Valley-Layer Coupling: A New Design Principle for Valleytronics

The current valleytronics research is based on the paradigm of time-reversal-connected valleys in two-dimensional (2D) hexagonal materials, which forbids the fully electric generation of valley polarization by a gate field. Here, we go beyond the existing paradigm to explore 2D systems with a novel valley-layer coupling (VLC) mechanism, where the electronic states in the emergent valleys have a valley-contrasted layer polarization. The VLC enables a direct coupling between a valley and a gate electric field. We analyze the symmetry requirements for a system to host VLC, demonstrate our idea via first-principles calculations and model analysis of a concrete 2D material example, and show that an electric, continuous, wide-range, and switchable control of valley polarization can be achieved by VLC. Furthermore, we find that systems with VLC can exhibit other interesting physics, such as valley-contrasting linear dichroism and optical selection of the valley and the electric polarization of interlayer excitons. Our finding opens a new direction for valleytronics and 2D materials research.

Figure 1

(a) A 2D material system viewed as consisting of two layers. Each layer may consist of a few atomic layers. (b) With valley-contrasting layer polarization ($P$), an applied gate electrical field can generate valley polarization. The solid (dashed) curves denote the bands in the presence (absence) of the electric field. $P>0$ ($P<0$) means the state is mainly localized on the top (bottom) layer.

Figure 2

(a) Side view and (b) top view of the crystal structure for monolayer TiSiCO. (c) The corresponding BZ. (d) Phonon spectrum for ML-TSCO.

Figure 3

(a) Electronic band structure for ML-TSCO. The size of the red (blue) dots in (a) is proportional to the weight of projection onto atomic orbitals in the bottom (top) Ti atoms. (b) Charge density distribution plotted for VBM and CBM states at the two valleys. (c) shows the band structure under a gate field of $E=0.1\mathrm{eV}/\AA$. (d) Valley splitting for VBM ($\delta E_v$) and CBM ($\delta E_c$) [indicated in (c)] versus the applied gate field.

Figure 4

(a) Valley optical transition selection rules. (b) $X^{\prime }$ and (c) $X$ valley-polarized interlayer excitons with opposite electric polarization can be selectively excited by ${\sigma }_x$ and ${\sigma }_y$ linear polarized optical fields, respectively. This optical selection of the electric dipole of interlayer excitons is an unique phenomenon only associated with VLC.