Quadratic and Cubic Nodal Lines Stabilized by Crystalline Symmetry

TL;DR

This paper systematically searches for and characterizes higher-order dispersions of nodal lines in electronic band structures, revealing the existence of quadratic and cubic nodal lines stabilized by crystalline symmetry, with potential experimental signatures.

Contribution

It identifies and models quadratic and cubic nodal lines in solid state systems, expanding the understanding of topological band degeneracies beyond linear nodal lines.

Findings

Quadratic and cubic nodal lines are possible and stabilized by crystalline symmetry.

Effective Hamiltonians for these nodal lines are derived and minimal models constructed.

Potential material candidates for these exotic nodal lines are identified via ab-initio calculations.

Abstract

In electronic band structures, nodal lines may arise when two (or more) bands contact and form a one-dimensional manifold of degeneracy in the Brillouin zone. Around a nodal line, the dispersion for the energy difference between the bands is typically linear in any plane transverse to the line. Here, we perform an exhaustive search over all 230 space groups for nodal lines with higher-order dispersions that can be stabilized by crystalline symmetry in solid state systems with spin-orbit coupling and time reversal symmetry. We find that besides conventional linear nodal lines, only lines with quadratic or cubic dispersions are possible, for which the allowed degeneracy cannot be larger than two. We derive effective Hamiltonians to characterize the novel low-energy fermionic excitations for the quadratic and cubic nodal lines, and explicitly construct minimal lattice models to further demonstrate their existence. Their signatures can manifest in a variety of physical properties such as the (joint) density of states, magneto-response, transport behavior, and topological surface states. Using ab-initio calculations, we also identify possible material candidates that realize these exotic nodal lines.