Anomalous valley Hall effect induced by mirror symmetry breaking in transition metal dichalcogenides

The control of the valley degree of freedom in Bloch electrons has opened up new avenues for information processing. The synthesis of ferrovalley materials, however, has been limited due to the stringent requirements for breaking both time and space inversion symmetries. To address this challenge, we propose a Janus method for inducing valley polarization in nonmagnetic transition metal dichalcogenides. Our study shows that the magnetic moment in monolayer TiTeI arises from the breaking of mirror symmetry and the presence of unpaired electrons. The Stoner criterion $I_{ex}N\left(E_F\right)>1$ confirms that the band splitting originates from the $d$ orbital of titanium. Moreover, the exchange interaction combined with spin-orbit coupling opens up the valley splitting. The anomalous valley Hall effect (AVHE) can be realized by applying an in-plane electric field, as a result of the valley-contrasting Berry curvature. The modulation of valley-selective circular dichroism and AVHE by optical, electronic, and magnetic fields make TiTeI a promising material for future studies and applications in valleytronics.

Figure 1

The schematic valley at $K$ and $K^{\prime }$. Left and right panels represent the circularly polarized light absorption rules at a nonmagnetic and ferromagnetic system, respectively. Blue and red lines are the spin-up and spin-down channels.

Figure 2

The atomic structure of 1L TiTeI. (a) The side view and (b) the top view of the TMD. (c) The phonon dispersion along high-symmetry points.

Figure 3

The electronic structure of 1L TiTeI by DFT calculations. The band structure of 1L TiTeI (a) without spin polarization and with SOC, and (b) with spin polarization and without SOC. Dark and red lines represent spin-up and spin-down channels, respectively. The $d$ orbital-resolved band structure with spin polarization and SOC for magnetic moment (c) parallel and (d) perpendicular to the $z$ axis.

Figure 4

The circular light absorption of 1L TiTeI. Upper panel: Circularly polarized light absorption at the $K^{\prime }$ valley. Lower panel: Circularly polarized light absorption at the $K$ valley. Blue and red lines represent left- and right-handed polarization light, respectively. Moreover, red and blue vertical solid lines represent the location of excitons A and B. The band gap of the $K^{\prime }$ and $K$ valleys has been marked as red and blue dashed lines.

Figure 5

The anomalous valley Hall effect of 1L TiTeI. (a) The right-handed light conductivity and (b) the total Berry curvature at the first Brillouin zone. The spin polarization is parallel to the $+Z$ axis. (c) The Berry curvature and (d) corresponding anomalous valley Hall effect at magnetic moment parallel to $+Z$ and $-Z$.

Figure 6

The valley and magnetic properties of 1L TiTeI. (a) The strain influence of the band gap at the $K$ (blue) and $K^{\prime }$ (red) valleys, and valley splitting between the two valleys (black). (b) The Berry curvature and (c) magnetic anisotropy with a biaxial strain. (d) The anomalous valley Hall device.