Dimensionality-mediated type-II Dirac semimetal to quantum spin Hall insulator phase transition in TiC

We present first-principles results on monolayer (ML) and bulk titanium carbide (TiC) exhibiting dual topological characteristics: a quantum spin Hall insulator state in two-dimensional ML and a type-II Dirac semimetal state in its three-dimensional bulk form. The nontrivial nature of ML TiC is confirmed through the calculation of a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi mathvariant="normal">Z</a:mi><a:mn>2</a:mn></a:msub></a:math> invariant, spin Hall conductivity, and edge states. The edge band structure of ML TiC displays a single pair of gapless edge states at the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>M</c:mi></c:mrow></c:math> point. The insulating topological phase in ML TiC is driven by a band inversion around the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>M</d:mi></d:mrow></d:math> point involving Ti-<e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>d</e:mi></e:math> orbitals, with a nontrivial band gap of 0.47 eV. Our findings also indicate that ML TiC possesses excellent dynamical and thermal stability. Moreover, the bulk, ML hollow sphere arrays, and a 4-nm-thick film of TiC have already been synthesized, suggesting the high feasibility of the experimental synthesizing of ML TiC. On the other hand, we demonstrate that the bulk TiC hosts both a type-II Dirac cone and a topological nodal surface without spin-orbit coupling, protected by a combined symmetry of inversion and time reversal. The presence of spin-orbit coupling removes the nodal surface while preserving the type-II Dirac cone. Surface states connecting bulk Dirac nodes in bulk TiC can be readily observed, making the surface characteristics easily detectable in experiments. Published by the American Physical Society 2024