相关论文: Exploiting $\vartheta -$functions for the identifi…

We demonstrate that nontrivial multiband topological invariants of electronic wavefunctions can be revealed through orbital magnetization responses to external magnetic fields. We find that decomposing orbital magnetization into energetic…

Wave functions on periodic lattices are commonly described by Bloch band theory. Besides Abelian Bloch states labeled by a momentum vector, hyperbolic lattices support non-Abelian Bloch states that have so far eluded analytical treatments.…

The topological invariants of a time-reversal-invariant band structure in two dimensions are multiple copies of the $\mathbb{Z}_2$ invariant found by Kane and Mele. Such invariants protect the topological insulator and give rise to a spin…

We define topological invariants in terms of the ground states wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magneto-electric $\theta$ term in…

To clarify the relationship between edge electronic states in open-boundary crystalline systems and their corresponding bulk electronic structure, Alase et al. [Phys. Rev. Lett. 117, 076804 (2016)] have recently generalized Bloch's theorem…

The electronic properties in a solid depend on the specific form of the wave-functions that represent the electronic states in the Brillouin zone. Since the discovery of topological insulators, much attention has been paid to the…

In this paper we solve the Cattaneo-Vernotte Equation for a periodic heterostructure made of alternate layers of different materials. The solutions describe thermal waves traveling in a periodic system, and it allows us to introduce the…

Density functional calculations of electronic structures of materials is one of the most used techniques in theoretical solid state physics. These calculations retrieve single electron wavefunctions and their eigenenergies. The berry suite…

The engineering of synthetic materials characterised by more than one class of topological invariants is one of the current challenges of solid-state based and synthetic materials. Using a synthetic photonic lattice implemented in a…

We revisit the Hofstadter butterfly for a subset of topologically trivial Bloch bands arising from a continuum free electron Hamiltonian in a periodic lattice potential. We employ the recently developed procedure -- which was previously…

In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here…

Analytic representation formulas and power series are developed to describe the band structure inside periodic elastic crystals made from high contrast inclusions. We use source free modes associated with structural spectra to represent the…

The topological mechanics is a perfect tool that can bridge the gap between the quantum and Newtonian physics and mechanics of materials. It requires discrete models of the material with analogies with the topological characteristics of…

Topological phases of matter have garnered significant interest over the past two decades for two main reasons: their identification, via topological invariants, relies on the quantum geometry of the Bloch states, bringing attention to an…

This paper provides a mathematical perspective on fragile topology phenomena in condensed matter physics. In dimension $d \leq 3$, vanishing Chern classes of bundles of Bloch eigenfunctions characterize operators with exponentially…

We address the problem of analytically extracting a countable infinity of flat, non-dispersive bands in a periodic array of cells that comprise branching Vicsek geometries of higher and higher generations. Through a geometric construction,…

Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in…

Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which…

The measurement of topological number is crucial in the research of topological systems. Recently, the relations between the topological number and the dynamics are built. But a direct method to read out the topological number via the…

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure. The algorithm applies to crystals with broken time-reversal, particle-hole, and chiral…