Motivated by recent experiments on the phonon contribution to the thermal Hall effect in the cuprates, we present an analysis of chiral phonon transport. We assume the chiral behavior arises from a non-zero phonon Hall vicosity, which is likely induced by the coupling to electrons. Phonons with a non-zero phonon Hall viscosity have an intrinsic thermal Hall conductivity, but Chen et al. (Phys. Rev. Lett. 124, 167601 (2020)) have argued that a significantly larger thermal Hall conductivity can arise from an extrinsic contribution which is inversely proportional to the density of impurities. We solve the Boltzmann equation for phonon transport and compute the temperature ($T$) dependence of the thermal Hall conductivity originating from skew scattering off point-like impurities. We find that the dominant source for thermal Hall transport is an interference between impurity skew scattering channels with opposite parity. The thermal Hall conductivity $\sim T^{d+2}$ at low $T$ in $d$ dimensions, and has a window of $T$-independent behavior for $T > T_{\rm imp}$, where $T_{\rm imp}$ is determined by the ratio of scattering potentials with opposite parity. We also consider the role of non-specular scattering off the sample boundary, and find that it leads to negligible corrections to thermal Hall transport at low $T$.
Gaussian-Bond Hall Viscosity and Nonlocal Hall Response of a Sampled Landau Level
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学理论物理研究所）；Institute of Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Department of Physics, Nagoya University（名古屋大学物理学系）；Center for Spintronics Research Network, Keio University（庆应义塾大学自旋电子学研究网络中心）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学拓扑量子计算卓越创新中心）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能研究开发机构先进科学研究中心）
We consider the time-reversal odd dynamics of the bilayer graphene at low energies in the quantum Hall regime. A generating functional for the effective action that captures the electromagnetic response to all orders in momentum and frequency is presented and evaluated to the third order in the space-time gradient $\mathcal O(\partial^3)$. In addition, we calculate the Hall viscosity and derive an explicit relationship with the $q^2$ coefficient of the Hall conductivity. It is reminiscent of the Hoyos--Son relation in the Galilean invariant systems, which can be recovered in the limit of large…
Transition from Intrinsic to Extrinsic Anomalous Hall Effect in the Ferromagnetic Weyl Semimetal PrAlGe$_{1-x}$Si$_x$
铁磁外尔半金属（FM WSM）中大的反常霍尔效应（AHE）引起了人们对这一神秘现象的兴趣。然而，由于缺乏可调材料，在FM WSM中，由Berry曲率引起的内在机制和由于散射引起的外在机制之间的相互作用仍然不清楚。在这方面的贡献，我们提出了一个彻底的调查的外在和内在的AHE在一个新的家庭FM WSM，PrAlGe $_{1-x}$ Si $_x$，其中$x$可以连续调谐。从DFT计算，我们表明，两个端员，PrAlGe和PrAlSi，有不同的费米面，但类似的Weyl节点结构。实验上，我们观察到适度的异常霍尔系数（$R_S$）的变化，但在普通霍尔系数（$R_0$）的显着变化，在PrAlGe $_{1-x}$ Si $_x$作为$x$的函数，确认费米面的变化。通过比较$R_0$和$R_S$的大小，我们确定了两种方案;当$x\le0.5$时为$|R_0|<|R_S|$，当$x>0.5$时为$|R_0|>|R_S|$。通过详细的标度分析，我们发现了$x\le0.5$的反常霍尔电导（AHC）。当$x>0.5$。因此，我们指出了FM WSMs的外在机制的意义，并报告了第一次观察到的过渡从本征到外在的AHE在PrAlGe $_{1-x}$ Si $_x$。
Motivated by experimental observations, Samajdar et al. [Nature Physics 15, 1290 (2019)] have proposed that the insulating Neel state in the parent compounds of the cuprates is proximate to a quantum phase transition to a state in which Neel order coexists with semion topological order. We study the manner in which proximity to this transition can make the phonons chiral, by inducing a significant phonon Hall viscosity. We describe the spinon-phonon coupling in a lattice spinon model coupled to a strain field, and also using a general continuum theory constrained only by symmetry. We find a no…
The nondissipative (Hall) viscosity is known to play an interesting role in two-dimensional (2D) topological states of matter, in the hydrodynamic regime of correlated materials, and in classical active fluids with broken time-reversal symmetry (TRS). However, generalizations of these effects to 3D have remained elusive. In this work, we address this question by studying the Hall viscoelastic response of 3D crystals. We show that for systems with tetrahedral symmetries, there exist new, intrinsically 3D Hall viscosity coefficients that cannot be obtained via a reduction to a quasi-2D system. T…
We compute the Hall viscosity and conductivity of non-relativistic two-dimensional chiral superconductors, where fermions pair due to a short-range attractive potential, e.g. $p+\mathrm{i}p$ pairing, and interact via a long-range repulsive Coulomb force. For a logarithmic Coulomb potential, the Hall viscosity tensor contains a contribution that is singular at low momentum, which encodes corrections to pressure induced by an external shear strain. Due to this contribution, the Hall viscosity cannot be extracted from the Hall conductivity in spite of Galilean symmetry. For mixed-dimensional chir…
