Kramers nodal line metals

Ying-Ming Xie,Jin-Xin Hu,Xue-Jian Gao,Jason Z Gao,Cheng-Ping Zhang,K T Law,Xiao Yan Xu

doi:10.1038/s41467-021-22903-9

Abstract

Recently, it was pointed out that all chiral crystals with spin-orbit coupling (SOC) can be Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta. In this work, we show that all achiral non-centrosymmetric materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there are doubly degenerate lines, which we call Kramers nodal lines (KNLs), connecting time-reversal invariant momenta. The KNLs create two types of Fermi surfaces, namely, the spindle torus type and the octdong type. Interestingly, all the electrons on octdong Fermi surfaces are described by two-dimensional massless Dirac Hamiltonians. These materials support quantized optical conductance in thin films. We further show that KNLMs can be regarded as parent states of KWSs. Therefore, we conclude that all non-centrosymmetric metals with SOC are topological, as they can be either KWSs or KNLMs.

Highlights

It was pointed out that all chiral crystals with spin-orbit coupling (SOC) can be Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta
As long as the Fermi surfaces enclose time-reversal invariant momentum (TRIM) that are connected by Kramers nodal lines (KNLs), the KNLs force spin-split Fermi surfaces to touch on the KNLs and create two types of Fermi surfaces, namely, the spindle torus type and the octdong type as shown in Fig. 1b, d, respectively
The band touching points of the Fermi surfaces are described by two-dimensional massless Dirac or higher-order Dirac Hamiltonians[20,50,68,69], with the Dirac points pinned at the Fermi energy

Summary

Results

Emergence of Kramers nodal lines from TRIMs with achiral little group symmetry. we demonstrate how nodal lines emerge out of a TRIM with achiral little group symmetry (which contains mirror or roto-inversion). For a TRIM with a little group symmetry that is chiral, Det ðM^ Þ ≠ 0, namely εj are all finite In this case, ∣ f(k)∣ > 0 as long as k is not at the TRIM, which results in a fully split Fermi surface as shown in Fig. 1a and makes the TRIM a Kramers Weyl point as pointed out in ref. The degeneracy is protected by time-reversal symmetry and the achiral little group symmetry We called these lines, KNLs. It is important to note that KNLs create touching points on the Fermi surface at any Fermi energy as long as the. These touching points, which are always pinned at the Fermi energy, are twodimensional Dirac points or higher-order Dirac points[20,50,68,69] with nontrivial topological properties (Supplementary Note 3).

A LH b1 M K Г b2

Discussion

Code availability