# Designing ultrarelativistic and ultraheavy quasiparticles in quantum matter experiments

Famous Einstein's memo *E = m c^2* is an "ultraheavy" limiting case of a more general mass-energy equivalence, generalized to Dirac equation in case of electrons. Another limiting case is *E = c p*, denoting "ultrarelativistic" quasiparticles (travelling at effective speed of light *c*). In our recent paper, we show how to construct stable ultraheavy and ultrarelativistic Dirac quasiparticles at the same energy scale.

Graphene is an atomically-thin crystal of carbon. Since its discovery in 2004, the material became a surprisingly vivid toy for theoretical physics due to its chemical simplicity, and yet the beautiful analogy of Quantum Electrodynamics (QED) "in the pencil": electronic excitations (quasiparticles) in a graphene sheet are accurately described by relativistic Dirac equation, with a different effective "speed of light". In other words, quasiparticles in graphene looks like if they were ultrarelativistic: they have a linear spectrum *E = ħck*, and are described by spinor, two-component wave functions corresponding to pseudospin, constructed from two graphene sublattices. This analogy is very robust, leading to a number of predictions on the basis of Dirac equations, for the first time confirmed experimentally (e.g. relativistic Landau levels with QED degeneracy). There was also a hope to dope graphene further to induce superconductivity in the monolayer; but it was not succeeded for the single layer alone. Thus the search is focused on producing dramatically different electronic structures on the basis of graphene, to reach different scenarios of superconductivity. One ultimate goal would be to have both "ultraheavy" and "ultrarelativistic" quasiparticles at the same energy scale, which will allow band hybridization and thus promote enhanced electronic mobility on the background of electronic localization.