Pseudo Electric Field and Pumping Valley Current in Graphene Nano-bubbles

TL;DR

The paper addresses how a time-dependent nano-bubble in graphene can harness strain-induced pseudo fields to pump valley currents without an external bias. It employs a tight-binding graphene model with a Gaussian deformation and analyzes both the induced pseudo magnetic and pseudo electric fields, along with the resulting charge and valley currents using time-dependent simulations. A key finding is that the valley current carries higher harmonics and a dominant $3\omega_0$ component while the net charge pumping remains zero, highlighting nonlinear valley dynamics. This work suggests a pathway toward low-dissipation valleytronic devices and motivates further exploration of dynamic strain effects and local current distributions in graphene.

Abstract

The extremely high pseudo-magnetic field emerging in strained graphene suggests that an oscillating nano-deformation will induce a very high current even without electric bias. In this paper, we demonstrate the sub-terahertz (THz) dynamics of a valley-current and the corresponding charge pumping with a periodically excited nano-bubble. We discuss the amplitude of the pseudo-electric field and investigate the dependence of the pumped valley current on the different parameters of the system. Finally, we report the signature of extra-harmonics generation in the valley current that might lead to potential modern devices development operating in the nonlinear regime

Figures (7)

• Figure 1: A mechanical deformation of a graphene sheet. The bump which can have different shapes (spherical, Gaussian, ...) induces an out-of-plane stretching of the hoppings between neighboring atoms.
• Figure 2: Tight-binding model for a quasi-1D graphene system with zigzag edges. a) shows the local deformation as a local bump in the center of the graphene sheet, altering the translational invariance of the quasi 1D waveguide. b) shows a face side of the Gaussian strain bump which is centered in the middle of the system. The green links in the zoom of c) represent the interface through which the pumped current is calculated. The red parts in c) are the leads (reservoirs) that indicate that the system is infinite in that direction. An animation sketching the system can be found in Supplemental
• Figure 3: The color map indicates the threefold symmetric pseudo-magnetic field caused by the circularly symmetric Gaussian deformation. The vector field illustrates the stimulated electric field by the time-dependent pseudo-magnetic field. 'a' is the lattice constant.
• Figure 4: The generated currents through the interface shown in Fig. \ref{['fig:G_sys']}. The two types of currents at $K$ and $K^\prime$ are in phase and average to zero. The charge current is obtained for $h_0=3.5 \text{ nm}$ and $\delta h=0.35 \text{ nm}$. $E_F=0.28t_0$. T is the period of oscillation of the bubble.
• Figure 5: The charge current (Left) and the valley current (Right) pumped through an interface with the lead (see figure \ref{['fig:G_sys']}). The average of each of them is zero. The charge oscillates at the same frequency as the nano-bubble, whereas the pumped valley current shows higher order harmonics.The blue dots represent the times at which the current maps were plotted in Fig. 7. T is the period of oscillation of the nanobubble