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 topological order. Aside from the usual $U(1)$ charge sector, there is an additional symmetry-enriched neutral sector described by the quantum double model $\mathcal{D}(\mathbb{Z}_p)$, which relies on the presence of both the $U(1)$ charge symmetry and the $\mathbb{Z}$ translation symmetry of the wire model. Translation symmetry distinguishes non-diagonal states from Laughlin states, in a way similar to how it distinguishes weak topological insulators from trivial band insulators. Moreover, the translation symmetry in non-diagonal states can be associated to the $\mathbf{e}\leftrightarrow\mathbf{m}$ anyonic symmetry in $\mathcal{D}(\mathbb{Z}_p)$, implying the role of dislocations as two-fold twist-defects. The boundary theory of non-diagonal states is derived microscopically. For the edge perpendicular to the direction of wires, the effective Hamiltonian has two components: a chiral Luttinger liquid and a generalized $p$-state clock model. Importantly, translation symmetry in the bulk is realized as self-duality on the edge. The symmetric edge is thus either gapless or gapped with spontaneously broken symmetry. For $p=2,3$, the respective electron tunneling exponents are predicted for experimental probes.
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…
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 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 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…
Frequency Dependence of Diagonal Resistance in Fractional Quantum Hall Effect via Periodic Modulation of Magnetic Field
分数量子霍尔（FractionalQuantumHall，简称FQH）态的能谱由忽略电子间库仑相互作用的单电子能量（朗道能量）、经典库仑能量和通过量子跃迁产生的量子能量组成。在此，朗道能和经典库仑能之和连续地取决于填充因子的值。然而，量子跃迁能量不连续地依赖于填充因子的值。这种不连续性产生了许多稳定的C3 H态的能隙。特定填充因子的能隙产生霍尔电阻的精确限制。一个新的实验被认为是如下;作为一个例子，磁场强度被固定为在2/3的填充因子下限制霍尔电阻的值。此外，频率为f的磁调制应用于系统。测量了对角电阻的频率依赖性。然后，它是在本文中示出的对角电阻急剧变化，在某些频率值f0。我们阐明了该值f_0与霍尔平台磁场强度宽度dB之间的关系为f_0 = e dB /（4 π m），其中-e为电子电荷，Pi =3.141592，m为电子质量。
By employing the holographic operator mixing technique to deal with coupled perturbations in the gauge/gravity duality, I numerically compute the real and imaginary parts of the diagonal and Hall AC conductivities in a strongly coupled quantum field theory dual to a bulk condensate of magnetic monopoles. The results obtained show that a conclusion previously derived in the literature, namely, the vanishing of holographic DC conductivities in 3-dimensional strongly coupled quantum field theories dual to a 4-dimensional bulk magnetic monopole condensate, also applies to the calculation of diagon…
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。
Employing exact diagonalization, we systematically study the anisotropic Heisenberg model which is related to rare-earth triangular-lattice materials. We probe its full 3D phase diagram afresh and identify a large region of quantum spin liquid (QSL) phase which can extend to the QSL region of the $J_1$--$J_2$ triangular Heisenberg model. Furthermore, we explore the magnetization curves of different phases and reproduce the 1/3-magnetization plateau in the quantum spin liquid phase region. More importantly, to study the possible chemical disorders in real materials, we consider the randomness o…
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 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…
Much has been learned about the topological transport in real materials. We investigate the interplay between magnetism and topology in the magneto-transport of PrRhC$_2$. The four-fold degeneracy reduces to two-fold followed by non-degenerate Weyl nodes when the orientation of the magnetic quantization axis is changed from easy axis to body-diagonal through face-diagonal. This engenders chirality imbalance between positive and negative chirality Weyl nodes around the Fermi energy. We observe a significant enhancement in the chiral anomaly mediated response such as planar Hall conductivity and…
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…
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…
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…
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 …
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…
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。
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…
Synthetic quantum Hall bilayer (SQHB), realized by optically driven monolayer graphene in the quantum Hall regime, provides a flexible platform for engineering quantum Hall phases as discussed in [Phys. Rev. Lett. 119, 247403]. The coherent driving which couples two Landau levels mimicks an effective tunneling between synthetic layers. The tunneling strength, the effective Zeeman coupling, and two-body interaction matrix elements are tunable by varying the driving frequency and the driving strength. Using infinite density matrix renormalization group (iDMRG) techniques combined with exact diag…
Magneto-cubic and magneto-linear dependence observed in an in-plane anomalous Hall magnet
Institute of Science Tokyo（东京科学大学）；Institute for Materials Research (IMR), Tohoku University（东北大学物质材料研究所）；Advanced Science Research Center, Japan Atomic Energy Agency (JAEA)（日本原子能研究开发机构先进科学研究中心）；Institute for Solid State Physics (ISSP), The University of Tokyo（东京大学固体物理研究所）；Toyota Physical and Chemical Research Institute (TPCRI)（丰田物理化学研究所）
We study the phase transitions of bosonic $ν=1/2$ fractional quantum Hall (FQH) effect in different topological lattice models under the interplay of onsite periodic potential and Hubbard repulsion. Through exact diagonalization and density matrix renormalization group methods, we demonstrate that the many-body ground state undergoes a continuous phase transition between bosonic FQH liquid and a trivial (Mott) insulator induced by the periodic potential, characterized by the smooth crossover of energy and entanglement entropy. When the Hubbard repulsion decreases, we claim that this bosonic FQ…
Anisotropic Magneto Resistance and Planar Hall Effect at the LaAlO$_3$/SrTiO$_3$ Heterointerfaces: Effect of Carrier Confinement on Magnetic Interactions
