A tiny lateral shift of only about 0.01 nm between graphene layers can strongly affect electron transport, even though it does not change the thickness of the tunneling barrier. We reveal that this unexpected effect originates from changes in the quantum phase relationships of electron wave functions rather than from a simple change in tunneling distance.
More specifically, we study electron transmission through a monolayer/gapped bilayer/monolayer
graphene junction (MBMGJ), where a perpendicular electric field opens a gap in the bilayer region. We show that the shear displacement modifies the evanescent electron waves inside the gapped bilayer by changing the relative phase between wave functions on the two sublattices within each graphene layer of the bilayer, thereby modifying the conductance.
This mechanism also suggests a new electrical approach to probe atomic-scale interlayer shear vibrations: a pump laser pulse can excite the vibration, which periodically changes how easily electrons pass through the graphene junction. When this motion is combined with an oscillating electric field from a probe light, the phase difference between these two AC signals produces a measurable DC current. The proposed method could transform the otherwise difficult-to-detect effects of atomic-scale motion on electron transport into a measurable electrical signal.
Ryo Tamura, “Effects of shear displacement on the conductance of monolayer/gapped bilayer/monolayer graphene junctions: Implications for AC-DC conversion, Phys. Rev. B, in press.
原著論文: Ryo Tamura, Phys. Rev. B 111, 245436 (2025).
Energy symmetry and interlayer wave function ratio of tunneling electrons in partially overlapped graphene
We investigate how electrons tunnel through a bilayer graphene barrier connected to monolayer leads under a vertical electric field, focusing on the energy gap region where the field-induced interlayer potential difference becomes comparable to the interlayer coupling. The transmission probability shows an oscillatory decay with barrier thickness, caused by complex wave vectors whose real parts are locked to the K+ and $K- valleys. This behavior suggests that the valley degree of freedom can be used to design novel tunneling devices.
We classify transmission probability according to whether the electron stays in the same layer or moves between layers, and whether its valley index is preserved or flipped. Interestingly, interlayer transmission probability is less sensitive to the interlayer wave function ratio than intralayer transmission probability, contrary to what one might expect. We explain this using symmetry arguments: only interlayer valley-flipping transmission is symmetric in energy, due to a combination of chiral symmetry (which flips the wave function on one sublattice), a 180-degree rotation (swapping the leads), and probability conservation. Together with the intrinsic energy asymmetry of the interlayer wave function ratio, these symmetries help explain the counterintuitive behavior.
Reference: Ryo Tamura, Phys. Rev. B 111, 245436 (2025).
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.
Fig.3
Reference
(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, J. Phys. Soc. Jpn. 92, 123704 (2023)
