Related papers: Study of the topological Hall effect on simple mod…
We consider two-dimensional Hamiltonians on a torus with finite range, finite strength interactions and a unique ground state with a non-vanishing spectral gap, and a conserved local charge, as defined precisely in the text. Using the local…
We study the orbital Hall response in buckled two-dimensional Dirac materials using a unified framework that includes an antiferromagnetic exchange field, a perpendicular electric field, and intrinsic spin-orbit coupling. We show that the…
We consider a two-dimensional system initialized in a topologically trivial state before its Hamiltonian is ramped through a phase transition into a Chern insulator regime. This scenario is motivated by current experiments with ultracold…
Electric current flows parallel to the outer product of an applied electric field and temperature gradient, a phenomenon we call the nonlinear chiral thermo-electric (NCTE) Hall effect. We present a general microscopic formulation of this…
Motivated by recent experiments on the observation of room temperature skyrmions in a layered heterostructure and subsequent demonstration of topological Hall effect in the same system, we have studied a minimal model of itinerant electrons…
By considering an extended double-exchange model with spin-orbit coupling (SOC), we derive a general form of the Berry phase $\gamma$ that electrons pick up when moving around a closed loop. This form generalizes the well-known result valid…
We consider a two-level system coupled to an environment that evolves non-adiabatically. We present a non-perturbative method for determining the persistence amplitude whose phase contains all the corrections to Berry's phase produced by…
The quasiclassical dynamics is studied for charge carriers moving on the surface of 3D topological insulator of Bi2Te3 type and subjected to static magnetic field. The effects connected to the symmetry changes of electron isoenergetic…
The geometric ideas underlying the Berry phase and the modern viewpoint of Karplus and Luttinger's theory of the anomalous Hall effect are discussed in an elementary way. We briefly review recent Hall and Nernst experiments which support…
To elucidate the origin of spin structure-driven anomalous Hall effect (AHE) in pyrochlore compounds, we construct the $t_{2g}$-orbital kagome lattice model and analyze the anomalous Hall conductivity (AHC). We reveal that a conduction…
A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one- and two-dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum…
In high-quality solid-state systems at low temperatures, the hydrodynamic or the ballistic regimes of heat and charge transport are realized in the electron and the phonon systems. In these regimes, the thermal and the electric conductance…
Analytical calculations and micromagnetic simulations are used to determine the Berry curvature and topological Hall effect (THE) due to conduction electrons in small ferromagnetic particles. Our focus is on small particles of…
The quantum Hall effect was originally observed in a two-dimensional electron gas forming Landau levels when exposed to a strong perpendicular magnetic field and was later generalized to Chern insulators without net magnetization. Here,…
We predict two spin-dependent transport phenomena in two-dimensional electron systems, which are induced by spatially fluctuating Rashba spin-orbit interaction. When the electron gas is magnetized, the random Rashba interaction leads to the…
Non-collinear triangular antiferromagnets with a coplanar spin arrangement and vanishing net magnetic moment can exhibit a large anomalous Hall effect owing to their non-vanishing momentum space Berry curvature. Here we show the existence…
While recent theoretical studies have positioned noncollinear polar magnets with $C_{nv}$ symmetry as compelling candidates for realizing topological magnetic phases and substantial intrinsic anomalous Hall conductivity, experimental…
Optoelectronic and nonlinear transport experiments probe the quantum geometric tensor of Bloch states, whose real and imaginary components -- the quantum metric and the Berry curvature -- are typically constrained by symmetry. Here, we show…
We study two-dimensional electron systems in the hydrodynamic regime. We show that a geometrical Berry curvature modifies the effective Navier-Stokes equation for viscous electron flow in topological materials. For small electric fields,…
In a magnetic metal, the Hall resistance is generally taken to be the sum of the ordinary Hall resistance and the anomalous Hall resistance. Here it is shown that this empirical relation is no longer valid when either the ordinary Hall…