When phonons couple to fermions in 2D semimetals, the interaction may turn the system into an insulator. There are several insulating phases in which the time reversal and the sublattice symmetries are spontaneously broken. Examples are many-body states commensurate to Haldane's staggered flux model or to lattice models with periodically modulated strain. We find that the effective field theories of these phases exhibit characteristic Chern-Simons terms, whose coefficients are related to the topological invariants of the microscopic model. This implies that the corresponding quantized Hall conductivities characterize these insulating states.
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-…
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 …
The recent observation of a half-integer quantized thermal Hall effect in $α$-RuCl$_3$ is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity $κ_xy$ is never exactly quantized in real materials. Here, we investigate how phonons affect the quantization of the thermal conductivity focusing on the edge theory. As an …
We investigate the thermal Hall effect in a Kitaev-Heisenberg system, a model for Kitaev candidate $α$-RuCl$_3$, in the presence of the coupling between spin and phonon arising from chlorine atoms' vibration. We observe that the coupling modifies the relative stability between different magnetic states under a magnetic field, especially stabilizing a canted zigzag antiferromagnetic state. Remarkably, the spin-phonon interaction has distinct effects on the thermal Hall conductivity in different magnetically ordered states. For the canted zigzag state, which is relevant to $α\text{-RuCl}_3$, the…
Phonons are known to generate a thermal Hall effect in certain insulators, including oxides with rare-earth impurities, quantum paraelectrics, multiferroic materials and cuprate Mott insulators. In each case, a special feature of the material is presumed relevant for the underlying mechanism that confers chirality to phonons in a magnetic field. The question is whether a phonon Hall effect is an unusual occurrence - linked to special characteristics such as skew scattering off rare-earth impurities, structural domains, ferroelectricity, ferromagnetism - or a much more common property of insula…
A distinct thermal Hall signal is observed in a quantum spin liquid candidate Ba$_3$CuSb$_2$O$_9$. The transverse thermal conduction shows a power-law temperature dependence below 40 K where a spin gap opens. We suggest that, through the very low longitudinal thermal conductivity and the thermal Hall signals, a phonon Hall effect is induced by strong phonon scatterings by orphan Cu$^{2+}$ spins formed in random domains of Cu$^{2+}$-Sb$^{5+}$ dumbbells.
We present computations of the thermal Hall coefficient of phonons scattering off a defect with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is proportional to the phonon lifetime, and has a `side-jump' interpretation. Consequently, the thermal Hall angle is independent of the phonon lifetime. The contribution to the thermal Hall coefficient is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for three different defect models, which a…
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…
Microscopic origin of an exceptionally large phonon thermal Hall effect from charge puddles in a topological insulator
Institute for Topological Insulators, Universität Würzburg（维尔茨堡大学拓扑绝缘体研究所）；II. Physikalisches Institut, Universität zu Köln（科隆大学第二物理研究所）；High Magnetic Field Lab. of Anhui Province, HFIPS, Chinese Academy of Sciences（中国科学院合肥物质科学研究院安徽省高磁场实验室）；Institute for Theoretical Physics, Universität zu Köln（科隆大学理论物理研究所）
Thermal Hall conductivity of semimetallic graphite dominated by ambipolar phonon drag
Wuhan National High Magnetic Field Center, School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院）；Laboratoire de Physique et d’Étude des Matériaux (ESPCI - CNRS - Sorbonne Université), PSL Research University（巴黎高等物理化工学院-法国国家科学研究中心-索邦大学物质物理与研究实验室）
We study the acoustic phonon response of crystals hosting a gapped time-reversal symmetry breaking electronic state. The phonon effective action can in general acquire a dissipationless "Hall" viscosity, which is determined by the adiabatic Berry curvature of the electron wave function. This Hall viscosity endows the system with a characteristic frequency, ω_v; for acoustic phonons of frequency ω, it shifts the phonon spectrum by an amount of order (ω/ω_v)^2 and it mixes the longitudinal and transverse acoustic phonons with a relative amplitude ratio of ω/ω_v and with a phase shift of +/- π/2,…
Because electrons and ions form a coupled system, it is a priori clear that the dynamics of the lattice should reflect symmetry breaking within the electronic degrees of freedom. This has been recently clearly evidenced for the case of time-reversal and mirror symmetry breakings by observations of a large phononic thermal Hall effect in many strongly correlated electronic materials. The mechanism by which time-reversal breaking and chirality is communicated to the lattice is, however, far from evident. In this paper we discuss how this occurs via many-body scattering of phonons by collective m…
