Strain-induced modifications of transport in gated graphene nanoribbons

Diana A. Cosma, Marcin Mucha-Kruczyński, Henning Schomerus, and Vladimir I. Fal'ko

Phys. Rev. B 90, 245409 – Published 3 December 2014

Abstract

We investigate the effects of homogeneous and inhomogeneous deformations and edge disorder on the conductance of gated graphene nanoribbons. Under increasing homogeneous strain the conductance of such devices initially decreases before it acquires a resonance structure and, finally, becomes completely suppressed at higher strain. Edge disorder induces mode mixing in the contact regions, which can restore the conductance to its ballistic value. The valley-antisymmetric pseudomagnetic field induced by inhomogeneous deformations leads to the formation of additional resonance states, which originate either from the coupling into Fabry-Pérot states that extend through the system or from the formation of states that are localized near the contacts, where the pseudomagnetic field is largest. In particular, the $n = 0$ pseudo-Landau level manifests itself via two groups of conductance resonances close to the charge neutrality point.

Received 24 September 2014
Revised 21 November 2014

DOI:https://doi.org/10.1103/PhysRevB.90.245409

Authors & Affiliations

Diana A. Cosma^1,*, Marcin Mucha-Kruczyński², Henning Schomerus¹, and Vladimir I. Fal'ko¹

¹Department of Physics, Lancaster University, Lancseter LA1 4YB, United Kingdom
²Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom

^*d.cosma@lancaster.ac.uk

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Vol. 90, Iss. 24 — 15 December 2014

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Images

Figure 1
(a) Sketch of a graphene nanoribbon (GNR) of aspect ratio $L / W = 4$ , where $L$ is the length and $W$ is the width of the system. The color code indicates the pseudomagnetic field $B$ (in teslas) for electrons in the $K$ valley; at $w = 0.05$ inhomogeneous tensile strain in the middle of a system of width $W ≃ 40$ nm. We also sketch the honeycomb lattice corresponding to the tight-binding model in Eq. (1). The leads are heavily doped by imposing an on-site potential $V = - 200$ meV. This potential step can be controlled via electrostatic gates. In the central region the strain modulates the hopping matrix elements $γ_{i j}$ and the on-site energy $V_{i}$ . (b) Shift of the Dirac cones from the corners $K$ and $K^{'}$ in the Brillouin zone of a homogeneously strained armchair GNR. (c) Fermi surfaces at $E_{F} = 100$ meV in the vicinity of a $K$ point in the BZ of the GNR shown in (a). We contrast the situation without strain $(w = 0$ ; red circles) to externally imposed homogeneous strain $(w = 0.015$ and $0.024$ ; blue circles). Green lines represent the quantized transverse momentum values of the unstrained GNR.
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Figure 2
(a)–(i) Linear-response conductance as a function of chemical potential $μ$ at several fixed temperatures $T$ , for a homogeneously strained GNR of width $W ≃ 40$ nm and aspect ratio $L / W = 3$ . The leads are doped via an on-site potential $V = - 200$ meV. Each panel corresponds to a different value of externally imposed homogeneous strain. (a), (e), (h) Spatial structure of electron wave amplitudes at energy $E_{F} = - 129.2$ meV, evaluated using Eq. (10).
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Figure 3
Linear-response conductance $G$ as a function of chemical potential $μ$ at a fixed temperature $T = 20$ K, for homogeneously strained GNRs, of width $W = 40$ nm and aspect ratio $L / W = 3$ , subjected to various types of disorder. (a) Effect of $f = 1 %$ and $5 %$ single-atom vacancies for strain $w = 0.02, 0.021, 0.022$ , and $0.023$ ; (b) corresponding effect of double-atom vacancies. (c) Conductance for various fractions of double-atom vacancies for a fixed strain $w = 0.024$ .
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Figure 4
(a) Suspended GNRs of width $W ≃ 40$ nm and aspect ratios $L / W = 2$ , 3, and 4, which are clamped at the highly doped contacts. The color code shows the strength of the pseudomagnetic fields $B$ (in teslas) for electrons in the $K$ valley, for inhomogeneous strain $w = 0.05$ . (b) Spatial structure of resonance states for selected resonances identified in Fig. 5.
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Figure 5
Left: Zero-temperature conductance $G$ as a function of Fermi energy for the GNRs shown in Fig. 4. Top, $L / W = 2$ ; middle, $L / W = 3$ ; bottom, $L / W = 4$ . Right: Highly resolved results for the groups of peaks identified in the panels at the left.
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Figure 6
Sublattice-resolved electron amplitude for the resonances in Fig. 5 $(L / W = 2$ , 3, and 4, at energies $E_{F} = - 5.84, - 6.57$ , and $- 23.83$ meV respectively), obtained from Eq. (10) by placing the probing perturbation $δ V_{i}$ onto $A$ sites (top) or onto $B$ sites (bottom).
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