Artificial gravity field, astrophysical analogues, and topological phase transitions in strained topological semimetals

Abstract

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.

Pseudo-electromagnetic fields in 3D topological semimetals

“…The interface of two distinct Weyl semimetals is expected to result in electronic Veselago lensing [98,99], which can be traced back to an emergent space-time metric for the Weyl fermions due to underlying strain [99]. The exact connection between the metric formulation [79,[100][101][102][103][104] and the pseudo-fields, as that existing for graphene [105], remains to be formally established. This connection can aid to realize effective black-hole metrics [101,103] and serve as design principles for metamaterials [99].…”

Hourglass Weyl loops in two dimensions: Theory and material realization in monolayer GaTeI family

“…The study was initiated by drawing insightful analogy between fundamental particles in the relativistic quantum field theory and low-energy emergent fermions in condensed matters. In this way, the Weyl and Dirac semimetals were discovered [5][6][7][8][9][10][11], which have twofold and fourfold degenerate band crossing points, and around these points, the low-energy electrons resemble the Weyl and Dirac fermions and can exhibit fascinating physical effects like their counterparts in high energy physics [12][13][14]. Moving forward, it was realized that crystalline solids may host more types of emergent fermions beyond the Weyl/Dirac paradigm [15][16][17][18][19].…”

High-pressure lithium as an elemental topological semimetal

“…For example, Weyl and Dirac semimetals host isolated twofold and fourfold degenerate points, respectively, with linear energy dispersions. Their electronic excitations are analogous to the relativistic Weyl and Dirac fermions [30][31][32][33][34], making it possible to simulate interesting highenergy physics phenomena in condensed matter systems [35]. Most materials studied either consist of binary compounds of heavy elements, such as Cd 3 As 2 [32], Na 3 Bi [31,33], or are still more complex compounds [36].…”