Generating quantizing pseudomagnetic fields by bending graphene ribbons

We analyze the mechanical deformations that are required to create uniform pseudomagnetic fields in graphene. It is shown that, if a ribbon is bent in-plane into a circular arc, this can lead to fields exceeding 10 T, which is sufficient for the observation of pseudo-Landau quantization. The arc geometry is simpler than those suggested previously and, in our opinion, has much better chances to be realized experimentally soon. The effects of a scalar potential induced by dilatation in this geometry is shown to be negligible.

Figure 1

(Color online) Sketch of the suggested bending geometry that would generate a uniform pseudomagnetic field and open band gaps in graphene’s electronic spectrum. The graphene rectangle (lower image) is bent into a circular arc (upper).

Figure 2

(Color online) Stretching geometry leading to a uniform pseudomagnetic field inside a rectangular graphene sample. Normal forces are applied at two opposite boundaries and their magnitude is indicated by the length of the plotted arrows.

Figure 3

(Color online) (a) Rectangular graphene sample deformed into an arc. The radii of the lower and upper edges are $R$ and $R+W$, respectively. The plot is for $R=5\times L$. (b) Effective magnetic field, in Teslas, for the same deformed ribbon. Dimensions are $W=200\text{nm}$, $L=192\text{nm}$, and $R=5\times L=960\text{nm}$. The maximum strain is 10%.

Figure 4

(Color online) Variation in density, $\delta \overline{\rho }\left(\overline{x},\overline{y}\right)$, in dimensionless units (see text) due to the screened scalar potential induced by strains. The aspect ratio is $L/W=1$.