Single-parameter charge pump in a zigzag graphene nanoribbon.

We report a theoretical study of a single-parameter quantum charge pump in the clean zigzag graphene nanoribbon (ZGNR) system. By Keldysh Green's function method, we show that a pumped current in the ZGNR with an even number of zigzag chains can sharply increase from zero as the frequency matches the Fermi energy, whereas the pumped charge current is always absent in the ZGNR with an odd number of zigzag chains as well as the GNR with armchair edges, it is attributed to the peculiar zero-energy edge state in the ZGNR and the symmetry breaking of the topologically inequivalent carbon atoms due to the zigzag edges. The pumped current in the even-ZGNR decreases with the Fermi energy and its direction is determined by Fermi energy below or above the Dirac point as well as the type of carbon atoms at one edge of the ZGNR. The two-parameter charge pump in the ZGNR is also discussed and the magnitude of the pumped current is comparable to the single-parameter pump when the pumping frequency matches the Fermi energy.