Fermions with one and two Dirac nodes are coupled to in-plane phonons to study a spontaneous transition into the Hall insulating phase. At sufficiently strong electron-phonon interaction a gap appears in the spectrum of fermions, signaling a transition into a phase with spontaneously broken parity and time-reversal symmetry. The structure of elementary excitations above the gap in the corresponding phase reveals the presence of scale invariant parity breaking terms which resemble Chern-Simons excitations. Evaluating the Kubo formula for both models we find quantized Hall plateaux in each case,…
SrTiO$_3$, a quantum paralectric, displays a detectable phonon thermal Hall effect (THE). Here we show that the amplitude of THE is extremely sensitive to stoichiometry. It drastically decreases upon substitution of a tiny fraction of Sr atoms with Ca, which stabilizes the ferroelectric order. It drastically increases by an even lower density of oxygen vacancies, which turn the system to a dilute metal. The enhancement in the metallic state exceeds by far the sum of the electronic and the phononic contributions. We explain this observation as an outcome of three features: i) heat is mostly tra…
The anomalous Hall effect in a multiband tight-binding model is numerically studied taking into account both elastic scattering by disorder and inelastic scattering by the electron-phonon interaction. The Hall conductivity is obtained as a function of temperature $T$, inelastic scattering rate $γ$, chemical potential $μ$, and impurity concentration $x_{\rm imp}$. We find that the new scaling law holds over a wide range of these parameters; $-σ_{xy}= (ασ_{xx0}^{-1} + βσ_{xx0}^{-2}) σ_{xx}^2 + b$, with $σ_{μν}$ ($σ_{μν0}$) being the conductivity tensor (with only elastic scattering), which corre…
Density-wave order enhances the phonon thermal Hall effect in a trilayer nickelate
Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院）；State Key Laboratory of Surface Physics and Department of Physics, Fudan University（复旦大学物理系）；State Key Laboratory of Quantum Functional Materials, School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院）；Department of Physics, Tsinghua University（清华大学物理系）
We study the nature of the debated thermal Hall effect in the candidate Kitaev material $α$-RuCl$_3$. Without assuming the existence of a gapped spin liquid, we show that a realistic minimal spin model in the canted zigzag phase suffices, at the level of linear spin-wave theory, to qualitatively explain the observed temperature and magnetic field dependence of the non-quantized thermal Hall conductivity $κ_{xy}$, with its origin lying in the Berry curvature of the magnon bands. The magnitude of the effect is however too small compared to the measurement by Czajka et al. [Nat. Mater. 22, 36-41 …
Thermal Hall Resistivity as a Unifying Description of Phonon Thermal Hall Effect in Various Insulators
Nanyang Technological University（南洋理工大学）；National High Magnetic Field Laboratory, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室国家高磁场实验室）；National High Magnetic Field Laboratory（国家高磁场实验室）；Institute of Science Tokyo（东京科学大学）；National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）
We study the transport properties of the quantum Hall bilayers systems looking closely at the effect that disorder and electron-phonon interaction have on the interlayer tunnelling current in the presence of an in-plane magnetic field $B_\parallel$. We find that it is important to take into account the effect of disorder and electron-phonon interactions in order to predict a finite current at a finite voltage when an in-plane magnetic field is present. We find a broadened resonant feature in the tunnelling current as a function of bias voltage, in qualitative agreement with experiments. We als…
We theoretically study the intrinsic thermal Hall and spin Nernst effect in collinear ferrimagnets on a honeycomb lattice with broken inversion symmetry. The broken inversion symmetry allows in-plane Dzyaloshinskii-Moriya interaction between the nearest neighbors, which does not affect the magnon spectrum in the linear spin wave theory. However, the Dzyaloshinskii-Moriya interaction can induce large Berry curvature in the magnetoelastic excitation spectrum through the magnon-phonon interaction to produce thermal Hall current. Furthermore, we find that the magnetoelastic excitations transport s…
Thermal Hall conductivity of electron-doped cuprates: Electrons and phonons
Université de Sherbrooke（舍布鲁克大学）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Univ. Toulouse（图卢兹大学）；INSA-T（图卢兹国立应用科学学院）；École Polytechnique（巴黎综合理工学院）；Institut Polytechnique de Paris（巴黎理工学院）；Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（斯坦福线性加速器中心）
