Effective gravity and gauge fields are emergent properties intrinsic for low-energy quasiparticles in topological semimetals. Here, taking two Dirac semimetals as examples, we demonstrate that applied lattice strain can generate warped spacetime, with fascinating analogues in astrophysics. Particularly, we study the possibility of simulating black-hole/white-hole event horizons and gravitational lensing effect. Furthermore, we discover strain-induced topological phase transitions, both in the bulk materials and in their thin films. Especially in thin films, the transition between the quantum spin Hall and the trivial insulating phases can be achieved by a small strain, naturally leading to the proposition of a novel piezo-topological transistor device. Possible experimental realizations and analogue of Hawking radiation effect are discussed. Our result bridges multiple disciplines, revealing topological semimetals as a unique table-top platform for exploring interesting phenomena in astrophysics and general relativity; it also suggests realistic materials and methods to achieve controlled topological phase transitions with great potential for device applications.npj Quantum Materials (2017) 2:23 ; doi:10.1038/s41535-017-0026-7
INTRODUCTIONRelativity is a fundamental aspect for all elementary particles in the high-energy regime. In condensed matter physics, however, the relevant energy scale we probe is much lower (compared with, e.g., the electron rest mass), hence the electronic dynamics is usually considered as non-relativistic. Nonetheless, due to interactions with lattice and between electrons themselves, the electron properties in crystalline solids are strongly renormalized, and the resulting low-energy electron quasiparticles can behave drastically different from free electrons. Remarkably, in a class of recently discovered topological semimetal materials, the band structures feature nontrivial band-crossings close to the Fermi level, around which the low-energy quasiparticles become massless and resemble relativistic particles. For example, in socalled Weyl semimetals, the Fermi surface consists of isolated band-crossing points, each carrying a topological charge of ±1 corresponding to its chirality, and the low-energy quasiparticles mimic the Weyl fermions in high-energy physics.1, 2 With further protection from crystalline symmetry, a pair of Weyl points can be stabilized at the same point (called the Dirac point) in the energy-momentum space, realizing the Dirac semimetal (DSM) phase.3 A number of 3D materials have been predicted to host Weyl/Dirac points.4-9 Some of them, including the DSMs Na 3 Bi and Cd 3 As 2 , 10,11 have been confirmed in recent experiments.