Singular elastic strains and magnetoconductance of suspended graphene

Graphene membranes suspended off electric contacts or other rigid supports are prone to elastic strain, which is concentrated at the edges and corners of the samples. Such a strain leads to an algebraically varying effective magnetic field that can reach a few Tesla in submicron wide flakes. In the quantum Hall regime the interplay of the effective and the physical magnetic fields causes backscattering of the chiral edge channels, which can destroy the quantized conductance plateaus.

Figure 1

(Color online) Conductance in units of $G_0=2e^2/h$ as a function of the filling factor $\nu$ for samples of electron density $2.8\times {10}^{11}{\text{cm}}^{-2}$ and widths $W=100$, 200, and 400 nm. The side contacts are assumed to have width $2l=30\text{nm}$ and to pull laterally outward with the force $P=78\text{nN}$ $\left(c_0=1\right)$ each.

Figure 2

(Color online) Schematics of the system. The rectangles at the extremes of the $x$ and $y$ axes are the contacts, which are attached to a graphene sheet (the central object). The deformation of the sheet is strongly exaggerated. The variable shading and honeycomb lattice are added for aesthetic purposes.

Figure 3

(Color online) (a) Pseudomagnetic field, in Tesla, induced by two stamps with parameters $2l=30\text{nm}$, $c_0=1$ in a sample of width 200 nm. (b) Effect of this pseudomagnetic field on the edge states of the $N=2$ Landau level at $B=1\text{T}$. The edge states are depicted as light gray ribbons of thickness $\ell \approx 26\text{nm}$. The arrows indicate their propagation direction.