Theoretical Study of Tunnel Valley Current Filter in the Partially Overlapped Graphene under the Vertical Electric Field

The tunnel current (TC) and valley current (VC) are crucial in realizing high-speed and energy-saving in next-generation devices. This issue presents theoretical calculations about the TC and VC link in the partially overlapped graphene shown in Fig. 1.

Fig. 1

Graphene possesses two inequivalent corner points, K+ and K, in the Brillouin zone. A critical issue is the control of the VC, J+J, where J+ and J denote the contributions of valleys K+ and K, respectively, to the charge current, J+ + J. Under the vertical electric field, the two graphene layers have the opposite AB sublattice symmetry, followed by a block on the intravalley transmission. In the allowed intervalley transmission, the difference in the phase of the decay factor prefers only one of the valleys in the output according to the overlapped length N.

Fig. 2

Figure 2 shows the valley polarization  (J+J ) / (J+ + J) as a function of the integer overlap length N for six energies E=+0.02, +0.06, +0.1,  -0.02, -0.06, -0.1 eV. The vertical electric field induces the band gap |E| < 0.17 eV. Data are classified according to the remainder of N divided by three, denoted by mod(N).  Steps (1)-(4) in Fig. 3 illustrate an optical measurement according to Ref. 1. The valley polarization in the right monolayer is detectable in step (4). We can also measure the electron transit time in step (2) from the delay time of the probe pulse. These results suggest that the band gap with no edge state is a new platform of valleytronics.



(1) M. S. Mrudul, A. Jimenez-Galan, M. Ivanov, and G. Dixit, Optica 8, 422 (2021).

(2) Ryo Tamura, J. Phys. Soc. Jpn. 92, 114706 (2023).

(3) Ryo Tamura, Phys. Rev. B 99, 155407 (2019).