The emerging field of valleytronics harnesses the valley degree of freedom of electrons, akin to how electronic and spintronic devices utilize the charge and spin degrees of freedom of electrons, respectively. The engineering of valleytronic devices typically relies on the coupling between valley and other degrees of freedom such as spin, giving rise to valley spintronics where an external magnetic field manipulates the information stored in valleys. Here, a valley gapless semiconductor is proposed as a potential electrically controlled valleytronic platform because the valley degree of freedom is coupled to the carrier type, i.e., electrons and holes. The valley degree of freedom can be electrically controlled by tuning the carrier type via the device gate voltage. We demonstrate the proposal for realizing a valley gapless semiconductor in the honeycomb lattice with the Haldane and modified Haldane models. The system's valley-carrier coupling is further studied for its transport properties in an all-electrically controlled valley filter device setting. Our work highlights the significance of the valley gapless semiconductor for valleytronic devices.

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• Valley degrees of freedom
• 2-dimensional systems
• Two-dimensional electron system
• Tight-binding model