We fabricate high-mobility p-type few-layer WSe2 field-effect transistors and surprisingly observe a series of quantum Hall (QH) states following an unconventional sequence predominated by odd-integer states under a moderate strength magnetic field. By tilting the magnetic field, we discover Landau level (LL) crossing effects at ultra-low coincident angles, revealing that the Zeeman energy is about three times as large as the cyclotron energy near the valence band top at Γ valley. This result implies the significant roles played by the exchange interactions in p-type few-layer WSe2, in which itinerant or QH ferromagnetism likely occurs. Evidently, the Γ valley of few-layer WSe2 offers a unique platform with unusually heavy hole-carriers and a substantially enhanced g-factor for exploring strongly correlated phenomena.
The bulk properties of nodal line materials have been an important research topic in recent years. In this paper, we study the orbital magnetic susceptibility and the Hall conductivity of nodal line materials using the formalism with thermal Green's functions and find characteristic singular behaviors of them. It is shown that, in the vicinity of the gapless nodal line, the orbital magnetic susceptibility shows a $δ$-function singularity and the Hall conductivity shows a step function behavior in their chemical potential dependences. Furthermore, these singular behaviors are found to show stro…
Higher odd-order nonlinear Hall effect in magnetic topological insulator Mn(Bi1-xSbx)2Te4
National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Jiangsu Physical Science Research Center, and School of Physics, Nanjing University（南京大学固体微观结构国家重点实验室、先进微结构协同创新中心、江苏省物理科学研究中心组和物理学院）；Institute of Atom Manufacturing, Nanjing University（南京大学原子制造研究所）；Nanjing Institute of Atomic Scale Manufacturing（南京原子尺度制造研究所）；School of Materials Science and Intelligent Engineering, Nanjing University（南京大学材料科学与智能工程学院）；Jiangsu Provincial Key Laboratory of Advanced Photonic and Electronic Materials, State Key Laboratory of Spintronics Devices and Technologies, School of Electronic Science and Engineering, Nanjing University（南京大学电子科学与工程学院、江苏省先进光子与电子材料重点实验室、自旋电子学器件与技术国家重点实验室）；Center for Quantum Transport and Thermal Energy Science, Institute of Physics Frontiers and Interdisciplinary Sciences, School of Physics and Technology, Nanjing Normal University（南京师范大学物理科学与技术学院、前沿交叉科学研究院、量子输运与热能科学中心）；Suzhou Laboratory（苏州实验室）
We report on the quantum Hall effect in two stacked graphene layers rotated by 2 degree. The tunneling strength among the layers can be varied from very weak to strong via the mechanism of magnetic breakdown when tuning the density. Odd-integer quantum Hall physics is not anticipated in the regime of suppressed tunneling for balanced layer densities, yet it is observed. We interpret this as a signature of Coulomb interaction induced interlayer coherence and Bose Einstein condensation of excitons that form at half filling of each layer. A density imbalance gives rise to reentrant behavior due t…
Various nonlinear characteristics of solid states, such as the circular photogalvanic effect of time-reversal symmetric insulators, the quantized photogalvanic effect of Weyl semimetals, and the nonlinear Hall effect of time-reversal symmetric metals, have been associated with the Berry curvature dipole (BCD). Here, we explore the question of whether the Berry curvature dipole and multipoles of time-reversal symmetric insulators can be traced in the nonlinear optical responses. We performed real-time time-dependent density functional theory calculations and examined the second harmonic generat…
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…
We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on $S^{2k-1}$ in the $SO(2k-1)$ monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold $S^{2k-1}$ to the one-dimension higher $SO(2k)$ gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resultin…
Under broken time reversal symmetry such as in the presence of external magnetic field or internal magnetization, a transverse voltage can be established in materials perpendicular to both longitudinal current and applied magnetic field, known as classical Hall effect. However, this symmetry constraint can be relaxed in the nonlinear regime, thereby enabling nonlinear anomalous Hall current in time-reversal invariant materials - an underexplored realm with exciting new opportunities beyond classical linear Hall effect. Here, using group theory and first-principles theory, we demonstrate a rema…
A central theme in condensed matter physics is to create and understand the exotic states of matter by incorporating magnetism into topological materials. One prime example is the quantum anomalous Hall (QAH) state. Recently, MnBi2Te4 has been demonstrated to be an intrinsic magnetic topological insulator and the QAH effect was observed in exfoliated MnBi2Te4 flakes. Here, we used molecular beam epitaxy (MBE) to grow MnBi2Te4 films with thickness down to 1 septuple layer (SL) and performed thickness-dependent transport measurements. We observed a non-square hysteresis loop in the antiferromagn…
