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

## TL;DR

This paper proposes a theoretical framework using the $8Pmmn$ borophene sheet to manipulate Dirac fermions with electric fields, enabling simulation of space-time phenomena and gravitational analogues in solid-state systems.

## Contribution

It introduces a generic Hamiltonian for $8Pmmn$ borophene under external fields, enabling control over Dirac tilt and space-time analogues, a novel approach in condensed matter physics.

## Key findings

- Electric fields can tune Dirac tilt from space- to time-dependent.
- Black-hole horizon analogues can be created in borophene.
- Electric fields can generate detectable gravitational wave analogues.

## Abstract

We construct the most generic Hamiltonian of the $8Pmmn$ structure of borophene sheet in 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 under-tilted 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. Our platform offers a way to generate analogues of gravitational waves by electric fields (instead of mass sources) which can be detected in solid state spectroscopies as waves of enhanced superconducting correlations.