Analog of cosmological particle production in Dirac materials

Two-dimensional van der Waals materials have recently been established experimentally as a highly-tunable condensed matter platform, facilitating the controlled manipulation of band structures and interactions. In several of these materials, Dirac cones are present in the low-energy regime near the Fermi level. Thus fermionic excitations emerging in these materials close to the Dirac cones have a linear dispersion relation near the Fermi surface as massless relativistic Dirac fermions. Here, we study low-energy fermionic excitations of such Dirac materials in the presence of a mass gap that may be generated by symmetry breaking. Introducing a dynamical Fermi velocity and/or time-dependent mass gap for the Dirac quasiparticles, we exhibit the emergence of an analog of cosmological fermion pair production in terms of observables such as the expected occupation number or two-point correlation functions. We find that it is necessary and sufficient for quasiparticle production that only the ratio between the mass gap and the Fermi velocity is time-dependent. In this way, we establish that highly-tunable Dirac materials can serve as analog models for cosmological spacetime geometries, in particular, for Friedmann-Lema\^{\i}tre-Robertson-Walker expanding cosmologies. We briefly discuss possibilities for experimental realization.