The origin of phonon thermal Hall Effect (THE) observed in a variety of insulators is yet to be identified. Here, we report on the observation of a thermal Hall conductivity in a non-magnetic elemental insulator, with an amplitude exceeding what has been previously observed. In black phosphorus (BP), the longitudinal ($κ_{ii}$), and the transverse, $κ_{ij}$, thermal conductivities peak at the same temperature and at this peak temperature, the $κ_{ij}/κ_{jj}/B $ is $\approx 10^{-4}$-$10^{-3}$ T$^{-1}$. Both these features are shared by other insulators displaying THE, despite an absolute amplit…
The thermal Hall effect, which arises when heat flows transverse to an applied thermal gradient, has become an important observable in the study of quantum materials. Recent experiments found a large thermal Hall conductivity $κ_{xy}$ in many high-temperature cuprate superconductors, including deep inside the Mott insulator, but the underlying mechanism remains unknown. Here, we uncover a surprising linear temperature dependence for the inverse thermal Hall resistivity, $1/ρ_H=-κ_{xx}^2/κ_{xy}$, in the Mott insulating cuprates $\mathrm{La_2CuO_4}$ and $\mathrm{Sr_2CuO_2Cl_2}$. We also find thi…
Microscopic Theory of the Phonon Thermal Hall Effect in Chiral Mott Insulators
Seoul National University（首尔大学）；Soongsil University（崇实大学）；Origin of Matter and Evolution of Galaxies (OMEG) institute, Soongsil University（崇实大学物质起源与星系演化研究所）
We have investigated the thermal-transport properties of the kagome antiferromagnet Cd-kapellasite (Cd-K). We find that a field suppression effect on the longitudinal thermal conductivity k_xx sets in below ~25 K, suggesting a large spin contribution k_xx^sp in k_xx. We also find clear thermal Hall signals in the spin liquid phase in all Cd-K samples. The magnitude of the thermal Hall conductivity k_xy shows a significant dependence on the sample's scattering time. On the other hand, the temperature dependence of k_xy is similar in all Cd-K samples; k_xy shows a peak at almost the same tempera…
It has become common knowledge that phonons can generate thermal Hall effect in a wide variety of materials, although the underlying mechanism is still controversial. We study longitudinal $κ_{xx}$ and transverse $κ_{xy}$ thermal conductivity in Pr$_2$Ir$_2$O$_7$, which is a metallic analogue of spin ice. Despite the presence of mobile charge carriers, we find that both $κ_{xx}$ and $κ_{xy}$ are dominated by phonons. A $T/H$ scaling of $κ_{xx}$ unambiguously reveals that longitudinal heat current is substantially impeded by resonant scattering of phonons on paramagnetic spins. Upon cooling, th…
The material $α$-RuCl$_3$ has been the subject of intense scrutiny as a potential Kitaev quantum spin liquid, predicted to display Majorana fermions as low energy excitations. In practice, $α$-RuCl$_3$ undergoes a transition to a state with antiferromagnetic order below a temperature $T_{\rm N}$ $\approx$ 7 K, but this order can be suppressed by applying an external in-plane magnetic field of $H_\parallel$ = 7 T. Whether a quantum spin liquid phase exists just above that field is still an open question, but the reported observation of a quantized thermal Hall conductivity at $H_\parallel$ $>$ …
The search for fractionalization in quantum spin liquids largely relies on their decoupling with the environment. However, the spin-lattice interaction is inevitable in a real setting. While the Majorana fermion evades a strong decay due to the gradient form of spin-lattice coupling, the study of the phonon dynamics may serve as an indirect probe of fractionalization of spin degrees of freedom. Here we propose that the signatures of fractionalization can be seen in the sound attenuation and the Hall viscosity. Despite the fact that both quantities can be related to the imaginary part of the ph…
The nature of the pseudogap phase of cuprates remains a major puzzle. One of its new signatures is a large negative thermal Hall conductivity $κ_{\rm xy}$, which appears for dopings $p$ below the pseudogap critical doping $p^*$, but whose origin is as yet unknown. Because this large $κ_{\rm xy}$ is observed even in the undoped Mott insulator La$_2$CuO$_4$, it cannot come from charge carriers, these being localized at $p = 0$. Here we show that the thermal Hall conductivity of La$_2$CuO$_4$ is roughly isotropic, being nearly the same for heat transport parallel and normal to the CuO$_2$ planes,…
Measurements of the thermal Hall conductivity in hole-doped cuprates have shown that phonons acquire chirality in a magnetic field, both in the pseudogap phase and in the Mott insulator state. The microscopic mechanism at play is still unclear. A number of theoretical proposals are being considered, including skew scattering of phonons by various defects, the coupling of phonons to spins, and a state of loop-current order with the appropriate symmetries, but more experimental information is required to constrain theoretical scenarios. Here we present our study of the thermal Hall conductivity …
We address the problem of Dirac fermions interacting with longitudinal phonons. A gap in the spectrum of fermions leads to the emergence of the Chern--Simons excitations in the spectrum of phonons. We study the effect of those excitations on observable quantities: the phonon dispersion, the phonon spectral density, and the Hall conductivity.
