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The surface states of 3D topological insulators possess geometric structures that imprint distinctive signatures on electronic transport. A prime example is the Berry curvature, which controls, for instance, electric frequency doubling via…
Quantum geometry - the geometry of electron Bloch wavefunctions - is central to modern condensed matter physics. Due to the quantum nature, quantum geometry has two parts, the real part quantum metric and the imaginary part Berry curvature.…
Electrons in materials with linear dispersion behave as massless Weyl- or Dirac-quasiparticles, and continue to intrigue physicists due to their close resemblance to elusive ultra-relativistic particles as well as their potential for future…
Nonlinear magnetic response driven by time-periodic magnetic fields offers a distinct route to probe spin-resolved quantum geometry beyond conventional electric-field-driven nonlinear effects. While linear magnetic responses depend on the…
We derive quantum geometric bounds in spinful systems with spin topology characterized by a single $\mathbb{Z}$ index protected by a spin gap. Our bounds provide geometric conditions on the spin topology, distinct from the known quantum…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
Nonlinear transport phenomena offer an exciting probe into the band geometry and symmetry properties of a system. While most studies on nonlinear transport have looked at second-order nonreciprocal responses in noncentrosymmetric systems,…
We propose a nonlinear orbital magnetoelectric effect, which generates orbital magnetization quadratically in centrosymmetric materials where the linear orbital magnetoelectric effect is strictly forbidden. Using extended semiclassical…
We review our recent works on the quantum transport, mainly in topological semimetals and also in topological insulators, organized according to the strength of the magnetic field. At weak magnetic fields, we explain the negative…
Quantum geometry provides an intrinsic framework for characterizing the geometric structure of quantum states. It highlights its relevance to various aspects of fundamental physics. However, its direct implications for magnetic phenomena…
The quantum metric, a key component of quantum geometry, plays a central role in a wide range of physical phenomena and has been extensively studied in periodic crystals and moir\'{e} materials. Here, we systematically investigate quantum…
Nonlinear transport has emerged as a powerful approach to probe the quantum geometry of electronic wavefunctions, such as Berry curvature and quantum metric, in topological materials. While nonlinear responses governed by bulk quantum…
Topological effects arising from the Berry curvature lead to intriguing transport signatures in quantum materials. Two such phenomena are the chiral anomaly and nonlinear Hall effect (NLHE). A unified description of these transport regimes…
Quantum metrology promises high-precision measurements of classical parameters with far reaching implications for science and technology. So far, research has concentrated almost exclusively on quantum-enhancements in integrable systems,…
We unveil novel spin-orbit torque mechanisms driven by topological edge states in magnetic graphene-based devices. Within the energy gap, a damping-like torque plateau emerges within the quantum anomalous Hall phase upon breaking…
The quantum geometry has significant consequences in determining transport and optical properties in quantum materials. Here, we use a semiclassical formalism coupled with perturbative corrections unifying the nonlinear anomalous Hall…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
The topological singularity of the Bloch states close to the Fermi level significantly enhances nonlinear electric responses in topological semimetals. Here, we systematically characterize this enhancement for a large class of topological…
The magneto-optic Kerr effect (MOKE), which describes the rotation and ellipticity of linearly polarized light upon reflection, is conventionally associated with time-reversal symmetry breaking. Here, we theoretically demonstrate that a…
The Weyl semimetal NbP was found to exhibit topological Fermi arcs and exotic magneto-transport properties. Here, we report on magnetic quantum-oscillation measurements on NbP and construct the 3D Fermi surface with the help of…