相关论文: Parallel Transport and Band Theory in Crystals
The semi-classical Bloch-Boltzmann theory is at the heart of our understanding of conduction in solids, ranging from metals to semi-conductors. Physical systems that are beyond the range of applicability of this theory are thus of…
The discovery of Berry curvature (BC) has spurred a tremendous surge of research into various quantum phenomena such as the anomalous transport of electrons and the topological phases of matter. In two-dimensional crystalline systems, the…
We present a comprehensive account of directed transport in one-dimensional Hamiltonian systems with spatial and temporal periodicity. They can be considered as Hamiltonian ratchets in the sense that ensembles of particles can show directed…
y formally diagonalizing with accuracy $\hbar$ the Hamiltonian of electrons in a crystal subject to electromagnetic perturbations, we resolve the debate on the Hamiltonian nature of semiclassical equations of motion with Berry-phase…
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…
We outline an approach to endow a plain vanilla material with topological properties by creating topological bands in stacks of manifestly nontopological atomically thin materials. The approach is illustrated with a model system comprised…
Excitons are neutral objects, that, naively, should have no response to a uniform, electric field. Could the Berry curvature of the underlying electronic bands alter this conclusion? In this work, we show that Berry curvature can indeed…
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…
Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations…
We provide a general theory for parallel transport on non-collapsed ${\sf RCD}$ spaces obtaining both existence and uniqueness results. Our theory covers the case of geodesics and, more generally, of curves obtained via the flow of…
The Bohmian interpretation of quantum mechanics adds particle trajectories to the wave function and ensures that the probability distribution of the particle positions agrees with quantum mechanics at any time. This is not sufficient to…
Braiding has attracted significant attention in physics because of its important role in describing the fundamental exchange of particles. Infusing the braiding with topological protection will make it robust against imperfections and…
We study the magnetic Bloch oscillations performed by a quantum particle moving in a two-dimensional lattice in the presence of a strong (synthetic) magnetic field and a uniform force. An elementary derivation of the Berry curvature effect…
Two-dimensional van der Waals heterostructures can be engineered into artificial superlattices that host flat bands with significant Berry curvature and provide a favorable environment for the emergence of novel electron dynamics. In…
Based on an optical analogy of spintronics, the generation of optical tornadoes is theoretically investigated in two-dimensional photonic crystals without space-inversion symmetry. We address its close relation to the Berry curvature in…
A geometric interpretation of curvature and torsion of linear transports along paths is presented. A number of (Bianchi type) identities satisfied by these quantities are derived. The obtained results contain as special cases the…
Parallel transport of vectors in curved spacetimes generally results in a deficit angle between the directions of the initial and final vectors. We examine such holonomy in the Schwarzschild-Droste geometry and find a number of interesting…
Berry curvature does not show itself in the relative phase correlation of wave-functions at different spatial points in a metal unless the fermions have closed trajectories in momentum space, for example those around isolated impurities.…
Artificial crystals such as moir\'e superlattices can have a real-space periodicity much larger than the underlying atomic scale. This facilitates the presence of Bloch oscillations in the presence of a static electric field. We demonstrate…
We present a perturbative approach to derive the semiclassical equations of motion for the two-dimensional electron dynamics under the simultaneous presence of static electric and magnetic fields, where the quantized Hall conductance is…