We show that Coulomb drag in hydrodynamic bilayer systems leads to additional viscosity terms in the hydrodynamic equations, i.e., the drag and drag-Hall viscosities, besides the well-known kinematic and Hall viscosities. These new viscosity terms arise from a change of the stress tensor due to the interlayer Coulomb interactions. All four viscosity terms are tunable by varying the applied magnetic field and the electron densities in the two layers. At certain ratios between the electron densities in the two layers, the drag viscosity dramatically changes the longitudinal transport resulting i…
We examine the physical implications of the viscous redundancy of two-dimensional anisotropic fluids, where different components of the viscosity tensor lead to identical effects in the bulk of a system [Rao and Bradlyn, Phys. Rev. X $\textbf{10}$, 021005 (2020)]. We first re-introduce the redundancy, show how it reflects a lack of knowledge of microscopic information of a system, and give microscopic examples. Next, we show that fluid flow in systems with a boundary can distinguish between otherwise redundant viscosity coefficients. In particular, we show how the dispersion and damping of gra…
Phonon Hall Viscosity and the Intrinsic Thermal Hall Effect of $α$-RuCl$_3$
Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固态物理实验室）；Department of Physics, University of Toronto（多伦多大学物理系）；Canadian Institute for Advanced Research（加拿大高级研究院）
The Phonon Hall Viscosity is the leading term evincing time-reversal symmetry breaking in the low energy description of lattice phonons. It may generate phonon Berry curvature, and can be observed experimentally through the acoustic Faraday effect and thermal Hall transport. We present a systematic procedure to obtain the phonon Hall viscosity induced by phonon-magnon interactions in magnetic insulators under an external magnetic field. We obtain a general symmetry criterion that leads to non-zero Faraday rotation and Hall conductivity, and clarify the interplay between lattice symmetry, spin-…
Hall viscosity from metric-sensitive dichroic probes
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Instituto de Telecomunicações（电信研究所）；Instituto Superior Técnico, Universidade de Lisboa（里斯本理工大学）；Advanced Institute for Materials Research (WPI-AIMR), Tohoku University（东北大学先进材料研究所）；Laboratoire Kastler Brossel, Collège de France（法兰西学院卡斯勒-布罗塞尔实验室）；ENS-Université PSL（巴黎高等师范学院-巴黎文理研究大学）；Sorbonne Université（索邦大学）；International Solvay Institutes（国际索尔维研究所）；Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles（布鲁塞尔自由大学非线性现象与复杂系统中心）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学科际理论数学科学中心）
Hall viscosity, also known as the Lorentz shear modulus, has been proposed as a topological property of a quantum Hall fluid. Using a recent formulation of the composite fermion theory on the torus, we evaluate the Hall viscosities for a large number of fractional quantum Hall states at filling factors of the form $ν=n/(2pn\pm 1)$, where $n$ and $p$ are integers, from the explicit wave functions for these states. The calculated Hall viscosities $η^A$ agree with the expression $η^A=(\hbar/4) {\cal S}ρ$, where $ρ$ is the density and ${\cal S}=2p\pm n$ is the "shift" in the spherical geometry. We…
We carried out a comprehensive study of electronic transport, thermal and thermodynamic properties in FeCr$_2$Te$_4$ single crystals. It exhibits bad-metallic behavior and anomalous Hall effect (AHE) below a weak-itinerant paramagentic-to-ferrimagnetic transition $T_c$ $\sim$ 123 K. The linear scaling between the anomalous Hall resistivity $ρ_{xy}$ and the longitudinal resistivity $ρ_{xx}$ implies that the AHE in FeCr$_2$Te$_4$ is most likely dominated by extrinsic skew-scattering mechanism rather than intrinsic KL or extrinsic side-jump mechanism, which is supported by our Berry phase calcula…
In the context of recent experimental observations of an unexpectedly large thermal Hall conductivity, $κ_H$, in insulating $\mathrm{La_2CuO_4}$ (LCO) and $\mathrm{SrTiO_3}$ (STO), we theoretically explore conditions under which acoustic phonons can give rise to such a large $κ_H$. Both the intrinsic and extrinsic contributions to $κ_H$ are large in proportion to the dielectric constant, $ε$, and the flexoelectric coupling, $F$. While the intrinsic contribution is still orders of magnitude smaller than the observed effect, an extrinsic contribution proportional to the phonon mean free path app…
Hall viscosity of the Laughlin state on noisy quantum computers
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；City College of the City University of New York（纽约市立学院）；Western Washington University（西华盛顿大学）；Graduate Center of City University of New York（纽约市立大学研究生中心）
