# Topological electronic properties of silicon

## TL;DR

This paper reveals that silicon's electronic states possess complex topological structures characterized by a network of Berry flux lines, making silicon a nodal-chain insulator with stable degeneracies and surface states.

## Contribution

It uncovers the topological nature of silicon's electronic states, introducing the concept of a Berry flux network and classifying silicon as a nodal-chain insulator.

## Key findings

- Silicon has a nontrivial topological Berry flux network.
- Silicon exhibits a topologically stable two-fold degeneracy.
- Surface states resemble drumhead-like states confined by the bulk flux network.

## Abstract

The central role that materials play in human history is exemplified by the three-age division of prehistory into the stone, bronze, and iron ages. References to our present time as the information age or silicon age epitomizes the important role that this semiconducting material came to play in the development of computers and devices that permeate our daily lives. Here we show that the electronic states in silicon have nontrivial topological structures that are captured by a network of Berry flux lines that link at points of high symmetry in the Brillouin zone. This complex network has ice-nodal points where fluxes satisfy ice rules, making silicon a "nodal-chain insulator". Fixing the longitudinal momentum parallel to such flux lines yields a two-dimensional Dirac Hamiltonian for the transverse degrees of freedom. This complex Berry-flux network implies a topologically stable two-fold degeneracy along the X-W direction in all of silicon bands, a fact that is supported by crystal symmetry arguments as well as direct inspection of the vast literature on silicon band structures. Similarly to nodal-chain semimetals, we find drumhead-like states in the regions that are delimited by the projections of the bulk Berry flux network on the surface Brillouin zone.