Model quantum Hall states including Laughlin, Moore-Read and Read-Rezayi states are generalized into appropriate anisotropic form. The generalized states are exact zero-energy eigenstates of corresponding anisotropic two- or multi-body Hamiltonians, and explicitly illustrate the existence of geometric degrees of in the fractional quantum Hall effect. These generalized model quantum Hall states can provide a good description of the quantum Hall system with anisotropic interactions. Some numeric results of these anisotropic quantum Hall states are also presented.
In this work, we argue that an anisotropic interaction potential may stabilize anisotropic liquid phases of electrons even in a strong magnetic field regime where normally one expects to see only isotropic quantum Hall or isotropic Fermi liquid states. We use this approach to support a theoretical framework that envisions the possibility of an anisotropic liquid crystalline state of electrons in the lowest Landau level. In particular, we argue that an anisotropic liquid state of electrons may stabilize in the lowest Landau level close to the liquid-solid transition region at filling factor $ν=…
We probe the relationship between magnetism and "non-metallic" transport in the magnetically frustrated metal FeCrAs using the low-field Hall effect. We find that the low-field Hall coefficient is dependent on crystal orientation, and exhibits two temperature-induced sign reversals when the current is within the $ab$-plane. We suggest that these observations are due to scattering from magnetic fluctuations that become momentum-dependent near the onset of long-range magnetic order. It seems, however, that this additional spin-fluctuation scattering rides on top of the non-metallic resistivity, …
Geometry of Compressible and Incompressible Quantum Hall States: Application to Anisotropic Composite Fermion Liquids
本文将分数量子霍尔态的几何描述推广到可压缩态。结果表明，在复合费米子费米表面的各向异性是这种内在的几何形状的直接反映。提出了一个简单的模型，该模型中的几何参数可以由包括电子质量各向异性在内的其它参数精确地求得。我们的结果与最近复合费米子费米面各向异性的测量结果[D. Kamburov，Y. Liu，M.沙耶甘湖N. Pfeiffer，K. W. West和K. W. Baldwin，Phys. Rev. Lett. 110，206801（2013）]。更广泛的影响，我们的研究结果进行了讨论。
The microscopic wave functions of the composite fermion theory can incorporate electron mass anisotropy by a trivial rescaling of the coordinates. These wave functions are very likely adiabatically connected to the actual wave functions of the anisotropic fractional quantum Hall states. We show in this article that they possess the nice property that their energies can be analytically related to the previously calculated energies for the isotropic states through a universal scale factor, thus allowing an estimation of several observables in the thermodynamic limit for all fractional quantum Ha…
We study the effects of anisotropic interactions in the quantum Hall effect in the presence of a fourfold discrete rotational ($C_4$) symmetry. Employing the density matrix renormalization group technique on an infinite cylinder geometry (iDMRG), we calculate the anisotropy response of the Laughlin state at $ν=1/3$ and the composite-Fermi liquid (CFL) state at $ν=1/2$. We find that the anisotropy transferred from the interaction potential to the $ν=1/3$ state is stronger when compared to the complementary case of an anisotropic band. Further, the strength of anisotropy reduces as the interacti…
The Hall effect in the organic conductor TTF-TCNQ: Choice of geometry for accurate measurements of highly anisotropic system
我们测量了最近合成的准一维有机导体TTF-TCNQ单晶的霍尔效应，TTF-TCNQ是一种众所周知的电荷转移复合物，具有两种导电堆叠：供体（TTF）和受体（TCNQ）链。在30 K < T < 300 K的温度区间内，针对通过晶体的几个不同的磁场和电流方向进行测量。通过应用等效各向同性样品（EIS）的方法，我们已经证明了最佳的几何形状的选择准确的霍尔效应测量的重要性。我们的结果表明，与过去的信念相反，霍尔系数不依赖于测量的几何形状，并且在高温区（T > 150 K）霍尔系数值约为零，这意味着没有TTF或TCNQ链的优势。在较低的温度下，我们的测量清楚地证明了所有的三个相变TTF-TCNQ可以识别从霍尔效应测量。
We theoretically investigate the anomalous Hall effect (AHE) that requires neither a net magnetization nor an external magnetic field in collinear antiferromagnets. We show that such an emergent AHE is essentially caused by a ferroic ordering of the anisotropic magnetic dipole (AMD), which provides an effective coupling between ordered magnetic moments and electronic motion in the crystal. We demonstrate that the AMD is naturally induced by the antiferromagnetic ordering, in which the magnetic moments have a quadrupole spatial distribution. In view of the ferroic AMD ordering, we analyze the b…
