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 "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.

Hawking radiation on the lattice as universal (Floquet) quench dynamics

“…These results now pave the way for exploring the Hawking effect in other quantum many-body systems, such as for example interacting spin chains (both analytically in integrable models, and numerically using e.g. matrix product state simulations), 2D materials with tilted Dirac cones [36][37][38], and cold-atom or trapped ion experiments. region of the horizon, and x < 0 is the 'inside' region.…”