Sunday, August 4, 2013

1308.0265 (Alfredo Iorio et al.)

Quantum field theory in curved graphene spacetimes, Lobachevsky
geometry, Weyl symmetry, Hawking effect, and all that

Alfredo Iorio, Gaetano Lambiase
We extensively discuss the theoretical framework to make curved monolayer graphene a realization of quantum field theory in curved spacetime. We rely upon a model of the electron-phonon interaction that reproduces the standard semiclassical Dirac quantum field in a curved spacetime. This model holds for very long wavelengths of the graphene conductivity electrons involved. Provided the full description of the phonon-electron interaction is of a modified gravity-type, the core of the results presented here apply, with due changes, to that case too. Using local Weyl symmetry, we probe into the possibility to reproduce a Hawking effect. For the sake of making the test easier in a laboratory, the whole study is carried out for the case of purely spatial curvatures, and for conformally flat spacetimes. Since we show that for the sphere there is no intrinsic horizon, the focus is on the infinite different surfaces of constant negative Gaussian curvature. Even though, in those cases, deep reasons of Lobachevsky geometry seem to lead to unreachable event horizons, we show under which conditions the horizon is within reach. The Hawking effect, then, takes place on the Beltrami surface. We also explicitly study the spacetimes of the other two pseudospheres, and show their relation to de Sitter, and BTZ black-hole spacetimes. In the same limit that gives a reachable event horizon, these two cases, essentially, reduce to Beltrami. This, together with the fact that all the infinite surfaces in point are applicable to either one of the three pseudospheres, make us conjecture about the possibility for a Hawking effect for a generic surface of the family. The Hawking effect here manifests itself through a finite (Hawking) temperature electronic local density of states, that we exhibit.
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