High spin-Chern-number insulator in α-antimonene with a hidden topological phase
Baokai Wang, Xiaoting Zhou, Yi-Chun Hung, Yen-Chuan Lin, Hsin Lin, Arun Bansil
Abstract
Abstract For a time-reversal symmetric system, the quantum spin Hall phase is assumed to be the same as the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> topological insulator phase in the existing literature. The spin Chern number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">C</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> </mml:math> is presumed to yield the same topological classification as the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> invariant. Here, by investigating the electronic structures of monolayer α -phase group V elements, we uncover the presence of a topological phase in α -Sb, which can be characterized by a spin Chern number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">C</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> </mml:math> = 2, even though it is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> trivial. Although α -As and Sb would thus be classified as trivial insulators within the classification schemes, we demonstrate the existence of a phase transition between α -As and Sb, which is induced by band inversions at two generic k points. Without spin–orbit coupling (SOC), α -As is a trivial insulator, while α -Sb is a Dirac semimetal with four Dirac points (DPs) located away from the high-symmetry lines. Inclusion of the SOC gaps out the DPs and induces a nontrivial Berry curvature, endowing α -Sb with a high spin Chern number of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">C</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> </mml:math> = 2. We further show that monolayer α -Sb exhibits either a gapless band structure or a gapless spin spectrum on its edges, as expected from topological considerations.