Strain-engineered graphene through a nanostructured substrate. II. Pseudomagnetic fields

The strain-induced pseudomagnetic field in supported graphene deposited on top of a nanostructured substrate is investigated by using atomistic simulations. A step, an elongated trench, a one-dimensional barrier, a spherical bubble, a Gaussian bump, and a Gaussian depression are considered as support structures for graphene. From the obtained optimum configurations we found very strong induced pseudomagnetic fields which can reach up to $\sim$1000 T due to the strain-induced deformations in the supported graphene. Different magnetic confinements with controllable geometries are found by tuning the pattern of the substrate. The resulting induced magnetic fields for graphene on top of a step, barrier, and trench are calculated. In contrast to the step and trench the middle part of graphene on top of a barrier has zero pseudomagnetic field. This study provides a theoretical background for designing magnetic structures in graphene by nanostructuring substrates. We found that altering the radial symmetry of the deformation changes the sixfold symmetry of the induced pseudomagnetic field.

Figure 1

The optimum configuration of armchair graphene over a step located at $x=0$ with supported longitudinal ends. The colors indicate the size of strain.

Figure 2

The averaged gauge fields (a) and the induced pseudomagnetic fields (b) averaged over the $y$ direction for graphene on top of a step as shown in Fig. 1 which has been supported from the longitudinal ends while it can freely move along the $z$ direction.

Figure 3

The optimum configuration of armchair graphene over a trench located at $\left|x\right|<1.5$ nm where both longitudinal ends were supported in the $x–y$ plane. The colors indicate the size of the strain.

Figure 4

The averaged gauge field (a) and the induced pseudomagnetic field (b) averaged over the $y$ direction for graphene on top of a well as shown in Fig. 3 which has been supported from the longitudinal ends while it can freely move along the $z$ direction.

Figure 5

The optimum configuration of armchair graphene over an elongated cubic barrier with $\left|x\right|<1.5$ nm where the zigzag edges were supported in the $x–y$ plane. The colors indicate the size of strain.

Figure 6

The averaged (a) gauge field and (b) the induced pseudomagnetic field averaged over the $y$ direction for a graphene on top of a barrier as shown in Fig. 5 which has been supported from the longitudinal ends while it can freely move along the $z$ direction.

Figure 7

The optimum configuration of armchair graphene, with two longitudinal ends supported in the $x–y$ plane, on top of a bubble. The inset shows a different view indicating the elongation of the deformation of graphene along the $x$ direction, i.e., armchair direction. The colors indicate the size of the strain.

Figure 8

(a) Vector plot of the gauge field and (b) the induced pseudomagnetic field for armchair graphene placed over a spherical bubble. The obtained deformation is shown in Fig. 7. Graphene was supported from the longitudinal ends while it can vibrate along the $z$ direction.

Figure 9

(a) Vector plot of the gauge field and (b) the induced pseudomagnetic field for armchair graphene deposited over a Gaussian depression. Graphene has been supported from the longitudinal ends while it can vibrate along the $z$ direction.