Phonon Thermal Hall Effect: The Roles of Disorder, Annealing, and Metallic Contacts
Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院与武汉国家强磁场中心）；Laboratoire de Physique et d’Étude des Matériaux (ESPCI - CNRS - Sorbonne Université), PSL Research University（巴黎高等物理化工大学院校物理与材料实验室（ESPCI-法国国家科学研究中心-索邦大学），PSL研究大学）
Thermal Hall resistivity and transverse entropy production in a phonon gas
Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院）；CPHT, CNRS, École polytechnique, Institut Polytechnique de Paris（巴黎理工学院）；Laboratoire de Physique et d’Étude de Matériaux (CNRS) ESPCI Paris, PSL Research University（巴黎高等物理化工大学）
Observation of anomalous thermal Hall effect in altermagnets
Fudan University（复旦大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究与创新中心）；ShanghaiTech University（上海科技大学）；Hefei National Laboratory（合肥国家实验室）；Collaborative Innovation Center of Advanced Microstructures（先进微结构协同创新中心）
We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev's non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity $κ_{xx}$ due to phonons is much larger than the expected quantized thermal Hall conductance $κ_{xy}^{\rm q}=\frac{πT}{12} \frac{k_B^2}{\hbar}$ of the ideal isolated edge mode, so that the thermal Hall angle, i.e., the angle between the thermal current and the temperature gradient, is small. By modeling the intera…
It has been known for more than a decade that phonons can produce an off-diagonal thermal conductivity in presence of magnetic field. Recent studies of thermal Hall conductivity, $κ_{xy}$, in a variety of contexts, however, have assumed a negligibly small phonon contribution. We present a study of $κ_{xy}$ in quantum paraelectric SrTiO$_3$, which is a non-magnetic insulator and find that its peak value exceeds what has been reported in any other insulator, including those in which the signal has been qualified as 'giant'. Remarkably, $κ_{xy}(T)$ and $κ(T)$ peak at the same temperature and the …
The heat carriers responsible for the unexpectedly large thermal Hall conductivity of the cuprate Mott insulator La$_2$CuO$_4$ were recently shown to be phonons. However, the mechanism by which phonons in cuprates acquire chirality in a magnetic field is still unknown. Here, we report a similar thermal Hall conductivity in two cuprate Mott insulators with significantly different crystal structures and magnetic orders - Nd$_2$CuO$_4$ and Sr$_2$CuO$_2$Cl$_2$ - and show that two potential mechanisms can be excluded - the scattering of phonons by rare-earth impurities and by structural domains. Ou…
Detailed far-infrared spectra of the optical phonons are reported for antiferromagnetic MnO. Eigenfrequencies, phonon damping and effective plasma frequencies are studied as a function of temperature. Special attention is paid to the phonon splitting at the antiferromagnetic phase transition. The results are compared to recent experimental and theoretical studies of the spin-phonon coupling in frustrated magnets, which are explained in terms of a spin-driven Jahn-Teller effect, and to ab initio and model calculations, which predict phonon splitting induced by magnetic order.
We predict a possible phonon softening instability in strongly correlated coupled semiconductor bilayer systems. By studying the plasmon-phonon coupling in coupled bilayer structures, we find that the renormalized acoustic phonon frequency may be softened at a finite wave vector due to many-body local field corrections, particularly in low density systems where correlation effects are strong. We discuss experimental possibilities to search for this predicted phonon softening phenomenon.
