Strained fold-assisted transport in graphene systems

Deformations in graphene systems are central elements in the novel field of straintronics. Various strain geometries have been proposed to produce specific properties, but their experimental realization has been limited. Because strained folds can be engineered on graphene samples on appropriate substrates, we study their effects on graphene transport properties. We show the existence of an enhanced local density of states (LDOS) along the direction of the strained fold that originates from localization of higher energy states and provides extra conductance channels at lower energies. In addition to exhibiting sublattice symmetry breaking, these states are valley polarized, with quasiballistic properties in smooth disorder potentials. We confirmed that these results persist in the presence of strong edge disorder, making these geometries viable electronic waveguides. These findings could be tested in properly engineered experimental settings.

Figure 1

Schematic representation of deformed zigzag graphene nanoribbon (width $W$ and length $L$) connected to leads with a Gaussian foldlike out-of plane deformation (amplitude $A$ and width $b$). Arrows indicate valley currents as described in main text. Color code given in Fig. 4.

Figure 2

(a) Strain distribution and (b) pseudomagnetic field profile at $K$ valley due to an extended Gaussian out-of-plane deformation. Parameters: amplitude $A=0.7\text{nm}$, width $b=1.4\text{nm}$.

Figure 3

(a) Conductance for ribbon ($L=27.4\text{nm}$ and $W=25.8\text{nm}$) with different strained folds parameters. Curves are shifted for clarity. Dashed horizontal lines mark zero value for proper comparison. (b) LDOS profile across the ribbon with upper/lower panels showing results for: ${\varepsilon }_m=0\%-9.2\%$ [black to green curves in (a)], (c) enhanced total LDOS produced by the strained fold, and (d) color map of sublattice polarization. Panels (b)–(d) obtained at $E=0.05\text{eV}$. Parameters: $W=27.4\text{nm}$, amplitude $A=0.7\text{nm}$, and width $b=1.4\text{nm}$.

Figure 4

Band structure for a ribbon with a flat (a) and (b) a strained fold configuration. Panels (c) and (d) show a zoom in close to the Dirac point $K$. (c) Color scale indicates confinement level measured by parameter $F$ in units of $1/A_c^2$, ($A_c=$ unit cell area) as defined in the main text. (d) Color scale indicates position across the ribbon measured by parameter $\delta \rho$ (in units of $1/A_c$) defined in the main text. Parameters: $W=23.7\text{nm}$, amplitude $A=0.7\text{nm}$, and width $b=1.4\text{nm}$.

Figure 5

Probability densities for states at energy $E=0.15\text{eV}$. Blue (red) curves correspond to state $k_1$ ($k_2$) with negative (positive) velocity. Filled (empty) symbols indicate sublattice A (B). (a) States near Dirac point $K$. (b) States near Dirac point $K^{\prime }$. Color scale indicates magnitude of pseudomagnetic field (bottom). (c) Position of states in band structure: right $K$ and left $K^{\prime }$, respectively. (d) Total LDOS with states from both valleys with same velocity. Color scale indicates location in band structure: yellow near $K$ and black near $K^{\prime }$. Parameters: $W=23.7\text{nm}$, amplitude $A=0.7\text{nm}$, and width $b=1.4\text{nm}$.

Figure 6

(a) Conductance for different fold amplitudes $A$ and widths $b$ averaged over 100 disorder realizations. Curves are shifted for clarity purposes. Dashed horizontal lines mark zero value for proper comparison. (b) LDOS and (c) sublattice polarization averaged over 10 disorder realizations. Parameters: $A=0.7\text{nm}$, $b=1.4\text{nm}$, and energy $E=0.05\text{eV}$. Scales (a.u.) normalized to exhibit areas with higher density of states. (Black color regions along the edges correspond to highly disordered sites.)