Emergence of topological semimetals in gap closing in semiconductors without inversion symmetry

Abstract

A band gap for electronic states in crystals governs various properties of solids, such as transport, optical and magnetic properties. Its estimation and control have been an important issue in solid state physics. The band gap can be controlled externally by various parameters, such as pressure, atomic compositions and external field. Sometimes, the gap even collapses by tuning some parameter. In the field of topological insulators, such closing of the gap at a time-reversal invariant momentum indicates a band inversion, i.e. it leads to a topological phase transition from a normal insulator to a topological insulator. Here we show that the gap losing in inversion-asymmetric crystals is universal, in the sense that the gap closing always leads either to a Weyl semimetal or a nodal-line semimetal, from an exhaustive study on possible space groups. We here consider three-dimensional spinful systems with time-reversal symmetry. The space group of the system and the wavevector at the gap closing uniquely determine which possibility occurs and where the gap-closing points or lines lie in the wavevector space after closing of the gap. In particular, we show that an insulator-to-insulator transition never happens, which is in sharp contrast with inversion-symmetric systems.

13 pages, 8 figures

References in corpus (11)

• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological response in Weyl semimetals and the chiral anomaly
• Topological Node-Line Semimetal in Three Dimensional Graphene Networks
• Potential ring of Dirac nodes in a new polymorph of Ca${}_3$P${}_2$
• Line of Dirac Nodes in Hyper-Honeycomb Lattices
• Weyl Node and Spin Texture in Trigonal Tellurium and Selenium
• Weyl semimetals from noncentrosymmetric topological insulators
• Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator
• Co-existence of Weyl Fermion and Massless Triply Degenerate Nodal Points
• Universal phase diagrams for the quantum spin Hall systems
• Topological semimetals and topological insulators in rare earth monopnictides

Cited by in corpus (42)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• Non-abelian topology of nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems
• Electrides as a New Platform of Topological Materials
• Pressure-induced topological phase transition in noncentrosymmetric elemental Tellurium
• Topological semimetals studied by ab initio calculations
• Excellent catalytic performance towards the hydrogen evolution reaction in topological semimetals
• Qsymm: Algorithmic symmetry finding and symmetric Hamiltonian generation
• Crossing-Line-Node Semimetals: General Theory and Application to Rare-Earth Trihydrides
• Negative piezoelectric response of van der Waals layered bismuth tellurohalides
• Topological semimetal in honeycomb lattice LnSI
• Weyl-Kondo semimetals in nonsymmorphic systems
• Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions
• Weyl Semimetal and Topological Phase Transition in Five Dimensions
• Universal phase transition and band structures for spinless nodal-line and Weyl semimetals
• Classification of accidental band crossings and emergent semimetals in two-dimensional noncentrosymmetric systems
• Topological quantum critical point in a triple-Weyl semimetal: non-Fermi-liquid behaviors and instabilities
• Disorder-Induced Weyl Semimetal Phase and Sequential Band Inversions in PbSe-SnSe Alloys
• Noncentrosymmetric topological Dirac semimetals in three dimensions
• Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators
• Nodal higher-order topological superconductivity from a ${\mathcal{C}}_4$-symmetric Dirac semimetal
• Appearance of the universal value $e^2/h$ of the zero-bias conductance in a Weyl semimetal-superconductor junction
• Nexus networks in carbon honeycombs
• Photocurrents in bulk tellurium
• Topological Magnon Insulator with a Kekule Bond Modulation
• Generic phase diagram for Weyl superconductivity in mirror-symmetric superconductors
• Superconductivity from piezoelectric interactions in Weyl semimetals
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• High-order harmonic generations in tilted Weyl semimetals
• Engineering a pure Dirac regime in ZrTe${}_5$
• Quantum Liouville's theorem based on Haar measure
• Geometric pumping and dephasing at topological phase transition
• Generating Weyl semimetals from alkali metals
• Parallel and anti-parallel helical surface states for topological semimetals
• Five-dimensional Floquet topological semimetals with emergent Yang monopoles and linked Weyl surfaces
• Evidence for Weyl fermions in the elemental semiconductor tellurium
• Relativistic horizon of interacting Weyl fermions in condensed matter systems
• Nonlinear bulk photocurrent probe Z2 topological phase transition
• Berry curvature generation detected by Nernst responses in ferroelectric Weyl semimetal
• Growth and Strain Engineering of Trigonal Te for Topological Quantum Phases in Non-Symmorphic Chiral Crystals
• Systematic study for two-dimensional $Z_2$ topological phase transitions at high-symmetry points in all layer groups