Valley physics and anomalous valley Hall effect in single-layer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>h</mml:mi><mml:mtext>−</mml:mtext><mml:mi>M</mml:mi><mml:mi mathvariant="normal">N</mml:mi><mml:mi>X</mml:mi></mml:mrow></mml:math> (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mi>Ti</mml:mi></mml:mrow></mml:math>, Zr, Hf; <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>Cl</mml:mi></mml:mrow></mml:math>, Br)
Pei Zhao, Yan Liang, Yandong Ma, Thomas Frauenheim
Abstract
Recently, the valley degree of freedom of electrons in two-dimensional materials has been attracting growing attention as an information carrier. Here, on the basis of first-principles calculations, we propose a series of unique 2D valleytronic materials in single-layer $h\text{\ensuremath{-}}M\mathrm{N}X$ ($M=\mathrm{Ti}$, Zr; Hf, $X=\mathrm{Cl}$, Br) and systematically investigate their valleytronic properties. The underlying valley-contrasting physics including valley spin splitting and valley-dependent optical selection rules in single-layer $h\text{\ensuremath{-}}M\mathrm{N}X$ is unveiled. Moreover, we find that the intriguing valley polarization in single-layer $h\text{\ensuremath{-}}M\mathrm{N}X$ can be achieved through both circularly polarized light and a ferromagnetic substrate. The substrate-induced valley polarization in SL $h\text{\ensuremath{-}}M\mathrm{N}X$ is stacking dependent and can be enhanced by decreasing the interlayer distance. Our findings thus provide a tantalizing platform for operating the valley index in two-dimensional materials.