Topological and conventional phases of a three-dimensional electronic glass

Abstract

We investigate a symmetry protected Z2 topological electron glass -a glassy equivalent of the Z2 topological band insulator in crystalline systems-and uncover associated quantum phase transitions in this three dimensional amorphous network of atoms. Through explicit numerical calculations of the Witten effect, we show that the Z2 glass is characterized by an anomalous electromagnetic response-dyons with 1/2 electronic charge. We further study, using a variety of numerical diagnostics including such electromagnetic responses, the phase transitions of the Z2 glass in to a metallic and/or a trivial insulating phase. We find that the phase transitions here are governed by subtle features of mobility edges and "spectral inversion" which are possibly unique to structurally amorphous systems. Our results provide a concrete setting to understand the general underpinnings of such phases -where strong structural disorder interplays with symmetry-protected topological order.

Criticality in amorphous topological matter -- beyond the universal scaling paradigm

“…However, there are rapidly emerging lines of research in topological systems without spatial symmetry. Since nontrivial topology in general does not rely on spatial order, amorphous systems provide an interesting new platform for topological matter [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Previously, the question as to whether the topological behaviour of amorphous systems and crystalline systems display fundamental differences has remained largely unclear.…”

Topological Weaire–Thorpe models of amorphous matter

“…This well-developed understanding dates back at least to studies of integer quantum Hall transitions (8)(9)(10). More recently, several classes of amorphous models have been shown to host integer quantum Hall (or Chern insulator) phases, as well as other topological states (7,(11)(12)(13)(14)(15)(16)(17)(18)(19), including numerical work that suggests differences compared to known quantum Hall transitions (19,20). Although the corresponding topological phase diagrams can be computed numerically, by simulating responses to external fields (18) or through real space topological markers (7,11), these methods are not generalizable to every discrete symmetry in every dimensionality.…”

“…More recently, several classes of amorphous models have been shown to host integer quantum Hall (or Chern insulator) phases, as well as other topological states (7,(11)(12)(13)(14)(15)(16)(17)(18)(19), including numerical work that suggests differences compared to known quantum Hall transitions (19,20). Although the corresponding topological phase diagrams can be computed numerically, by simulating responses to external fields (18) or through real space topological markers (7,11), these methods are not generalizable to every discrete symmetry in every dimensionality. Crucially, a symmetry-based approach (21)(22)(23)(24) for amorphous solids, which proved to be successful in high-throughput classifications of topological crystals (1-3), seems out of reach due to the absence of long-range atomic order.…”

Amorphous Bi$_2$Se$_3$ structural, electronic, and topological nature by first-principles

“…Recent works investigating 2D and 3D model Hamiltonians have shown that non-crystalline and amorphous systems can also support topological phases [43][44][45][46]. These findings have the potential to vastly expand the field, provided one finds material system realizations.…”