Analogue gravity approach to the electronic properties of curved graphene
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The two-dimensional Dirac material graphene can be bent and folded into countless shapes and structures, in which case the low-energy electronic excitations in the material are described by the mathematics of quantum ﬁeld theory in curved space and subject to geometric forces an alogous to gravity. It is shown how the Dirac equation can be adapted to curved spacetimes using the vierbein picture of general relativity, and this procedure is applied to two different types of 2D systems which can be realised experimentally using graphene: cylindrically symmetric transverse distortions in a place, and a spherical surface. Finally, the relationship between curvature and the emergence of a pseudomagnetic ﬁeld is discussed.