Condensed matter systems can be used to emulate and explore phenomena from a completely different field of physics, for example, elementary particle physics or gravity. Such analog condensed matter models provide a novel perspective to approach questions that are not directly accessible in the original systems as they can potentially be realized experimentally in a well-controlled setup. As a recent example, the production of bosonic particles in an expanding universe has been experimentally simulated via Bose-Einstein condensates [1].

Expanding on our work on bosonic particle production, we address for the first time the cosmological fermion production in expanding universes using Dirac materials as analog models [2]. This is inspired by the development that two-dimensional Dirac materials, such as twisted bilayer graphene, have been established as highly tunable condensed matter platforms allowing us to manipulate electronic band structures and interaction effects in a controlled manner. A remarkable feature of Dirac materials is that the Fermi velocity of the low-energy excitations can be tuned dynamically over several orders of magnitude leading to a time-dependent metric for the Dirac fermions. In addition, we consider the presence of time-dependent Dirac masses that may originate from symmetry breaking and lead to a finite band gap in the energy dispersion. These ingredients allow us to construct an analog model for the phenomenon of cosmological fermion production in expanding universes, arising due to a time-dependent metric and conformal symmetry breaking. Finally, I will also briefly discuss finite-temperature effects of the dynamical generation of Dirac masses through quantum phase transitions into symmetry-broken states, closely resembling fermionic mass generation and chiral symmetry breaking in elementary particle physics [3].

[1] C. Viermann, M. Sparn, N. Liebster, M. Hans, E. Kath, Á. Parra-López, M. Tolosa-Simeón, N. Sánchez-Kuntz, T. Haas, H. Strobel, S. Floerchinger and M. K. Oberthaler, Quantum field simulator for dynamics in curved spacetime, Nature 611, 260–264 (2022).

[2] M. Tolosa-Simeón, M. M. Scherer and S. Floerchinger, Analog of cosmological particle production in Dirac materials, Phys. Rev. B 110, 085421 (2024).

[3] M. Tolosa-Simeón, L. Classen and M. M. Scherer, Relativistic Mott transitions, quantum criticality, and finite-temperature effects in tunable Dirac materials from functional renormalization, arXiv:2503.04911 (2025)."