Obstructed insulators and flat bands in topological phase-change materials

Amorphous topological matter: Theory and experiment

“…Amorphous strong topological states include 2D Chern insulators in class A [7][8][9][10]20,[30][31][32][33][34], 2D and 3D time-reversal invariant topological insulators in class AII [7,33,[35][36][37][38], and 2D time-reversal breaking topological superconductors in class D [39,40]. Amorphous structures also support phases a priori protected by crystalline symmetries, such as 2D reflection-symmetry-protected topological insulators [41], 2D and 3D higher-order topological insulators [42][43][44], 2D and 3D obstructed insulators [45], and 3D topological metals [46]. While structural disorder is detrimental to some of these states, it can also induce nontrivial phases when starting from a trivial crystalline state [38,43,46], and it can give rise to new phenomenology intrinsically associated with amorphous topological matter and phase transitions [33,34,41,45,46].…”

“…For example the angular dependence can be modelled using the Slater-Koster parametrization [47], and the readial dependence can be accounted for by an exponential [7,33,34,[40][41][42][43]46,48] or polynomial [38] decay with the radial distance. There are several ways to introduce structural disorder, including lattices with uncorrelated random sites [7,33,34,[39][40][41][42][43]46,48], more realistic models which preserve the local coordination number [8,30,32,45], and lattices with controllable deviations from the crystalline limit [9,10,38,43].…”

“…Amorphous systems support and induce topological phases beyond strong topological states, including systems protected by spatial symmetries. [41][42][43]45,46]. The appearance of these phases is related to the concept of statistical topological insulators [85][86][87][88], which are spectral insulators protected by an average symmetry.…”

Structural spillage: an efficient method to identify non-crystalline topological materials

“…Prior work on topology in non-crystalline materials used convenient amorphous tight-binding models with average and local symmetries [11,[14][15][16]39], however these do not include the full chemical and structural specificity found in real matter. Similarly, real-space invariants [40][41][42][43], including Wannierbased tight-binding formalism, require the system be treated on a case-by-case basis and can be computationally costly.…”

“…assuming that P αβ p,p ∝ δ p,p . This assumption has been successfully used to determine the topology of non-crystalline systems using the effective Hamiltonian approach [14][15][16]35].…”