Circuit realization of tilted Dirac cone: A platform for fabrication of curved spacetime geometry on a chip

Abstract: We present a LC circuit model that supports tilted {\it Dirac cone} in its spectrum. The tilt of the Dirac cone is specified by the parameters of the model consisting of mutual inductance between the neighboring sites and a capacitance C0 at every lattice site. These parameters can be completely measured by impedance spectroscopy. Given that a tilted Dirac cone can be described by a background spacetime metric, the impedance spectroscopy can perfectly provide (local) information about the metric of the spacetime. Non-uniform spatial dependence of the mutual inductance or capacitance induces non-trivial geometrical structure on the emergent spacetime.