A spin valve is a prototype of spin-based electronic devices found on ferromagnets, in which an antiferromagnet plays a supporting role. Recent findings in antiferromagnetic spintronics show that an antiferromagnetic order in single-phase materials solely governs dynamic transport, and antiferromagnets are considered promising candidates for spintronic technology. In this work, we demonstrated antiferromagnet-based spintronic functionality on an itinerant Ising antiferromagnet of Ca0.9Sr0.1Co2As2 by integrating nanoscale spin-valve-type structure and investigating anisotropic magnetic properti…
Fractional quantum Hall (FQH) states are known to possess an internal metric degree of freedom that allows them to minimize their energy when contrasting geometries are present in the problem (e.g., electron band mass and dielectric tensor). We investigate the internal metric of several incompressible FQH states by probing its response to band mass anisotropy using infinite DMRG simulations on a cylinder geometry. We test and apply a method to extract the internal metric of a FQH state from its guiding center structure factor. We find that the response to band mass anisotropy is approximately …
We generalize the notion of Haldane pseudopotentials to anisotropic fractional quantum Hall (FQH) systems which are physically realized, e.g., in tilted magnetic field experiments or anisotropic band structures. This formalism allows us to expand any translation-invariant interaction over a complete basis, and directly reveals the intrinsic metric of incompressible FQH fluids. We show that purely anisotropic pseudopotentials give rise to new types of bound states for small particle clusters in the infinite plane, and can be used as a diagnostic of FQH nematic order. We also demonstrate that ge…
Anisotropic hysteretic Hall-effect and magnetic control of chiral domains in the chiral spin states of Pr$_2$Ir$_2$O$_7$
我们发现Pr $_2$ Ir $_2$ O $_7$的手征自旋态的反常霍尔效应（AHE）和磁电阻都具有很强的各向异性.在零磁场下低于1.5 K时出现的AHE显示出磁滞现象，这对于沿[111]方向循环的场最为明显。这种滞后是兼容的领域组成的3-在1-出自旋状态，保持共存的2-在2-出自旋冰流形，一旦该领域被删除的场诱导的增长。只有在[111]方向上施加磁场时，我们才观察到一个大的正磁阻和在变磁临界场以上的Shubnikov de Haas振荡。这些观察结果表明，场致自旋织构重构的电子结构的传导电子。
In the presence of mass anisotropy, anisotropic interaction, or in-plane magnetic field, quantum Hall droplets can exhibit shape deformation and internal geometrical degree of freedom. We characterize the geometry of quantum Hall states by principal component analysis, which is a statistical technique that emphasizes variation in a dataset. We first test the method in an integer quantum Hall droplet with dipole-dipole interaction in disk geometry. In the subsequent application to fractional quantum Hall systems with anisotropic Coulomb interaction in torus geometry, we demonstrate that the pri…
We present a study of the thermal Hall effect in the extended Heisenberg model with $XXZ$ anisotropy in the kagome lattice. This model has the particularity that, in the classical case, and for a broad region in parameter space, an external magnetic field induces a chiral symmetry breaking: the ground state is a doubly degenerate $q=0$ order with either positive or negative net chirality. Here, we focus on the effect of this chiral phase transition in the thermal Hall conductivity using Linear-Spin-Waves theory. We explore the topology and calculate the Chern numbers of the magnonic bands, obt…
We present a study of Hall transport in semi-Dirac critical phases. The construction is based on a covariant formulation of relativistic systems with spatial anisotropy. Geometric data together with external electromagnetic fields is used to devise an expansion procedure that leads to a low-energy effective action consistent with the discrete $PT$ symmetry that we impose. We use the action to discuss terms contributing to the Hall transport and extract the coefficients. We also discuss the associated scaling symmetry.
