Circuit realization of a tilted Dirac cone: Platform for fabrication of curved spacetime geometry on a chip
Ahmad Motavassal, S. A. Jafari
Abstract
We present an $LC$ circuit model that supports a tilted ``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 ${C}_{0}$ 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. Nonuniform spatial dependence of the mutual inductance or capacitance induces a nontrivial geometrical structure on the emergent spacetime. Our work extends the range of usefulness of circuit models to emulate nontrivial spacetime structures.