The three "layers" of graphene monolayer and their analog generalized uncertainty principles

TL;DR

This paper demonstrates that graphene can serve as a practical model for exploring generalized uncertainty principles related to quantum gravity, revealing three energy regimes with distinct physical behaviors and new algebraic structures.

Contribution

It identifies three energy regimes in graphene where physics resembles quantum gravity scenarios and derives two new generalized Heisenberg algebras with improved physical interpretations.

Findings

Three energy regimes with pseudorelativistic physics in graphene.

Derivation of two new generalized Heisenberg algebras.

Physical interpretation of high-energy coordinates in lab measurements.

Abstract

We show that graphene, in its simplest form and settings, is a practical table-top realization of the analog of exotic quantum gravity scenarios, which are speculated to lead to certain generalized Heisenberg algebras. In particular, we identify three different energy regimes (the ``layers'') where the physics is still of a pseudorelativistic (Dirac) type but more and more sensitive to the effects of the lattice. This plays here a role analog to that of a discrete space, where the Dirac quasiparticles live. This work improves and pushes further earlier results, where the physical meaning of the high energy momenta was clear, but the conjugate coordinates only had a purely abstract description. Here we find the physical meaning of the latter by identifying the mapping between the high-energy coordinates and low-energy ones, i.e., those measured in the lab. We then obtain two generalized Heisenberg algebras that were not noticed earlier. In these two cases, we have the striking result that the high-energy coordinates just coincide with the standard ones, measured in the lab. A third generalized Heisenberg algebra is obtained, and it is an improvement of the results obtained earlier in two respects: we now have an expression of the generalized coordinates in terms of the standard phase-space variables, and we obtain higher order terms. All mentioned results clearly open the doors to table-top experimental verifications of many generalized uncertainty principle-corrected predictions of the quantum gravity phenomenology.