Crossed magnetic responses between spin and orbital angular momentum are studied in time-reversal symmetric topological insulators. Due to spin-orbit coupling in the quantum spin Hall systems and three-dimensional topological insulators, the magnetic susceptibility has crossed (intersectional) components between spin and orbital part of magnetism. In this study, the crossed susceptibility for the orbital magnetization is studied in two- and three-dimensional topological insulator models, in which an external magnetic field interacts with the electron spin by Zeeman coupling via distinct g-fact…
A study of the fractional quantum Hall effect: Odd and even denominator plateaux
我们提出了一种不同的方法来分数量子霍尔效应（Fractional quantum Hall effect，简称FQHE），将其聚焦为在磁场的作用下，在存在电离杂质的静电势的情况下，二维电子气（2DEG）中每个电子的哈密顿量的对称性发生变化的结果，并导致朗道能级退化的破坏。随着磁场的增加，静电势的影响也在变化，从而改变了哈密顿量的空间对称性：从连续到离散。这两项工作的目的是给一个不同的图片，不仅是量子霍尔效应的现象，但一个相干的整数量子霍尔效应（IQHE）和已在Hidalgo 7，8，9中描述的模型一致。因此，该模型给出了两种效应的全局视图，表明它们是同一现象的各个方面，并且不仅证明了奇数分母平台的出现，而且证明了偶数分母平台的出现;并且给出了实验事实的一些物理原因，即奇数分母平台比偶数分母平台多得多，几乎没有观察到
NbSe$_2$ is one of metallic two-dimensional (2D) transition-metal dichalcogenide (TMDC) materials. Because of broken crystal inversion symmetry, large spin splitting is induced by Ising-type spin-orbit coupling in odd-number-layered NbSe$_2$, but absent for even-number-layered NbSe$_2$ with the inversion symmetry. In this paper, we numerically calculate nonlinear optical charge and spin Hall conductivities of few-layered NbSe$_2$ based on an effective tight-binding model which includes $d_{z^2}$, $d_{x^2-y^2}$ and $d_{xy}$ orbitals of Nb atom. We show that the nonlinear optical Hall conductivi…
The flow of momentum and energy in a fluid is typically associated with dissipative transport coefficients: viscosity and thermal conductivity. Fluids that break certain symmetries such as mirror symmetry and time-reversal invariance can display non-dissipative transport coefficients called odd (or Hall) viscosities and thermal conductivities. The goal of this paper is to elucidate the microscopic origin of these dissipationless transport coefficients using kinetic theory. We show that odd viscosity and odd thermal conductivity arise when the linearized collision operator is not Hermitian. Thi…
We give a review of theoretical and experimental results concerning the magnetic susceptibility of the Weyl, Dirac, and nodal-line semimetals. In particular, dependences of the susceptibility on the chemical potential, temperature, and magnitude of the magnetic field are discussed. The presented results show that the specific features of the magnetic susceptibility can serve as a hallmark of the topological semimetals, and hence magnetic measurements can be useful in investigating these materials.
Monolayer (ML) semiconducting transition-metal dichalcogenides (TMDs) represent a unique class of two-dimensional (2D) electron systems. Their atomically thin structure -- just like graphene -- facilitates gate-tunability, while the sizable band gap and strong spin-orbit coupling hold promise for properties beyond graphene. Measurements under large magnetic fields have revealed an unusual LL structure, distinct from other 2D electron systems. However, owing to limited sample quality and poor electrical contact, probing the lowest Landau levels (LLs) has been challenging, and observation of ele…
Spiral-induced anomalous Hall effect from odd-parity spin-nodal lines
The University of Tokyo（东京大学）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所 emergent matter science 中心）；Hiroshima University（广岛大学）；Department of Applied Physics, The University of Tokyo（东京大学应用物理系）
Even-Odd Layer-Dependent Exchange Bias Effect in MnBi2Te4 Chern Insulator Devices
The Pennsylvania State University（宾夕法尼亚州立大学）；Nanjing University（南京大学）；Nankai University（南开大学）；National Institute for Materials Science（国立材料研究所）；Oak Ridge National Laboratory（橡树岭国家实验室）；University of California, Riverside（加州大学河滨分校）
Chiral topological superconductors are expected to appear as intermediate states when a quantum anomalous Hall system is proximity coupled to an s-wave superconductor and the magnetization direction is reversed. In this paper we address the edge state properties of ordinary quantum Hall systems proximity coupled to s-wave superconductors, accounting explicitly for Landau quantization. We find that the appearance of topological superconducting phases with an odd number of Majorana edge modes is dependent on the structure of the system's vortex lattice. More precisely, vortex lattices containing…
The Landau bands of mirror symmetric 2D Dirac semi-metals (for example odd-layers of ABA-graphene) can be identified by their parity with respect to mirror symmetry. This symmetry facilitates a new class of counter-propagating Hall states at opposite but equal electron and hole filling factors $|ν_{\pm}|=1/m$ ({\it m} odd). Here, we propose a Laughlin-like correlated liquid wavefunction, at the charge neutrality point, that exhibits fractionally charged quasi-particle/hole pair excitation of opposite parity. Using a bosonized one-dimensional edge state theory, we show that the longitudinal con…
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 …
