Enhanced asymmetric valley scattering by scalar fields in nonuniform out-of-plane deformations in graphene

Abstract

We study the electron scattering produced by local out-of-plane strain deformations in the form of Gaussian bumps in graphene. Of special interest is to take into account the scalar field associated with the redistribution of charge due to deformations, and in the same footing as the pseudomagnetic field. Working with the Born approximation approach we show analytically that even when a relatively small scalar field is considered, a strong backscattering and enhancement of the valley splitting effect could arise as a function of the energy and angle of incidence. In addition, we find that the valley polarization can reverse its sign as the incident energy is increased. These behaviors are totally absent if the scalar field is neglected or screened. Interestingly, we find that there is a further possibility of controlling the valley scattering polarization purely by electrical means through the presence of external scalar fields in combination with strain fields. These results are supported by quantum dynamical simulations of electron wave packets. Results for the average trajectories of wave packets in locally strained graphene clearly show focusing and beam splitting effects enhanced by the presence of the scalar field that can be of interest in the implementation of valleytronic devices.

Valley engineering by strain in Kekulé-distorted graphene

“…The former has been recently observed in graphene superlattices by nonlocal transport measurement 42,43 . The effects of the latter [44][45][46] are strong, measurable and expected to be valley asymmetric [30][31][32][33] . In fact, both couple asymmetrically with each valley by breaking the inversion symmetry while preserving time reversal.…”

Valley-driven Zitterbewegung in Kekulé-distorted graphene

“…We numerically evaluate the dynamics of the Gaussian wave packet ( 16) by adopting the methodology in Ref. [40]. In such a numerical approach, a suitable, discretized time-evolution operator of the system is obtained using the Zassenhaus formula and Cayley expansion.…”

Valley notch filter in a graphene strain superlattice: Green's function and machine learning approach

“…The transport properties of a single graphene nanobubble have been previously investigated [15][16][17][18]37 , in this section for completeness reasons we start presenting the main results for conductance and valley polarization, then, we use the wave function matching technique to gain physical insight into the origin of the observed valley effect. We consider a scattering region with dimensions L 0 ≈ 12.8 nm and W 0 ≈ 14.8 nm with a Gaussian bump of fixed-parameter b = 22a c = 3.12 nm localized exactly at the center of the system.…”

“…On the other hand, inhomogeneous mechanical deformations such as bubbles and ripples routinely appear in graphene 14 ; these are seen by electrons in opposite valleys as regions with opposite polarity pseudomagnetic fields. This attribute has been used in devices with one graphene bubble [15][16][17][18][19] to show separation of valley currents and valley filtering; unfortunately, the observed effects require fine-tuning of the energy, defined height/width ratio of the bubble, high values of strain, narrow contacts, location of the nanobubble near to the right contact and crystalline orientation. Clearly, the proposals with a single graphene bubble present serious disadvantages to efficiently generate and detect valley currents 20 .…”