Transport Signatures of Pseudomagnetic Landau Levels in Strained Graphene Ribbons

In inhomogeneously strained graphene, low-energy electrons experience a valley-antisymmetric pseudomagnetic field which leads to the formation of localized states at the edge between the valence and conduction bands, understood in terms of peculiar $n=0$ pseudomagnetic Landau levels. Here we show that such states can manifest themselves as an isolated quadruplet of low-energy conductance resonances in a suspended stretched graphene ribbon, where clamping by the metallic contacts results in a strong inhomogeneity of strain near the ribbon ends.

Figure 1

We consider the transport through strained suspended graphene nanoribbons (GNR) which are clamped at highly doped contacts. (a) Distribution of pseudomagnetic fields $\mathcal{B}$ (in Tesla), defined according to Eq. (3), for electrons in the $K$ valley for GNR with $W\simeq 40\mathrm{nm}$ and aspect ratios $L/W=2$, 3, and 4. The inhomogeneous tensile strain in the middle of the nanoribbon is $w=0.05$. (b) Spatial structure of electron wave amplitudes corresponding to several resonances identified in (d), which displays the zero-temperature conductance of the ribbons as a function of the Fermi energy. For comparison, (c) shows the conductance for the ribbon with $L/W=3$ and no strain ($w=0$, blue) or artificially imposed homogeneous strain ($w=0.05$, red).

Figure 2

Sketch of the tight-binding model (1) of the GNR junction with armchair boundaries. The system is composed of two ideal heavily doped leads ($V=-200\mathrm{meV}$) and a central suspended region, in which strain modulates the hopping matrix elements ${\gamma }_{ij}$ and the on-site energy $V_i$.

Figure 3

Sublattice-resolved electron amplitude for one of the resonances in Fig. 1d ($L/W=2$, $E=-5.84\mathrm{meV}$), obtained by placing the probing perturbation on the A (left) or B (right) sites.