Six-fold Excitations in Electrides

TL;DR

This paper predicts a unique six-fold topological excitation in electride Li$_{12}$Mg$_3$Si$_4$, revealing novel bulk-surface-edge relationships and higher-order topological insulating phases protected by symmetries.

Contribution

It introduces the discovery of a six-fold excitation in electrides, linking it to higher-order topological phases and symmetry protections, expanding the understanding of topological states in condensed matter.

Findings

Six-fold excitation found in Li$_{12}$Mg$_3$Si$_4$ electrides.

Unique topological bulk-surface-edge correspondence identified.

Electrides exhibit higher-order topological insulating phases.

Abstract

Due to the lack of full rotational symmetry in condensed matter physics, solids exhibit new excitations beyond Dirac and Weyl fermions, of which the six-fold excitations have attracted considerable interest owing to the presence of the maximum degeneracy in bosonic systems. Here, we propose that a single linear dispersive six-fold excitation can be found in the electride Li$_{12}$Mg$_3$Si$_4$ and its derivatives. The six-fold excitation is formed by the floating bands of elementary band representation -- $A@12a$ -- originating from the excess electrons centered at the vacancies (${\it i.e.}$, the $12a$ Wyckoff sites). There exists a unique topological bulk-surface-edge correspondence for the spinless six-fold excitation, resulting in trivial surface 'Fermi arcs' but nontrivial hinge arcs. All energetically-gapped $k_z$-slices belong to a two-dimensional (2D) higher-order topological insulating phase, which is protected by a combined symmetry ${\mathcal T}{\widetilde S_{4z}}$ and characterized by a quantized fractional corner charge $Q_{corner}=\frac{3|e|}{4}$. Consequently, the hinge arcs are obtained in the hinge spectra of the $\widetilde S_{4z}$-symmetric rod structure. The state with a single six-fold excitation, stabilized by both nonsymmorphic crystalline symmetries and time-reversal symmetry, is located at the phase boundary and can be driven into various topologically distinct phases by explicit breaking of symmetries, making these electrides promising platforms for the systematic studies of different topological phases.