Related papers: Topological electronic bands in crystalline solids
The Berry phase is a fundamental concept in quantum mechanics with profound implications for understanding topological properties of quantum systems. This tutorial provides a comprehensive introduction to the Berry phase, beginning with the…
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,…
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…
Electronic flat bands have localized Wannier-like orbitals as zero modes. In the Lieb or the kagome models, the localized orbitals satisfy a topological condition that entails two non-contractible loop eigenstates along $x/y$-axis in real…
In this paper, we study several structural models of amorphous silicon, and discuss structural and electronic features common to all. We note spatial correlations between short bonds, and similar correlations between long bonds. Such…
We elucidate the general rule governing the response of dislocation lines in three-dimensional topological band insulators. According to this ${\bf K}\text{-}{\bf b}\text{-}{\bf t}$ rule, the lattice topology, represented by dislocation…
Berry curvature physics and quantum geometric effects have been instrumental in advancing topological condensed matter physics in recent decades. Although Landau level-based flat bands and conventional 3D solids have been pivotal in…
Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this…
Here, we introduce and apply non-Abelian tensor Berry connections to topological phases in multi-band systems. These gauge connections behave as non-Abelian antisymmetric tensor gauge fields in momentum space and naturally generalize…
The central role that materials play in human history is exemplified by the three-age division of prehistory into the stone, bronze, and iron ages. References to our present time as the information age or silicon age epitomizes the…
In crystalline systems with a superstructure, the electron dispersion can form a nontrivial covering of the Brillouin zone. It is proved that the number of sheets in this covering and its monodromy are topological invariants under ambient…
Electronic topological phases of matter, characterized by robust boundary states derived from topologically nontrivial bulk states, are pivotal for next-generation electronic devices. However, understanding their complex quantum phases,…
The low-energy band-structure of electrons propagating on a lateral surface of a heterostructure consisting of three dimensional topological insulator (TI) and magnetic insulator layers has been calculated. The energy spectrum is highly…
Topological materials ranging from topological insulators to semimetals host many novel quantum phenomena including quantum spin Hall effect and topological Fermi arcs. Transitions between these topological phases have attracted much…
The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at…
Following the intense studies on topological insulators, significant efforts have recently been devoted to the search for gapless topological systems. These materials not only broaden the topological classification of matter but also…
Macroscopic two-dimensional sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be…
The rapid development of topological photonics and acoustics calls for accurate understanding of band topology in classical waves, which is not yet achieved in many situations. Here, we present the Wilson-loop approach for exact numerical…
Nodal topological lattice is a form of magnetic crystal with topologically non-trivial spin texture, which further exhibits a periodic array of nodes with vanishing magnetization. Electronic structure for conduction electrons strongly…
Topological semimetals have energy bands near the Fermi energy sticking together at isolated points/lines/planes in the momentum space, which are often accompanied by stable surface states and intriguing bulk topological responses. Although…