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We construct the most generic Hamiltonian of the $8Pmmn$ structure ofborophene sheet in presence of spin-orbit, as well as background electric andmagnetic fields. In addition to spin and valley Hall effects, this structureoffers a framework to conveniently manipulate the resulting "tilt" of the Diracequation by applying appropriate electric fields. Therefore, the tilt can bemade space-, as well as time-dependent. The border separating the low-fieldregion with under-tilted Dirac fermions from the high-field region withover-tilted Dirac fermions will correspond to a black-hole horizon. In thisway, space-time dependent electric fields can be used to design the metric ofthe resulting space-time felt by electrons and holes satisfying the tiltedDirac equation. Our platform offers a way to generate analogues ofgravitational waves by electric fields (instead of mass sources) which can bedetected in solid state spectroscopies as waves of enhanced superconductingcorrelations.

The $8Pmmn$ borophene sheet: A solid-state platform for space-time engineering