We report the occurrence of ferromagnetic-like anomalous Hall effect (AHE) below $30$ mT in bismuth single and policrystals. The signatures of ferromagnetism in transport are not corroborated in magnetization measurements, thus suggesting the induction of non-intrinsic magnetism at surfaces and grain boundaries in bismuth. The suppression of the AHE with the increase of magnetic field and temperature coincides with previous reports of superconductivity in Bi, suggesting an interplay between the two phenomena.
Field theory arguments suggest the possibility of $\mathbb{Z}$-classification of quantum spin Hall effect with magnetic flux tubes, that cause separation of spin and charge degrees of freedom, and pumping of spin or Kramers pair. However, the \emph{proof of principle} demonstration of spin-charge separation is yet to be accomplished for realistic, \emph{ab initio} band structures of spin-orbit-coupled materials, lacking spin-conservation law. In this work, we perform thought experiments with magnetic flux tubes on $β$-bismuthene to demonstrate spin-charge separation, and quantized pumping of s…
We present a density functional theory (DFT) based study of a two-dimensional phase of chromium bismuthate (CrBi), previously unknown material with exceptional magnetic and magnetooptical characteristics. Monolayer CrBi is a ferromagnetic metal with strong spin-orbit coupling induced by the heavy bismuth atoms, resulting in a strongly anisotropic Ising-type magnetic ordering with the Curie temperature estimated to be higher than 300 K. The electronic structure of the system is topologically nontrivial, giving rise to a nonzero Berry curvature in the ground magnetic state, leading to the anomal…
The interface between a solid and vacuum can become electronically distinct from the bulk. This feature, encountered in the case of quantum Hall effect, has a manifestation in insulators with topologically protected metallic surface states. Non-trivial Berry curvature of the Bloch waves or periodically driven perturbation are known to generate it. Here, by studying the angle-dependent magnetoresistance in prismatic bismuth crystals of different shapes, we detect a robust surface contribution to electric conductivity when the magnetic field is aligned parallel to a two-dimensional boundary betw…
Motivated by recent experiments demonstrating intricate quantum Hall physics on the surface of elemental bismuth, we consider proximity coupling an $s$-wave superconductor to a two-dimensional electron gas with strong Rashba spin-orbit interactions in the presence of a strong perpendicular magnetic field. We focus on the high-field limit so that the superconductivity can be treated as a perturbation to the low-lying Landau levels. In the clean case, wherein the superconducting order parameter takes the form of an Abrikosov vortex lattice, we show that a lattice of hybridized Majorana modes eme…
Motived by time-reversal symmetry breaking and giant anomalous Hall effect in kagome superconductor \textit{A}V$_3$Sb$_5$ (\textit{A} = Cs, K, Rb), we carried out the thermal transport measurements on CsV$_3$Sb$_5$. In addition to the anomalous Hall effect, the anomalous Nernst effect and the anomalous thermal Hall effect emerge. Interestingly, the longitudinal thermal conductivity $κ_{xx}$ largely deviates from the electronic contribution obtained from the longitudinal conductivity $σ_{xx}$ by the Wiedemann-Franz law. In contrast, the thermal Hall conductivity $κ_{xy}$ is roughly consistent w…
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…
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）
It is well established that the anomalous Hall effect that a ferromagnet displays scales with its magnetization. Therefore, an antiferromagnet that has no net magnetization should exhibit no anomalous Hall effect. Here we show that the non-collinear triangular antiferromagnet Mn3Ge exhibits a large anomalous Hall effect comparable to that of ferromagnetic metals; the magnitude of the anomalous conductivity is 500 per ohm per cm at 2 K and 50 per ohm per cm at room temperature. The angular dependence of the anomalous Hall effect measurements confirm that the small residual in-plane magnetic mom…
Analytic Formulas for the Anomalous Hall Effect in Itinerant Magnets
French American Center for Theoretical Science, CNRS（法美理论科学中心，法国国家科学研究中心）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（卡弗里理论物理研究所，加州大学圣塔芭芭拉分校）；École Normale Supérieure de Lyon, CNRS, Laboratoire de physique（里昂高等师范学校，法国国家科学研究中心，物理实验室）
We demonstrate an electric field control of anomalous Hall effect emerging in CaIrO$_3$/CaMnO$_3$ heterostructures. We fabricate both electron-type and hole-type carrier samples by tuning epitaxial strain and then control the carrier density in CaIrO$_3$ layer via electric double layer gating technique. As the Fermi energy of CaIrO$_3$ is tuned close to the Dirac line node, anomalous Hall conductivity is enlarged in both carrier-type samples. This result reveals that the anomalous Hall effect comes from the intrinsic origin reflecting the Dirac like dispersion in CaIrO$_3$. We propose that ban…
It is known that the Shubnikov--de Haas oscillations can be observed in the Hall resistivity, although their amplitude is much weaker than the amplitude of the diagonal resistivity oscillations. Employing a model of two-dimensional massive Dirac fermions that exhibits anomalous Hall effect, we demonstrate that the amplitude of the Shubnikov--de Haas oscillations of the anomalous Hall conductivity is the same as that of the diagonal conductivity. We argue that the oscillations of the anomalous Hall conductivity can be observed by studying the valley Hall effect in graphene superlattices and the…
Normal and intrinsic anomalous Hall effect in Nb1-yFe2+y
本文研究了Nb_（1-y）Fe_（2 +y）系列样品的霍尔效应。正常和异常的贡献，观察到正正常霍尔效应在高温下占主导地位。一致的异常贡献的分析是唯一可能的富铁Nb 0.985 Fe 2.015具有铁磁基态。在这里，一个积极的正常霍尔系数被发现在所有的温度与适度的最大值在自旋密度波过渡。反常的霍尔效应与本征（贝里相）贡献一致，本征贡献在有序温度TC以下是恒定的，在TC以上连续消失。对于化学计量的NbFe 2和富Nb的Nb 1.01 Fe 1.99-都具有自旋密度波基态-霍尔电阻率的额外贡献阻碍了完整的分析，并表明需要更复杂的模型的异常霍尔效应在巡回反铁磁体。
Orthorhombic CuMnAs has been proposed as an antiferromagnetic semimetal hosting nodal line and Dirac points around the Fermi level. We investigate relations between the topological bands and transport phenomena, i.e. spin Hall effect and anomalous Hall effect, in orthorhombic CuMnAs with first-principles calculations combined with symmetry analysis of magnetic structures and of (spin) Berry curvature. We show the nodal line gapped with spin-orbit coupling in CuMnAs dominantly generates large spin Hall conductivity in the ground state. Although the magnetic symmetry in the ground state of CuMnA…
Ab initio prediction of anomalous Hall effect in antiferromagnetic CaCrO$_3$
Institute of Scientific and Industrial Research, Osaka University（大阪大学科学工业研究所）；Department of Precision Engineering, Graduate School of Engineering, Osaka University（大阪大学大学院工学研究科精密工程专攻）
In this paper, we study $(2+1)$-dimensional quantum anomalous Hall states, i.e. band insulators with quantized Hall conductance, using the exact holographic mapping. The exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in $(3+1)$-dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a $(3+1)$-dimensional topological insulator. The dual description enables a new characterizat…
