Hunting Quantum Gravity with Analogs: The Case of Graphene

Abstract

Analogs of fundamental physical phenomena can be used in two ways. One way consists in reproducing specific aspects of the classical or quantum gravity of quantum fields in curved space or of other high-energy scenarios on lower-energy corresponding systems. The “reverse way” consists in building fundamental physical theories, for instance, quantum gravity models, inspired by the lower-energy corresponding systems. Here, we present the case of graphene and other Dirac materials.

Classical space from quantum condensates

“…[21], this mechanism is realized in the QG quasiparticle picture (see Refs. [14,18]), but it can be equally well-applied in other scenarios as condensed matter analogs of QG [6,7,8,9,10,11,12,13].…”

“…[21], this is a good description of the Xons model of Refs. [14,17,18,13], for an observer whose energy scale is "low", compared to Planck's. The presentation will closely follow the one of Ref.…”

Spinor solutions of a Chern-Simons model for the superconformal algebra

“…As a future work it would be interesting to explore the existence of similar self-gravitating spinor configurations in Dirac materials [32] or planar QED [33].…”

“…Therefore the system is not over constrained as long as the Dirac equation is compatible with conditions ( 29) and (32). Now, in d = 3, we can write the most general solution to the covariantly constant torsion condition, which is implied by (26) and the field eq.…”

Time-loops to spot torsion on bidimensional Dirac materials with dislocations

“…Given the natural occurrence of topological defects in graphene [10,11] and other Dirac materials [12], and given that such materials have been proposed as versatile analogs of classical and quantum gravitational phenomena, as told in [13][14][15][16][17][18][19][20][21][22][23] and in the recent review [24], then it is very natural to seek for the role of torsion in the analog gravitational physics realized there. However, early attempts in that direction (that we shall recall later in Section 2) had negative outcomes due to the geometrical obstruction existing in two-space-dimensional materials [11].…”