Fractional disclination charge in two-dimensional Cn -symmetric topological crystalline insulators

Abstract

Robust fractional charge localized at disclination defects has been recently found as a topological response in C6 symmetric 2D topological crystalline insulators (TCIs). In this article, we thoroughly investigate the fractional charge on disclinations in Cn symmetric TCIs, with or without time reversal symmetry, and including spinless and spin-1 2 cases. We compute the fractional disclination charges from the Wannier representations in real space and use band representation theory to construct topological indices of the fractional disclination charge for all 2D TCIs that admit a (generalized) Wannier representation. We find the disclination charge is fractionalized in units of e n for Cn symmetric TCIs; and for spin-1 2 TCIs, with additional time reversal symmetry, the disclination charge is fractionalized in units of 2e n . We extend our results to interacting phases and prove that the fractional disclination charge determined by our topological indices is robust against electronelectron interactions that preserve the Cn symmetry and many-body bulk gap. Moreover, we use an algebraic technique to generalize the indices for TCIs with non-zero Chern numbers, where a Wannier representation is not applicable. With the inclusion of the Chern number, our generalized fractional disclination indices apply for all Cn symmetric TCIs. Finally, we briefly discuss the connection between the Chern number dependence of our generalized indices and the Wen-Zee term.

Electrons broken into pieces at crystal defects

“…Leucine is a potent activator of the 'mechanistic target of rapamycin' (mTOR) protein, which serves as a key regulator of cell growth and differentiation. Both dietary protein restriction (which results in low levels of leucine and other BCAAs) and inhibition of mTOR can extend lifespan in animals 3,4 .…”

“…Such entities typically arise as excitations (quasiparticles) in certain solid-state structures that have strong electron interactions 1 . In the past few years, researchers have predicted that the equilibrium state of peculiar materials known as topological crystalline insulators 2 could contain fractionally charged objects that stick to imperfections in the material structure 3,4 . On pages 376 and 381, respectively, Peterson et al 5 and Liu et al 6 bring this concept to reality by reporting experimental observations of fractional charges at structural defects called disclinations.…”

Transport induced dimer state from topological corner states

“…Recently, higher-order topological insulators (TIs) have been theoretically proposed in various systems [41][42][43][44][45][46][47][48], which are characterized by hinge modes in three-dimensional (3D) materials [49][50][51][52] or corner states in two-dimensional (2D) systems [53][54][55][56][57][58][59]. The existence of one-dimensional hinge states has been experimentally confirmed in bismuth [60] and multi-layer WTe 2 [61].…”

Vortex states in an acoustic Weyl crystal with a topological lattice defect

“…Aside from topological band insulators 5 , 9 – 12 , other topological phases are predicted to have their own unique interactions with TLDs, including Weyl semimetals, topological crystalline insulators, and higher-order topological insulators 13 – 18 . TLD-induced modes provide a way to probe bandstructure topology independent of standard bulk-boundary correspondences 6 – 8 , 11 , 15 , 17 , and may give rise to exotic material properties such as anomalous torsional effects 13 . Experimental confirmations have, however, been hampered by the difficulty of accessing TLDs in real topological materials 19 – 21 .…”