Coupled spin and valley polarization in monolayer HfN2 and valley-contrasting physics at the HfN2−WS

Despite extensive studies on coupled spin and valley physics, occurrence of these properties is currently limited to transition-metal dichalcogenides (TMDCs) and graphene. Therefore, exploration of materials beyond TMDCs and graphene is necessary for a further advancement in valleytronics. In this work, the $\mathrm{Hf}{\mathrm{N}}_{2}$ monolayer, a theoretically reported semiconductor having a direct band gap has been investigated in-depth for its applications in valleytronics and spintronics. It exhibits a large valley spin splitting (VSS) \ensuremath{\sim}314 meV at the conduction band (CB) due to strong spin-orbit coupling (SOC). Such a large VSS at the CB is unique and comparable to that of tungsten-based dichalcogenide monolayers at its valence band (VB). The spin splitting is nearly insensitive to small in-plane strain, whereas the optical transition frequencies between the spin states $({\ensuremath{\omega}}_{\mathrm{up}},\phantom{\rule{4pt}{0ex}}{\ensuremath{\omega}}_{\mathrm{down}})$ in the CB and VB is effectively strain tunable. Inspired by the experimentally observed higher exciton lifetime 1.8 ns in $\mathrm{MoS}{\mathrm{e}}_{2}/\mathrm{WS}{\mathrm{e}}_{2}$ type-II van der Waals heterostructure (vdWH) than in the monolayers \ensuremath{\sim}2.1 (2.5) $ps$ in monolayer $\mathrm{Mo}{\mathrm{S}}_{2}$ $(\mathrm{W}{\mathrm{S}}_{2})$, a type-II (vdWH) prototype has been demonstrated by stacking $\mathrm{Hf}{\mathrm{N}}_{2}$ monolayer over $1\mathrm{H}\ensuremath{-}\mathrm{WS}{\mathrm{e}}_{2}$ monolayer for an extended lifetime of valley polarized excitons and large magnitude of spin splitting at both CB and VB. The elastic properties highlight the robustness of $\mathrm{Hf}{\mathrm{N}}_{2}$ monolayer and vdWH, as the bending modulus and critical buckling strain are found to be superior to that in graphene. Further, carrier mobility calculated using the deformation potential theory in $\mathrm{Hf}{\mathrm{N}}_{2}/\mathrm{WS}{\mathrm{e}}_{2}$ is as high as ${\ensuremath{\mu}}_{h}=16\phantom{\rule{4pt}{0ex}}\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}{\mathrm{V}}^{1}{\mathrm{s}}^{\ensuremath{-}1}$. Moreover, this work introduces the $\mathrm{Hf}{\mathrm{N}}_{2}$ monolayer as an exceptionally promising valleytronic material having valley properties complementary to that of Group VI TMDC. This is a report on valley contrasting physics and VSS at the CB, which would strongly motivate experimentalists to synthesize and explore this predicted two-dimensional material.