Solid-state platform for space-time engineering: The 8Pmmn borophene sheet

We construct the most generic Hamiltonian of the 8Pmmn structure of a borophene sheet in the presence of spin orbit, as well as background electric and magnetic fields. In addition to spin and valley Hall effects, this structure offers a framework to conveniently manipulate the resulting "tilt" of the Dirac equation by applying appropriate electric fields. Therefore, the tilt can be made space as well as time dependent. The border separating the low-field region with undertilted Dirac fermions from the high-field region with over-tilted Dirac fermions will correspond to a black-hole horizon. In this way, space-time-dependent electric fields can be used to design the metric of the resulting space-time felt by electrons and holes satisfying the tilted Dirac equation. Given that the velocity of light is replaced by a two to three orders-of-magnitude smaller Fermi velocity, the tests of gravity when imported to our solid-state setting will correspond to four to six orders-of-magnitude larger effects. Our platform offers a way to generate analogues of (nonpropagating) gravitational waves by electric fields (rather than by mass sources) which can be detected in solid-state spectroscopies as enhanced superconducting correlations.