Related papers: Tutorial: From Topology to Hall Effects -- Implica…
Phonons as collective excitations of lattice vibrations are the main heat carriers in solids. Tremendous effort has been devoted to investigate phonons and related properties, giving rise to an intriguing field of phononics, which is of…
We discuss the anomalous Hall effect in a two-dimensional electron gas subject to a spatially varying magnetization. This topological Hall effect (THE) does not require any spin-orbit coupling, and arises solely from Berry phase acquired by…
We study topological properties of phase transition points of two topologically non-trivial $\mathbb{Z}_2$ classes (D and DIII) in one dimension by assigning a Berry phase defined on closed circles around the gap closing points in the…
The geometric phase (Berry phase) of an electronic wave function is the fundamental basis of the topological properties in solids. Modulating band structure provides a tuning knob for the Berry phase, and in the extreme case drives a…
The intrinsic anomalous Hall effect in metallic ferromagnets is shown to be controlled by Berry phases accumulated by adiabatic motion of quasiparticles on the Fermi surface, and is purely a Fermi-liquid property, not a ``bulk'' Fermi sea…
Despite the extensive studies of topological states, their characterization in strongly nonlinear classical systems has been lacking. In this work, we identify the proper definition of Berry phase for nonlinear bulk modes and characterize…
Geometric phases in condensed matter play a central role in topological transport phenomena such as the quantum, spin and anomalous Hall effect (AHE). In contrast to the quantum Hall effect - which is characterized by a topological…
We study a class of translational-invariant insulators with discrete rotational symmetry. These insulators have no spin-orbit coupling, and in some cases have no time-reversal symmetry as well, i.e., the relevant symmetries are purely…
The phase of quantum magneto-oscillations is often associated with the Berry phase and is widely used to argue in favor of topological nontriviality of the system (Berry phase $2\pi n+\pi$). Nevertheless, the experimentally determined value…
We develop a theory for the electrical and thermal transverse linear response functions such as the Hall, Nernst and thermal Hall effects in magnetic materials that harbor topological spin textures like skyrmions. In addition to the…
We have analysed here the equivalence of RVB states with $\nu=1/2$ FQH states in terms of the Berry Phase which is associated with the chiral anomaly in 3+1 dimensions. It is observed that the 3-dimensional spinons and holons are…
Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological…
The topological phases of matter are characterized using the Berry phase, a geometrical phase, associated with the energy-momentum band structure. The quantization of the Berry phase, and the associated wavefunction polarization, manifest…
Berry phase plays an important role in many non-trivial phenomena over a broad range of many-body systems. In this thesis we focus on the Berry phase due to the change of the particles' momenta, and study its effects in free and interacting…
Geometrical properties of energy bands underlie fascinating phenomena in a wide-range of systems, including solid-state materials, ultracold gases and photonics. Most famously, local geometrical characteristics like the Berry curvature can…
When quasiparticles move in condensed matters, the texture of their internal quantum structure as a function of position and momentum can give rise to Berry phases that have profound effects on materials properties. Seminal examples include…
Under symmetry breaking, a three-dimensional nodal-line semimetal can turn into a topological insulator or Weyl semimetal, accompanied by the generation of momentum-space Berry curvature. We develop a theory that unifies their circular…
Berry phase effect plays a central role in many mesoscale condensed matter and quantum chemical systems that are naturally under the environmental influence of dissipation. We propose and microscopically derive a prototypical quantum…
In non-relativistic physics, the concepts of geometry and topology are usually applied to characterize spatial structures or structures in momentum space. We introduce the concept of temporal geometry, which encompasses the geometric and…
Hall experiments in chiral magnets are often analyzed as the sum of an anomalous Hall effect, dominated by momentum-space Berry curvature, and a topological Hall effect, arising from the real-space Berry curvature in the presence of…