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Register a new userFunctional dependence of the Hall viscosity-induced transverse voltage in two-dimensional Fermi liquids
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Added by
Ioannis Matthaiakakis
Publication date
2019
fields
Physics
and research's language is
English
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The breaking of parity and time-reversal symmetry in two-dimensional Fermi liquids gives rise to non-dissipative transport features characterized by the Hall viscosity. In magnetic fields, the Hall viscous force directly competes with the Lorentz force, since both mechanisms contribute to the Hall voltage. In this work, we present a channel geometry that allows us to uniquely distinguish these two contributions and derive, for the first time, their functional dependency on all external parameters. We show that the ratio of the Hall viscous to the Lorentz force contribution is negative and that its modulus decreases with increasing width, slip-length and carrier density, while it increases with the electron-electron mean free path of our channel. In typical materials such as GaAs the Hall viscous contribution can dominate the Lorentz signal up to a few tens of millitesla until the total Hall voltage vanishes and subsequently is overcome by the Lorentz contribution. Moreover, we prove that the total Hall electric field is parabolic due to Lorentz effects, whereas the offset of this parabola is characterized by the Hall viscosity. Hence, our results pave the way to measure and identify the Hall viscosity via both global and local voltage measurements.
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The combination of Dirac physics and elasticity has been explored at length in graphene where the so--called elastic gauge fields have given rise to an entire new field of research and applications: Straintronics. The fact that these elastic fields couple to fermions as the electromagnetic field, implies that many electromagnetic responses will have elastic counterparts not explored before. In this work we will first show that the presence of elastic gauge fields will be the rule rather than the exception in most of the topologically non--trivial materials in two and three dimensions. In particular we will extract the elastic gauge fields associated to the recently observed Weyl semimetals, the three dimensional graphene. As it is known, quantum electrodynamics suffers from the chiral anomaly whose consequences have been recently explored in matter systems. We will show that, associated to the physics of the anomalies, and as a counterpart of the Hall conductivity, elastic materials will have a Hall viscosity in two and three dimensions with a coefficient orders of magnitude bigger than the previously studied response. The magnitude and generality of the new effect will greatly improve the chances for the experimental observation of this topological, non dissipative response.
We show that 3D Lifshitz fermions arising as the critical theory at the Weyl semimetal/insulator transition naturally develop an anomalous Hall viscosity at finite temperature. We discuss how to couple the system to non-relativistic background sources for stress-tensor and momentum currents via a form of Newton-Cartan geometry with torsion and derive the Kubo formulas for the Hall viscosities. While the Lifshitz system that arises most naturally has scaling exponent $z=2$ we also generalize the theory for arbitrary Lifshitz scaling $z$ and show that, in the limit $z to 0$, it may be given a Chern-Simons interpretation by dimensionally reducing along the anisotropic direction. The Hall viscosities are expressed in terms of zeta functions and their temperature dependence is dictated by the scaling exponent.
The Hall viscosity has been proposed as a topological property of incompressible fractional quantum Hall states and can be evaluated as Berry curvature. This paper reports on the Hall viscosities of composite-fermion Fermi seas at $ u=1/m$, where $m$ is even for fermions and odd for bosons. A well-defined value for the Hall viscosity is not obtained by viewing the $1/m$ composite-fermion Fermi seas as the $nrightarrow infty$ limit of the Jain $ u=n/(nmpm 1)$ states, whose Hall viscosities $(pm n+m)hbar rho/4$ ($rho$ is the two-dimensional density) approach $pm infty$ in the limit $nrightarrow infty$. A direct calculation shows that the Hall viscosities of the composite-fermion Fermi sea states are finite, and also relatively stable with system size variation, although they are not topologically quantized in the entire $tau$ space. I find that the $ u=1/2$ composite-fermion Fermi sea wave function for a square torus yields a Hall viscosity that is expected from particle-hole symmetry and is also consistent with the orbital spin of $1/2$ for Dirac composite fermions. I compare my numerical results with some theoretical conjectures.
A circularly polarized a.c. pump field illuminated near resonance on two-dimensional transition metal dichalcogenides (TMDs) produces an anomalous Hall effect in response to a d.c. bias field. In this work, we develop a theory for this photo-induced anomalous Hall effect in undoped TMDs irradiated by a strong coherent laser field. The strong field renormalizes the equilibrium bands and opens up a dynamical energy gap where single-photon resonance occurs. The resulting photon dressed states, or Floquet states, are treated within the rotating wave approximation. A quantum kinetic equation approach is developed to study the non-equilibrium density matrix and time-averaged transport currents under the simultaneous influence of the strong a.c. pump field and the weak d.c. probe field. Dissipative effects are taken into account in the kinetic equation that captures relaxation and dephasing. The photo-induced longitudinal and Hall conductivities display notable resonant signatures when the pump field frequency reaches the spin-split interband transition energies. Rather than valley polarization, we find that the anomalous Hall current is mainly driven by the intraband response of photon-dressed electron populations near the dynamical gap at both valleys, accompanied by a smaller contribution due to interband coherences. These findings highlight the importance of photon-dressed bands and non-equilibrium distribution functions in achieving a proper understanding of photo-induced anomalous Hall effect in a strong pump field.
While nondissipative hydrodynamics in two-dimensional electron systems has been extensively studied, the role of nondissipative viscosity in three-dimensional transport has remained elusive. In this work, we address this question by studying the nondissipative viscoelastic response of three dimensional crystals. We show that for systems with tetrahedral symmetries, there exist new, intrinsically three-dimensional Hall viscosity coefficients that cannot be obtained via a reduction to a quasi-two-dimensional system. To study these coefficients, we specialize to a theoretically and experimentally motivated tight binding model for a chiral magentic metal in (magnetic) space group [(M)SG] $P2_13$ (No.~198$.$9), a nonpolar group of recent experimental interest which hosts both chiral magnets and topological semimetals. Using the Kubo formula for viscosity, we compute the nondissipative Hall viscosity for the spin-1 fermion in two ways. First we use an electron-phonon coupling ansatz to derive the phonon strain coupling and associated phonon Hall viscosity. Second we use a momentum continuity equation to derive the viscosity corresponding to the conserved momentum density. We conclude by discussing the implication of our results for hydrodynamic transport in three-dimensional magnetic metals, and discuss some candidate materials in which these effects may be observed.
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