Related papers: Lecture Notes on Berry Phases and Topology
The existing paradigm for topological insulators asserts that an energy gap separates conduction and valence bands with opposite topological invariants. Here, we propose that \textit{equal}-energy bands with opposite Chern invariants can be…
Illustration of the geometric and topological properties of Berry phase is often in an obscure and abstract language of fiber bundles. In this article, we demonstrate these properties with a lucid and concrete system whose parameter space…
The nonlinear optical behavior of quantum systems plays a crucial role in various photonic applications. This study introduces a novel framework for understanding these nonlinear effects by incorporating gauge-covariant formulations based…
Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may…
Berry phases offer a geometric perspective on wave propagation and are key to designing materials with topological wave transport. However, controlling Berry phases is challenging due to their dependence on global integrals over the…
We show that the topological central charge of a topological phase can be directly accessed from the ground-state wavefunctions for a system on a surface as a Berry curvature produced by adiabatic variation of the metric on the surface, at…
Within the semiclassical approach, we calculate contributions of the Berry phase and of the Zeeman coupling of the electron moment with the magnetic field to the phase of the Shubnikov - de Haas oscillations for the surface electrons in the…
A new method is proposed to predict the topological properties of one-dimensional periodic structures in wave physics, including quantum mechanics. From Bloch waves, a unique complex valued function is constructed, exhibiting poles and…
The Berry phase is analyzed for Weyl and Dirac fermions in a phase space representation of the worldline formalism. Kinetic theories are constructed for both at a classical level. Whereas the Weyl fermion case reduces in dimension,…
The Berry phase is a geometric phase acquired during adiabatic evolution over a closed loop in parameter space. It plays an essential role in geometric quantum gates and other phase-based protocols. In non-Hermitian systems, the Berry phase…
We consider the scattering of an atom by a sequence of two near-resonant standing light waves each formed by two running waves with slightly different wave vectors. Due to opposite detunings of the two standing waves and within the rotating…
The interface between a superconductor and a topological insulator has been proposed to harbor novel quasiparticles that realize physical schemes for fault-tolerant quantum computation. Here, we present high resolution angle-resolved…
We discuss the thermodynamic and finite size scaling properties of the geometric phase in the adiabatic Dicke model, describing the super-radiant phase transition for an $N$ qubit register coupled to a slow oscillator mode. We show that, in…
The Thouless pump, a cornerstone of topological physics, enables unidirectional quantized wave/particle transport via geometric Berry phase engineering in periodically driven systems. While decades of research have been dedicated to…
The coexistence of edge states and skin effects provides the topologically protected localized states at the corners of two-dimensional systems. In this paper, we realize such corner states in the two-dimensional Su-Schrieffer-Heeger model…
In this paper we define a non-dynamical phase for a spin-1/2 particle in a rotating magnetic field in the non-adiabatic non-cyclic case, and this phase can be considered as a generalized Berry phase. We show that this phase reduces to the…
Recently, it has been shown that multi-terminal superconducting nanostructures may possess topological properties that involve Berry curvatures in the parametric space of the superconducting phases of the terminals, and associated Chern…
The modern theory of electric polarization in crystals associates the dipole moment of an insulator with a Berry phase of its electronic ground state [1, 2]. This concept constituted a breakthrough that not only solved the long-standing…
Topological phases of matter lie at the heart of physics, connecting elegant mathematical principles to real materials that are believed to shape future electronic and quantum computing technologies. To date, studies in this discipline have…
We show that topological transitions in electronic spin transport are feasible by a controlled manipulation of spin-guiding fields. The transitions are determined by the topology of the fields texture through an effective Berry phase…