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In recent years it has become clear that electronic Berry curvature (BC) is a key concept to understand and predict physical properties of crystalline materials. A wealth of interesting Hall-type responses in charge, spin and heat transport…

Three-dimensional topological insulators (TIs) are a perfectly tuned quantum-mechanical machinery in which counter-propagating and oppositely spin-polarized conduction channels balance each other on the surface of the material. This…

We predict a nonlinear Hall effect in certain Weyl semimetals with broken inversion symmetry. When the energy dispersions about pairs of Weyl nodes are skewed -- the Weyl cones are "tilted" -- the concerted actions of the anomalous velocity…

The three-dimensional Dirac semimetal is distinct from its two-dimensional counterpart due to its dimensionality and symmetry. Here, we observe that molecule-based quasi-two-dimensional Dirac fermion system, $\alpha$-(BEDT-TTF)$_2$I$_3$,…

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…

Noncollinear magnets with near-zero net magnetization and nontrivial bulk electronic topology hold significant promise for spintronic applications, though their scarcity necessitates purposeful design strategies. In this work, we report a…

The photo-excitation of multi-layered potassium doped black phosphorus that exists as a gapped semi-Dirac two-dimensional normal insulator (NI), transforms it into a time-reversal symmetry broken Chern insulator (CI). This transition from…

In two-dimensional insulators with time-reversal (TR) symmetry, a nonzero local Berry curvature of low-energy massive Dirac fermions can give rise to nontrivial spin and charge responses, even though the integral of the Berry curvature over…

Recently, higher-order topological matter and 3D quantum Hall effects have attracted great attention. The Fermi-arc mechanism of the 3D quantum Hall effect proposed in Weyl semimetals is characterized by the one-sided hinge states, which do…

The nonlinear Hall effect has recently attracted significant interest due to its potential as a promising spectral tool and device applications. A theory of the nonlinear Hall effect on a disordered lattice is a crucial step towards…

The topological properties of a material's electronic structure are encoded in its Berry curvature, a quantity which is intimately related to the transverse electrical conductivity. In transition metal dichalcogenides with broken inversion…

While in pristine bilayer graphene the Berry curvature dipole (BCD), a necessary ingredient for the nonlinear anomalous Hall effect, is zero, uniaxial strain can give rise to finite BCD. We investigate this by using a tight-binding (TB)…

Physics arising from two-dimensional~(2D) Dirac cones has been a topic of great theoretical and experimental interest to studies of gapless topological phases and to simulations of relativistic systems. Such $2$D Dirac cones are often…

The half-quantized Hall conductance is characteristic of quantum systems with parity anomaly. Here we investigate topological and transport properties of a class of parity anomalous semimetals, in which massive Dirac fermions coexist with…

Berry phase physics is closely related to a number of topological states of matter. Recently discovered topological semimetals are believed to host a nontrivial $\pi$ Berry phase to induce a phase shift of $\pm 1/8$ in the quantum…

Detecting symmetry-breaking hidden orders with conventional probes has been a long-standing challenge in the field of magnetism. Higher-rank multipolar ordering $-$ anisotropic charge and magnetization distributions arising from a…

The anomalous velocity term in the semiclassical model of a Bloch electron deviates the trajectory from the conventional one. When the Berry curvature (alias noncommutative parameter) is a monopole in momentum space as found recently in…

Topological matter is a trending topic in condensed matter: From a fundamental point of view it has introduced new phenomena and tools, and for technological applications, it holds the promise of basic stable quantum computing. Similarly,…

The quantum anomalous Hall effect is a fundamental transport response of a topologically non-trivial system in zero magnetic field. Its physical origin relies on the intrinsically inverted electronic band structure and ferromagnetism, and…

The Berry curvature (BC), a quantity encoding the geometry of electronic wavefunctions, governs various electronic transport effects in quantum materials. In magnetic systems, the BC is reponsible for the intrinsic part of the anomalous…