Layer-number-dependent spin Hall effects in transition metal monocarbides $M_{2}\rm{C}$ ($M=\rm{V}, \rm{Nb}, \rm{Ta}$)

TL;DR

This study reveals that the spin Hall effect in layered transition metal carbides $M_{2} m{C}$ ($M= m{V}, m{Nb}, m{Ta}$) is significantly enhanced by increasing layer number, due to layer-dependent nodal line structures affecting spin Berry curvature.

Contribution

It systematically investigates the topological properties and intrinsic spin Hall effects of layered transition metal carbides, highlighting layer-dependent enhancement of spin Hall conductivity.

Findings

Large spin Hall conductivity up to ~1100 $(rac{ ext{ħ}}{e})( ext{Ω·cm})^{-1}$ in bulk Ta$_2$C.

Maximum SHC of ~600 $(rac{ ext{ħ}}{e})( ext{Ω·cm})^{-1}$ in eight-layer Ta$_2$C.

Layer number influences nodal line structures, leading to giant SHE.

Abstract

The recent discovery of strong spin Hall effects (SHE) in 2D layered topological semimetals has attracted intensive attention due to its exotic electronic properties and potential applications in spintronic devices. In this paper, we systematically study the topological properties and intrinsic SHE of layered transition metal carbides $M_{2}\rm{C}$ ($M=\rm{V}, \rm{Nb}, \rm{Ta}$). The results show that both bulk and monolayer $M_{2}\rm{C}$ have symmetry-protected nodal points (NPs) and lines (NLs) originating from the $d$ band crossing near the Fermi level ($E_F$). The inclusion of SOC breaks the degeneracy of NLs and NPs, contributing to large spin Hall conductivity (SHC) up to $\sim$1100 and $\sim$200 $(\hbar / e)(\Omega \mathrm{cm})^{-1}$ for bulk and monolayer Ta$_{2}$C, respectively. Remarkably, we find that magnitude of SHC exhibits a significant enhancement by increasing the layer number. For eight-layer Ta$_{2}$C, the maximum value of SHC can reach up to $\sim$600 $(\hbar / e)(\Omega \mathrm{cm})^{-1}$, comparable to many reported 3D topological materials. Analysis of spin Berry curvature reveals that the large SHC originates from layer-number-dependent nodal line structure near the $E_F$, in which the repeated crossover between valence and conduction bands creates large amounts of NPs along the $\Gamma\rm{-K}$ route. Our findings not only provide a new platform for experimental research of low-dimensional SHE, but also suggest an effective way of realizing giant SHE by controlling layer thickness.