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The Hall effect, the anomalous Hall effect and the spin Hall effect are fundamental transport processes in solids arising from the Lorentz force and the spin-orbit coupling respectively. The quantum versions of the Hall effect and the spin…
Studies on the heavy-fermion pyrochlore iridate (Pr$_2$Ir$_2$O$_7$) point to the role of time-reversal-symmetry breaking in geometrically frustrated Kondo lattices. With this motivation, here we study the effect of Kondo coupling and chiral…
We report a nearly ideal quantum anomalous Hall effect in a three-dimensional topological insulator thin film with ferromagnetic doping. Near zero applied magnetic field we measure exact quantization in Hall resistance to within a part per…
We introduce a new generic model of a deformed Composite Fermion-Fermi Surface (CF-FS) for the Fractional Quantum Hall Effect near $/nu=1/2$ in the presence of a periodic density modulation. Our model permits us to explain recent Surface…
We explore the relationship among the magnetic ordering in real space, the resulting spin texture on the Fermi surface, and the related superconducting gap structure in non-collinear antiferromagnetic metals without spin-orbit coupling. Via…
The Hall coefficient is related to the effective carrier density and Fermi surface topology in noninteracting and weakly interacting systems. In strongly correlated systems, the relation between the Hall coefficient and single-particle…
The quantum anomalous Hall effect (QAHE) is a quantum phenomenon in which a two-dimensional system exhibits a quantized Hall resistance $h/e^2$ in the absence of magnetic field, where $h$ is the Planck constant and $e$ is the electron…
The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators - topologically non-trivial states of two-dimensional matter with broken…
We investigate the algebraic structure of flat energy bands a partial filling of which may give rise to a fractional quantum anomalous Hall effect (or a fractional Chern insulator) and a fractional quantum spin Hall effect. Both effects…
The recent experimental observations of the quantum Hall effect in 3D topological semimetals have attracted great attention, but there are still debates on its origin. We systematically study the dependence of the quantum Hall effect in…
In [Can et al. 2016], quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic…
Two-dimensional systems with honeycomb lattice are known to be a paradigmatic platform to explore the various types of Hall effects, owing to that the interplay of lattice geometry, spin-orbit coupling and magnetism can give rise to very…
The quantum anomalous Hall (QAH) effect is a novel topological spintronic phenomenon arising from inherent magnetization and spin-orbit coupling. Various theoretical and experimental efforts have been devoted in search of robust intrinsic…
In this paper we present detailed theoretical analysis of the frequency and/or magnetic field dependence of the surface impedance of a metal at the anomalous skin effect. We calculate the surface impedance in the presence of a magnetic…
The anomalous Hall effect (AHE) is a consequence of spin-orbit coupling in a ferromagnetic metal and is related primarily to density-matrix response to an electric field that is off-diagonal in band index. For this reason disorder…
We study magnetic Schrodinger operators with random or almost periodic electric potentials on the hyperbolic plane, motivated by the quantum Hall effect in which the hyperbolic geometry provides an effective Hamiltonian. In addition we add…
We study the quantum anomalous thermal Hall effect in a topological superconductor which possesses an integer bulk topological number, and supports Majorana excitations on the surface. To realize the quantum thermal Hall effect, a finite…
We propose models of two dimensional paramagnetic semiconductors where the intrinsic spin Hall effect is exactly quantized in integer units of a topological charge. The model describes a topological insulator in the bulk, and a "holographic…
Strange metals exhibit linear resistivity and anomalous Hall transport, yet a comprehensive theory that accounts for both phenomena is still lacking. Recent studies have shown SYK-like spatially random couplings between a Fermi surface and…
We theoretically study the interplay between bulk Weyl electrons and magnetic topological defects, including magnetic domains, domain walls, and $\mathbb{Z}_6$ vortex lines, in the antiferromagnetic Weyl semimetals \mnsn\ and Mn$_3$Ge with…