Condensed matter realization of fermion quasiparticles in Minkowski space

TL;DR

This paper introduces Minkowski fermions as quasiparticles in 2+1D Minkowski spacetime, classifies them, and predicts their realization in a specific boron allotrope using first-principles calculations.

Contribution

It proposes the concept of Minkowski fermions in condensed matter and predicts their realization in a metastable boron phase, bridging relativity and material physics.

Findings

Minkowski fermions classified as Klein-Gordon and Dirac-Minkowski types.

Realization of Dirac-Minkowski fermions in Pnnm-B16 boron.

First-principles calculations confirm the existence of massless Dirac-Minkowski fermions.

Abstract

"What is the difference between space and time?" is an ancient question that remains a matter of intense debate. In Newtonian mechanics time is absolute, while in Einstein's theory of relativity time and space combine into Minkowski spacetime. Here, we firstly propose Minkowski fermions in 2+1 dimensional Minkowski spacetime which have two space-like and one time-like momentum axes. These quasiparticles can be further classified as Klein-Gordon fermions and Dirac-Minkowski fermions according to the linearly and quadratically dispersing excitations. Realization of Dirac-Minkowski quasiparticles requires systems with particular topological nodal-line band degeneracies, such as hyperbolic nodal lines or coplanar band crossings. With the help of first-principles calculations we find that novel massless Dirac-Minkowski fermions are realized in a metastable bulk boron allotrope, Pnnm-B16.