Tight-binding molecular dynamics study of mechanical and electronic properties in twisted graphene nanoribbons

We study numerically the effect of mechanical twisting on the geometrical and electronic properties of graphene nanoribbon (GNR) devices. By employing the tight-binding molecular dynamics method for structural relaxation calculations in the presence of twisting, we found that the geometry of the twisted GNR changes abruptly when the twisting angle exceeds a threthold angle. Moreover it has been found that such twisting induced abrupt change in the geometry of AGNR can actually cause the abrupt change in the electronic property as well. I. I NTRODUCTION Since the experimental success in the exfoliation of single layer graphene (SLG) in 2004 [1], [2], [3], various types of graphene based new functional devices have been proposed, including the bi-layer graphene transistors, graphene nanoribbon transistors, spin filters, gas sensors, pressure sensors, and so on [4], [5], [6], [7]. Among these interesting devices based on graphene, the idea to engineer the electronic properties by introducing the mechanical deformation is especially important since it is one of special features which can be most flexibly designed if we use graphene as base materials. Having motivated by such interesting properties of graphene, here we study another graphene based electromechanical devices, the twisted graphene nanoribbon (GNR) devices, where the electronic properties of GNR are expected to be modulated by changing the twisting angle. Fig. 1. Schematic illustrations of our model, where an armchair edged GNR (AGNR) is suspended in between two electrodes, and one of the electrodes is allowed to change its angle along the axis threading through AGNR with respect to opposite electrode. II. M ODEL AND METHOD A. Model of twisted graphene nanoribbon devices Figure 1 is the schematic illustration of our model, where an armchair edged GNR (AGNR) is suspended in between two electrodes. We further assume that one of the electrodes is allowed to change its angle along the axis threading through the ribbon with respect to the other electrode. B. Tight binding molecular dynamics method In order to obtain the stable structure for a given twisting angle, we employ the structural relaxation based on the tightbinding molecular dynamics (TBMD) method [8], [9], where the electronic energy is calculated quantum mechanically starting from the sp tight binding Hamiltonian, while the repulsive energy due mainly to ion-ion interaction is calculated using the pairwise potential. The TBMD method is advantageous over classical bond order potential method since it allows us to simulate the mechanical and electronics properties of AGNR on the equal footing. Moreover, in order to treat the large number of atoms contained in AGNR within the framework of TBMD, we also employ the orderN algorithm based on the Fermi operator expansion (FOE) method. Below we describe briefly these calculation method. The electronic structure in twisted GNRs can basically be obtained by diagonalizing the standard two-center TB Hamiltonian H αβ(rij), whereα (β) is the index of the atomic orbital in the i (j)th atom in the system. Once we calculate the energy eigenvalues (band structure) of the above Hamiltonian, the total energy of the system is given following the TBMD scheme as Etot = Ebs + Erep, (1) whereEbs is the band structure energy and Erep is the repulsion energy. HereEbs andErep are respectively calculated as