Generation of Pure Bulk Valley Current in Graphene

The generation of valley current is a fundamental goal in graphene valleytronics but no practical ways of its realization are known yet. We propose a workable scheme for the generation of bulk valley current in a graphene mechanical resonator through adiabatic cyclic deformations of the strains and a chemical potential in the suspended region. The accompanied strain gauge fields can break the spatial mirror symmetry of the problem within each of the two inequivalent valleys, leading to a finite valley current due to quantum pumping. An all-electrical measurement configuration is designed to detect the novel state with pure bulk valley currents.

Figure 1

Illustration and definitions of the (a) graphene based NEMS device and (b) crystallographic coordinate systems used in the Letter.

Figure 2

The pumped charge per cycle of the $K$ valley, denoted as $Q_c^K$. The valley current can be obtained by $e\omega Q_c^K/2\pi$. The width is fixed to be $5000a$ ($\approx 700\mathrm{nm}$), calculated for two different lengths as indicated. We fixed the phase difference of the driving parameters $\varphi =\pi /2$ and take $|{\overrightarrow{A}}_{av}|/k_f\approx 0.002$, which amounts to a strain $u\approx 1.75\times {10}^{-4}$.

Figure 3

Sketch of the pumping generation of pure valley current and an all-electrical detection scheme. The Hall voltage difference $V_{12}=V_1-V_2$ and $V_{34}=V_3-V_4$ across the NEMS is predicted to bear the opposite sign due to the flow of pure valley current.