Topological semi-metals with line nodes and drumhead surface states

TL;DR

This paper explores how various symmetries protect line nodes in topological semimetals, establishing their stability through crystalline invariants and linking them to surface states like drumheads, exemplified by Ca$_3$P$_2$.

Contribution

It identifies the symmetry-protected topological invariants that stabilize line nodes and connects these invariants to observable surface states in topological semimetals.

Findings

Crystalline invariants guarantee line node stability.

Quantized Berry phase leads to protected surface states.

Ca$_3$P$_2$ exhibits nearly flat drumhead surface states.

Abstract

In an ordinary three-dimensional metal the Fermi surface forms a two-dimensional closed sheet separating the filled from the empty states. Topological semimetals, on the other hand, can exhibit protected one-dimensional Fermi lines or zero-dimensional Fermi points, which arise due to an intricate interplay between symmetry and topology of the electronic wavefunctions. Here, we study how reflection symmetry, time-reversal symmetry, SU(2) spin-rotation symmetry, and inversion symmetry lead to the topological protection of line nodes in three-dimensional semi-metals. We obtain the crystalline invariants that guarantee the stability of the line nodes in the bulk and show that a quantized Berry phase leads to the appearance of protected surfaces states with a nearly flat dispersion. By deriving a relation between the crystalline invariants and the Berry phase, we establish a direct connection between the stability of the line nodes and the topological surface states. As a representative example of a topological semimetal with line nodes, we consider Ca$_3$P$_2$ and discuss the topological properties of its Fermi line in terms of a low-energy effective theory and a tight-binding model, derived from ab initio DFT calculations. Due to the bulk-boundary correspondence, Ca$_3$P$_2$ displays nearly dispersionless surface states, which take the shape of a drumhead. These surface states could potentially give rise to novel topological response phenomena and provide an avenue for exotic correlation physics at the surface.