We analytically derived the effective two-body interaction for a finite thickness quantum Hall system with a harmonic perpendicular confinement and an in-plane magnetic field. The anisotropic effective interaction in the lowest Landau level (LLL) and first Landau level (1LL) are expanded in the basis of the generalized pseudopotentials (PPs), and we analyze how the coefficients of some prominent isotropic and anisotropic PPs depend on the thickness of the sample and the strength of the in-plane magnetic field. We also investigate the stability of the topological quantum Hall states, especially…
We construct a low energy effective theory of anisotropic fractional quantum Hall (FQH) states. We develop a formalism similar to that used in the bi-metric approach to massive gravity, and apply it to describe abelian anisotropic FQH states in the presence of external electromagnetic and geometric backgrounds. We derive a relationship between the shift, the Hall viscosity, and a new quantized coupling to anisotropy, which we term "anisospin". We verify this relationship by numerically computing the Hall viscosity for a variety of anisotropic quantum Hall states using the density matrix renorm…
When a conduction electron couples with a non-coplanar localized magnetic moment, the realspace Berry curvature is exerted to cause the geometrical Hall effect, which is not simply proportional to the magnetization. So far, it has been identified in the case mostly where the non-coplanar magnetic order is present on the sublattice of conduction electrons. Here, we demonstrate that the geometrical Hall effect shows up even without long-range magnetic order of conduction electrons, as induced by non-coplanar exchange fields from the localized magnetic moments, in hole-doped phyrochlore molybdate…
We investigate parity-odd non-dissipative transport in an anisotropic Dirac semi-metal in two spatial dimensions. The analysis is relevant for interacting electronic systems with merging Dirac points at charge neutrality. For such systems the dispersion relation is relativistic in one direction and non-relativistic in the other. We give a proposal how to calculate the Berry curvature for this system and use it to derive more than one odd viscosities, in contrast to rotationally invariant systems. We observe that in such a model the odd part of stress tensor is parameterised by two independent …
In recent experiments, external anisotropy has been a useful tool to tune different phases and study their competitions. In this paper, we look at the quantum Hall charge density wave states in the $N=2$ Landau level. Without anisotropy, there are two first-order phase transitions between the Wigner crystal, the $2$-electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the $2$-electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that m…
We study broken symmetry states at integer Landau level fillings in multivalley quantum Hall systems whose low energy dispersions are anisotropic. When the Fermi surface of individual pockets lacks twofold rotational symmetry, like in Bismuth (111) and in Sn$_{1-x}$Pb$_x$Se (001) surfaces, interactions tend to drive the formation of quantum Hall ferroelectric states. We demonstrate that the dipole moment in these states has an intimate relation to the Fermi surface geometry of the parent metal. In quantum Hall nematic states, like those arising in AlAs quantum wells, we demonstrate the existen…
Weyl semimetals are promising quantum materials that offer unique topological properties. Lately, it has been shown that laser-driven electron dynamics have characteristic signatures in two-dimensional and three-dimensional Dirac semimetals. The transition from Dirac to Weyl semimetal requires the breaking of either inversion or time-reversal symmetry. The present work shows that the laser-driven electron dynamics in a Weyl semimetal with broken time-reversal symmetry has intriguing features in its high-harmonic spectrum. It is found that the parity and magnitude of the non-zero Berry curvatur…
