a $D_6$ fluid of electrons. In particular, we propose a local current imaging experiment (which is present-day realizable with nitrogen vacancy center magnetometry) in a hexagonal device, whose $D_6$-exploiting boundary conditions enable the unambiguous detection of these novel transport coefficients.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2022-11-28 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2202.08269v2, delivered 2022-11-28, doi: 10.21468/SciPost.Report.6215
Report
The authors present a rather detailed discussion of a conjectured hydrodynamic theory of a D_6 electronic fluid. Two experiments in ultra-pure materials with D_6-invariant Fermi surfaces are suggested in order to detect new dissipative kinetic coefficients that are proposed in this work.
The paper is well-written and well-organized. I do however have a few questions mostly about what's not included in the manuscript.
The authors focus on symmetry properties (which is completely understandable in the context of hydrodynamics), but don't mention anything about microscopic interactions, both respecting and breaking the assumed symmetries. As a result, it is unclear how could one establish a parameter range (e.g., in temperature, magnetic field, etc.) where the proposed hydrodynamic behavior could be expected to be observable, as well as essential features such as the temerature and magnetic field dependence of transport coefficients. Similarly, the authors do not discuss details of the band structure that might affect the hydrodynamic behavior (similar to the striking difference between hydrodynamics in neutral and doped graphene), which is especially important in regards to the assumed Galilean invariance or lack thereof. Finally, there is not much discussion regarding specific materials where the proposed behavior could be expected apart for a very brief section on trilayer graphene.
The proposed behavior is clearly dependent on the choice of the D_6 symmetry. In the absence of specific experiments (recent, ongoing, or planned), the choice of the symmetry group is perhaps motivated by the result itself, but it would be nice if the authors commented on that as well - after all, there is quite a number of point groups that are not usually discussed in the literature.