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Circuit realization of tilted Dirac cone: A platform for fabrication of curved spacetime geometry on a chip
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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.
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Smart Holes: Analogue black holes with the right temperature and entropy
The entropy of a tilted Dirac cone material, integrated across a spatially varying tilt, grows linearly with temperature behind the analogue horizon and can be mapped to BTZ black hole entropy.
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