Anomalous Klein tunnelling with magnetic barriers in strained graphene

Abstract

We study electron transport in a strained graphene sheet subjected to a sequence of $N$ electrostatic and magnetic barriers. Employing a modified and improved transfer-matrix framework, we examine how the transmission and reflection coefficients evolve with variations in uniaxial strain and in the number of barriers. The interplay of mechanical deformation and external magnetic fields is found to generate an anomalous Klein tunnelling, allowing the conductance to be effectively modulated through strain and barrier configurations. These findings highlight the role of strain engineering and magnetic field modulation as powerful tools for tailoring charge transport in two-dimensional materials. More broadly, they underscore how mechanical and electromagnetic control can be used to design next-generation solid-state devices with tunable electronic properties.

Figures (10)

• Figure 1: Uniaxially strained graphene is considered with the zigzag (armchair) direction aligned along the $x$-axis ($y$-axis), alternating every $30^\circ$. Strain along these high-symmetry directions modifies the nearest-neighbor hopping amplitudes to two distinct values, $t_{1}$ and $t_{2}$. The nearest-neighbor positions are given by $\vec{\delta}_{1}$, $\vec{\delta}_{2}$, and $\vec{\delta}_{3}$, while the lattice vectors $\vec{a}_{1}$ and $\vec{a}_{2}$ span the deformed hexagonal structure. The unit cell is colored in yellow.
• Figure 2: Energy contour of the conduction band in \ref{['TB-energy']} near the first Brillouin zone for different strain values $\epsilon$.
• Figure 3: Diagram of the system of $N$ magnetic and electrostatic barriers disposed along the $x$ axis on a material surface.
• Figure 4: Electron transmission $T$ in uniaxially strained graphene with a single electrostatic and magnetic barrier. Panels (a) and (b) show the dependence on the incidence angle $\phi_{0}$ for different values of incident energy $E$. Panels (c) and (d) present the dependence on the Fermi energy $E$ for different incidence angles $\phi_{0}$. The electrostatic barrier height is fixed at $V_0 = 14$ meV, while the magnetic field strength is set to $B = 0.1$ T, with a width $D \approx 81.1$ nm for both. The black-dotted line in the lower graphs corresponds to anomalous Klein tunnelling.
• Figure 5: Conductance $G/G_{0}$ as a function of the Fermi level $E$ for a single electrostatic and magnetic barrier. The solid black, dashed red, and dotted blue curves correspond to pristine graphene and to strained graphene along the $\mathcal{ZZ}$ and $\mathcal{AC}$ directions, respectively. The parameters are set as $V_0 = 14$ meV and $D \approx 81.1$ nm.