Hydrodynamics with triangular point group

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.

Hydrodynamic effective field theories with discrete rotational symmetry

“…In contrast, transport coefficients associated with the discrete rotational symmetry were largely unconstrained, and here our results appear to agree with earlier literature in overlapping regimes. In tandem with a concurrent paper [42], we have also emphasized the possibility for novel new hydrodynamic phenomena in fluids with discrete rotational symmetries without inversion. In these dihedral-symmetric fluids, with a small enough point group, terms that seem to be compatible with Landau's hydrodynamic phenomenology (an entropy current can be constructed) are nevertheless forbidden by factorizability, or alternatively, the ability to couple the theory to background gauge fields.…”

“…As we will see, there are a few peculiarities which are somewhat surprising from a microscopic perspective, and which it is desirable to have a more universal understanding of. For example, we will see that in fluids with triangular point group [42], there are certain terms which seem to be allowed in the conventional Landau paradigm (an entropy current can be constructed): in particular within linear response, it seems possible to construct a spatial stress tensor c • λ ijk v k ⊂ T ij , with v k fluid velocity and λ an invariant tensor under the discrete point group. However, kinetic theory calculations reveal that c = 0 [42].…”

“…For example, we will see that in fluids with triangular point group [42], there are certain terms which seem to be allowed in the conventional Landau paradigm (an entropy current can be constructed): in particular within linear response, it seems possible to construct a spatial stress tensor c • λ ijk v k ⊂ T ij , with v k fluid velocity and λ an invariant tensor under the discrete point group. However, kinetic theory calculations reveal that c = 0 [42]. In this paper, we will explain why c = 0 in this model based on very general arguments which are most natural within the effective theory approach.…”

“…We find that the dynamical KMS condition (2.26) with Θ = T requires that t 13 = t 23 = 0, thus γ 13 = γ 23 = γ 31 = γ 32 = 0. As emphasized in [42], it appears that typically when the rotation symmetry group does not include inversion, in practical applications to electron fluids one will choose Θ = IT .…”

“…However, there are new dissipative coefficients [42] which couple gradients of temperature and density to the traceless symmetric velocity strain tensor:…”