Valleytronics in two-dimensional merging Dirac cone system: Universal reversible Boolean gate*

Due to the logical irreverisbility, the energy efficiency of Boolean logic gates is fundamentally capped by the Landauer's waste heate generation limit of k_BTlog2 per bit of irreversible operation. Here we show that valley degree of freedom in two-dimensional (2D) material can be harnessed to ressurect the logical reverisbility of classical two-input Boolean logics. The valley index manifests macroscopically in the electrical current as three distinct polarization states: two opposite valley polarizations plus one null state. These triplet of valley polarization states can be used to encode additional information, thus removing all ambiguity and recovering logical reveribility in Boolean logic gates. We use 2D merging Dirac cone system, which occurs in few-layer black phosphorus, strained graphene, and 2D topological Dirac semimetal, as a toy model to demonstrate three fundamental valleytronic building blocks: valley filter, valve, and logic gates. We show that the all-important universal reversible gate, such as the NAND gate, can be realized using this valleytronic approach. Our findings provide a new valleytronic route towards ultimately energy-efficient classical reverisble computing.