Condensed matter realization of fermion quasiparticles in Minkowski space

"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.