Topological energy braiding of non-Bloch bands

Topological Bloch bands in graphene superlattices.

We outline a designer approach to endow widely available plain materials with topological properties by stacking them atop other nontopological materials. The approach is illustrated with a model system comprising graphene stacked atop hexagonal boron nitride. In this case, the Berry curvature of the electron Bloch bands is highly sensitive to the stacking configuration. As a result, electron t...

Direct measurement of the Zak phase in topological Bloch bands

Loops of Energy Bands for Bloch Waves in Optical Lattices

We consider stationary Bloch waves in a Bose–Einstein condensate placed in a periodic potential for varying strengths of inter-atomic interactions. Bifurcations of the stationary states are known to occur in this context. These bifurcations generate loops in the energy bands of the Bloch waves near the ends and the center of the Brillouin zone. Using themethod of Lyapunov–Schmidt reductions, we...

Topological vacuum bubbles by anyon braiding

According to a basic rule of fermionic and bosonic many-body physics, known as the linked cluster theorem, physical observables are not affected by vacuum bubbles, which represent virtual particles created from vacuum and self-annihilating without interacting with real particles. Here we show that this conventional knowledge must be revised for anyons, quasiparticles that obey fractional exchan...

Berry curvature and energy bands of graphene

In this paper energy bands and Berry curvature of graphene was studied. Desired Hamiltonian regarding the next-nearest neighbors obtained by tight binding model. By using the second quantization approach, the transformation matrix is calculated and the Hamiltonian of system is diagonalized. With this Hamiltonian, the band structure and wave function can be calculated. By using calculated wave f...