Geometry-dependent conductance oscillations in graphene quantum dots

Utilizing rectangular graphene quantum dots with zigzag horizontal boundaries as a paradigm, we find that the conductance of the dots can exhibit significant oscillations with the position of the leads. The oscillation patterns are a result of quantum interference determined by the band structure of the underlying graphene nanoribbon. In particular, the power spectrum of the conductance variation concentrates on a selective set of bands of the ribbon. The computational results are substantiated by a heuristic theory that provides selection rules for the concentration on the specific dispersion bands. Copyright c © EPLA, 2011 Graphene, a single layer of carbon atoms arranged in a honeycomb lattice, has attracted much recent interest [1]. Potential applications of graphene range from electronics [2] to nano-biosensors [3]. For example, due to the distinctly high mobility of charge carriers in graphene [4], nanoscale electronic devices made of graphene, such as p-n junctions and transistors, can be superior to their Si-based counterparts [5]. For most applications, there is a need to connect the graphene device to external voltage or current source via metal leads. Ideally, there should be zero resistance between the metal lead and the graphene. However, experiments have shown that the contact resistance can approach or even exceed the quantum resistance [6]. This indicates that some form of injection barrier must exist at the metal-graphene interface, as demonstrated in fig. 1(a), restricting the transmitting modes to a few [6,7]. In this letter, we use a zigzag graphene quantum-dot model where the size of the leads is assumed to be small to mimic the injection characteristics of a few transmitting modes and study, systematically, how the conductance of the quantum dot depends on the position of the leads (fig. 1(b)). It has been noticed that the geometry of the device can affect the electronic transport properties [7–10]. Intuitively, if the lead is located in a region where the local density of states (LDS) is low, electrons can hardly hop out of the localized pattern to get into the lead, resulting in a small conductance [11]. Opposite situations can occur when the lead is in a different region, leading to a large conductance. Our systematic computations with varying lead positions reveal significant conductance oscillations. A heuristic analysis indicates that the oscillations are caused by standing-wave–like patterns in the quantum dot. In particular, the wave vector of the wave function follows the underlying dispersion relation. For tall and narrow quantum dots, as sketched in fig. 1(b), the relation can be approximated by the band structure of the corresponding armchair graphene ribbon when viewed vertically (y-direction) in the absence of leads. There are two sets of bands depending on the phase difference of the two atoms (denoted by A and B) in a unit cell. At the bottom of these bands, for one set, the wave function for A atoms has the same phase as that for B atoms. For the other set, the wave function for the two set atoms has the opposite phase, which do not contribute to the transmission as they annihilate from destructive interference. In the nanotransport literature, conductance oscillations/fluctuations are usually referred to those with respect to varying electron energy or changing magnetic field [12], the origin of which can generally be attributed to scarred or pointer states in the underlying dot structure [11]. The