Nonsymmorphic cubic Dirac point and crossed nodal rings across the ferroelectric phase transition in LiOsO$_3$

TL;DR

This paper reveals how nonsymmorphic symmetries stabilize a cubic Dirac point in LiOsO$_3$, which transforms into crossed nodal rings during a ferroelectric phase transition, unveiling new topological features linked to structural symmetry changes.

Contribution

It demonstrates the stabilization of a cubic Dirac point on a threefold axis via nonsymmorphic symmetry and its transformation into crossed nodal rings across a ferroelectric phase transition in LiOsO$_3$.

Findings

Cubic Dirac point stabilized by nonsymmorphic glide mirror symmetry.

Transition from Dirac point to crossed nodal rings during phase change.

Presence of linear Dirac points transforming into nodal rings.

Abstract

Crystalline symmetries can generate exotic band-crossing features, which can lead to unconventional fermionic excitations with interesting physical properties. We show how a cubic Dirac point---a four-fold-degenerate band-crossing point with cubic dispersion in a plane and a linear dispersion in the third direction---can be stabilized through the presence of a nonsymmorphic glide mirror symmetry in the space group of the crystal. Notably, the cubic Dirac point in our case appears on a threefold axis, even though it has been believed previously that such a point can only appear on a sixfold axis. We show that a cubic Dirac point involving a threefold axis can be realized close to the Fermi level in the non-ferroelectric phase of LiOsO$_3$. Upon lowering temperature, LiOsO$_3$ has been shown experimentally to undergo a structural phase transition from the non-ferroelectric phase to the ferroelectric phase with spontaneously broken inversion symmetry. Remarkably, we find that the broken symmetry transforms the cubic Dirac point into three mutually-crossed nodal rings. There also exist several linear Dirac points in the low-energy band structure of LiOsO$_3$, each of which is transformed into a single nodal ring across the phase transition.