In highly conductive metals with sufficiently strong momentum-conserving scattering, the electron momentum is regarded as a long-lived quantity, whose dynamics is described by an emergent hydrodynamic theory. Actually, such hydrodynamic behaviors have been reported, since 2016, in various ultrapure materials such as GaAs quantum wells [1], 2D monovalent layered metal PdCoO2 [2], Weyl semimetal WP2 [3] and graphene [4-6] through various unconventional DC transport phenomena. However, in spite of a rapidly increasing number of reports on the candidates, it remains an unexplored important issue what kind of roles the crystal symmetry and the geometry of Bloch electrons play in the hydrodynamic transport. In this work [7], we formulate the hydrodynamic theory for time-reversal-symmetry preserved noncentrosymmetric metals. The obtained equations reveal the emergence of unprecedented anomalous forces in the Euler equation, which highlights an unexpected analogy between our fluids and the inviscid chiral fluids in vacuum. It is remarkable that this analogy indicates the existence of vorticity-induced electric current (we refer to it as generalized vortical effect) in condensed matter without nontrivial topology, which is a phenomenon analogous to the chiral vortical effect in chiral fluids. In particular, we reveal that this novel phenomenon gives rise to a novel anomalous hydrodynamic flow, that is, the anomalous edge current and the asymmetric Poiseuille flow. Furthermore, our theory is also able to describe the hydrodynamic counterparts of various nonlinear anomalous transport phenomena which has been formulated so far only in dissipative or ballistic regime. For example, the anomalous transport corresponding to so-called the quantum nonlinear Hall effect and the magnus Hall effect are integrated into a unified framework described by the velocity field in our work. Furthermore, towards an experimental observation of the predicted phenomena, we provide a symmetry consideration on the existing hydrodynamic materials and also give a quantitative estimation of the observable quantities, based on an effective model for strained-TMD and graphene.
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[6] R. K. Kumar, et al., Nature Physics 13, 1182 (2017).
[7] RT, K. Takasan, N. Kawakami, arXiv:2005.03406 (2020).