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We describe the charge transport in ferromagnets with spin orbit coupled Bloch bands by combining the wave-packet evolution equations with the classical Boltzmann equation. This approach can be justified in the limit of smooth disorder…
The electronic topology is generally related to the Berry curvature, which can induce the anomalous Hall effect in time-reversal symmetry breaking systems. Intrinsic monolayer transition metal dichalcogenides possesses two nonequivalent K…
Geometric analogs of Bloch oscillations studied so far have relied on Berry curvature. We show that a weakly inhomogeneous electric field adds a distinct quantum-metric term to semiclassical wavepacket dynamics, generating an oscillatory…
Berry curvature-related topological phenomena have been a central topic in condensed matter physics. Yet, until recently other quantum geometric quantities such as the metric and connection received only little attention due to the…
Many quantum materials of interest, ex., bilayer graphene, possess a number of closely spaced but not fully degenerate bands near the Fermi level, where the coupling to the far detuned remote bands can induce Berry curvatures of the…
In the presence of time reversal symmetry, a non-linear Hall effect can occur in systems without an inversion symmetry. One of the prominent candidates for detection of such Hall signals are Weyl semimetals. In this article, we investigate…
This paper focuses on the study of linear exciton Hall and Nernst effects in monolayer two-dimensional (2D) semiconductors, employing the semi-classical transport theory. By deriving the exciton Berry curvature in momentum space for a…
2D materials based superlattices have emerged as a promising platform to modulate band structure and its symmetries. In particular, moir\'e periodicity in twisted graphene systems produces flat Chern bands. The recent observation of…
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…
The third-order nonlinear Hall effect induced by Berry-connection polarizability tensor has been observed in Weyl semimetals T$_d$-MoTe$_2$ as well as T$_d$-TaIrTe$_4$. The experiments were performed on bulk samples, and the results were…
In a time-reversal invariant system, while the anomalous Hall effect identically vanishes in the linear response regime due to the constraint of time-reversal symmetry on the distribution of Berry curvature, a nonlinear Hall effect can…
Nonlinear responses in condensed matters attract recent intensive interest because they provide rich information about the materials and hold the possibility of being applied in diodes or high-frequency optical devices. Nonlinear responses…
Drude weight, historically associated with the longitudinal Drude conductivity, can be generalized to describe the transverse or Hall component of the extrinsic conductivity tensor. In particular, transverse Drude weights, such as band…
The Hall effect occurs only in systems with broken time-reversal symmetry, such as solids under an external magnetic field in the ordinary Hall effect and magnetic materials in the anomalous Hall effect (AHE). Here we show a new Hall effect…
We demonstrate robust and reversible electric-current control of the anomalous Hall effect (AHE) in a two-dimensional WTe2/Fe3GeTe2 (FGT) stack. Applying a current through Td-WTe2 leads to a giant modulation of the AHE of the adjacent FGT…
The Berry curvature (BC) - a quantity encoding the geometric properties of the electronic wavefunctions in a solid - is at the heart of different Hall-like transport phenomena, including the anomalous Hall and the non-linear Hall and Nernst…
The valley Hall effect arises from valley contrasting Berry curvature and requires inversion symmetry breaking. Here, we propose a nonlinear mechanism to generate a valley Hall current in systems with both inversion and time-reversal…
It has been known that the semiclassical theory and the response theory can equivalently give the Drude and the intrinsic anomalous Hall conductivities in the linear order of electric field. However, recent theoretical advances implied that…
Quantum geometry plays a pivotal role in the second-order response of $\cal PT$-symmetric antiferromagnets. Here we study the nonlinear response of 2D altermagnets protected by $C_n\cal T$ symmetry and show that their leading nonlinear…
In recent years, there is an increasing interest in transport phenomena that are fundamentally linked to the presence of multiple bands. In this thesis, we develop, discuss, and apply a theory of the electrical conductivity that includes…