Sixfold excitations in electrides

Due to the lack of full rotational symmetry in condensed matter physics, solids exhibit new excitations beyond Dirac and Weyl fermions, of which the sixfold excitations have attracted considerable interest owing to the presence of maximum degeneracy in bosonic systems. Here, we propose that a single linear dispersive sixfold excitation can be found in the electride Li_{12}Mg_{3}Si_{4} and its derivatives. The sixfold excitation is formed by the floating bands of elementary band representation A@12a originating from the excess electrons centered at the vacancies (i.e., the 12a Wyckoff sites). There exists a unique topological bulk-surface-edge correspondence for the spinless sixfold excitation, resulting in trivial surface “Fermi arcs” but topological hinge arcs. All gapped k_{z} slices belong to a two-dimensional higher-order topological insulating phase, which is protected by a combined symmetry TS[over ̃]_{4z} and characterized by a quantized fractional corner charge Q_{corner}=3|e|/4. Consequently, the hinge arcs are obtained in the hinge spectra of the S[over ̃]_{4z}-symmetric rod structure. The state with a single sixfold 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.