Anisotropic Magneto Resistance and Planar Hall Effect at the LaAlO$_3$/SrTiO$_3$ Heterointerfaces: Effect of Carrier Confinement on Magnetic Interactions
Fractional quantum Hall states (FQHSs) at even-denominator Landau level filling factors ($ν$) are of prime interest as they are predicted to host exotic, topological states of matter. We report here the observation of a FQHS at $ν=1/2$ in a two-dimensional electron system of exceptionally high quality, confined to a wide AlAs quantum well, where the electrons can occupy multiple conduction-band valleys with an anisotropic effective mass. The anisotropy and multi-valley degree of freedom offer an unprecedented tunability of the $ν=1/2$ FQHS as we can control both the valley occupancy via the ap…
We present a microscopic study of quasiholes in bosonic fractional quantum Hall (FQH) liquids at filling factor $ν=1/2$ in the lowest Landau level with anisotropic band mass tensors. We use the spatial density profile to characterize the shape of a quasihole and analyze its anisotropy. We then compare the quasihole's anisotropy with the intrinsic geometric metric of the system that is extracted from the maximal overlap between the numerically obtained quasihole ground state and a set of model wave functions of anisotropic quasiholes. For a static system, we find that the quasihole's anisotropy…
We study the $ν={\pm}1/2$ fractional quantum Hall states in graphene observed by Zibrov et al. [Nat. Phys. 14, 930 (2018)]. The parton construction is employed to provide a valley unpolarized trial wave function for these states. The lattice scale valley anisotropic terms in the Hamiltonian soften the repulsion between electrons in different valleys to favor the valley unpolarized state. The validity of our proposal is corroborated by numerical calculations.
Perfect elliptic dichroism: Probing the metric of anisotropic quantum Hall droplets
Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等理工学院）；Advanced Institute for Materials Research (WPI-AIMR), Tohoku University（东北大学先进材料研究所（WPI-AIMR））；Université Paris-Saclay, CNRS, LPTMS（巴黎萨克雷大学，法国国家科学研究中心，理论与实验物理实验室）；Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université（卡斯勒-布罗塞尔实验室，法兰西公学院，法国国家科学研究中心，巴黎文理研究大学，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（理化学研究所跨学科理论与数学科学中心（iTHEMS））
Volborthite offers an interesting example of a highly frustrated quantum magnet in which ferromagnetic and antiferromagnetic interactions compete on anisotropic kagome lattices. A recent density functional theory calculation has provided a magnetic model based on coupled trimers, which is consistent with a broad 1/3-magnetization plateau observed experimentally. Here we study the effects of Dzyaloshinskii-Moriya (DM) interactions in volborthite. We derive an effective model in which pseudospin-1/2 moments emerging on trimers form a network of an anisotropic triangular lattice. Using the effect…
We propose a family of Abelian quantum Hall states termed the non-diagonal states, which arise at filling factors $ν=p/2q$ for bosonic systems and $ν=p/(p+2q)$ for fermionic systems, with $p$ and $q$ being two coprime integers. Non-diagonal quantum Hall states are constructed in a coupled wire model, which shows an intimate relation to the non-diagonal conformal field theory and has a constrained pattern of motion for bulk quasiparticles, featuring a non-trivial interplay between charge symmetry and translation symmetry. The non-diagonal state is established as a distinctive symmetry-enriched …
Theoretical and experimental studies have revealed that electrons in condensed matter can behave hydrodynamically, exhibiting fluid phenomena such as Stokes flow and vortices. Unlike classical fluids, preferred directions inside crystals lift isotropic restrictions, necessitating a generalized treatment of electron hydrodynamics. We explore electron fluid behaviors arising from the most general viscosity tensors in two and three dimensions, constrained only by thermodynamics and crystal symmetries. Hexagonal 2D materials such as graphene support flows indistinguishable from those of an isotrop…
