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The use of Berry-phase concepts has established a strong link between the anomalous Hall effect (AHE) and the topological character of the Hall currents. However, the occurrence of sign competition in the Berry curvature often hinders the…
A three-dimensional non-Hermitian Hamiltonian with parity-time symmetry can exhibit a closed exceptional surface (EP surface) in momentum space, which is a non-Hermitian deformation of the degeneracy line (DL). Since the degeneracy line…
Landau's Fermi-liquid theory is the standard model for metals, characterized by the existence of electron quasiparticles near a Fermi surface as long as Landau's interaction parameters lie below critical values for instabilities. Recently,…
In this account, we will give an overview of our research progress on novel quantum properties in topological quantum materials with kagome lattice. Here, there are mainly two categories of kagome materials: magnetic kagome materials and…
The nonlinear optical responses from topological semimetals are crucial in both understanding the fundamental properties of quantum materials and designing next-generation light-sensors or solar-cells. However, previous work was focusing on…
Topological semimetals in crystals with a chiral structure (which possess a handedness due to a lack of mirror and inversion symmetries) are expected to display numerous exotic physical phenomena, including fermionic excitations with large…
We consider a magnetic skyrmion crystal formed at the surface of a topological insulator. Incorporating the exchange interaction between the helical Dirac surface states and the periodic N\'eel or Bloch skyrmion texture, we obtain the…
Topological node of electronic bands can carry emergent charge degree of freedom such as the Berry curvature monopole of the Weyl semimetals, which results in intriguing transport and optical phenomena. In this study, we discuss the…
We compute the intrinsic contributions to the Berry-phase mediated anomalous Hall and Nernst effects in electron- and hole-doped semiconductors in the presence of an in-plane magnetic field as well as Rashba and Dresselhaus spin orbit…
The influence of the topology and curvature of objects on photonic properties represents an intriguing fundamental problem from cosmology to nanostructure physics. The classical topological transition from a ring to a M\"obius strip is…
Topologically non-trivial states characterized by Berry curvature appear in a number of materials ranging from spin-orbit-coupling driven topological insulators to graphene. In multivalley conductors, such as mono- and bilayer graphene,…
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…
The spin chirality, created by magnetic atoms, has been comprehensively understood to generate and control the magneto-optical effects. In comparison, the role of the crystal chirality that relates to nonmagnetic atoms has received much…
We show that excitons forming between moir\'e flat Chern bands possess a substantial electric dipole moment comparable to the moir\'e lattice parameter times the elementary charge ($\sim10^2$ Debye). At a hole filling factor of one in…
The observation of zero field fractional quantum Hall analogs in twisted transition metal dichalcogenides (TMDs) asks for a deeper understanding of what mechanisms lead to topological flat bands in two-dimensional heterostructures, and what…
Stoner magnetism in bands endowed with Berry curvature is shown to be profoundly influenced by the coupling between spin chirality density $\vec s\cdot(\partial_x\vec s\times\partial_y\vec s)$ and Berry's orbital magnetization. The key…
Quantum materials can display physical phenomena rooted in the geometry of electronic wavefunctions. The corresponding geometric tensor is characterized by an emergent field known as Berry curvature (BC). Large BCs typically arise when…
The geometry of Bloch bands affects many physical properties of crystalline solids and other spatially periodic systems. Direct experimental determination of such geometry is an active area of research. In this work, we focus on the…
Characterized by the absence of inversion symmetry, non-centrosymmetric materials are of great interest because they exhibit ferroelectricity, second harmonic generation, emergent Weyl fermions, and other fascinating phenomena. It is…
Magnetic orders characterized by multiple ordering vectors harbor noncollinear and noncoplanar spin textures and can be a source of unusual electronic properties through the spin Berry phase mechanism. We theoretically show that such…