Observation of Aharonov-Bohm conductance oscillations in a graphene ring

Abstract

We investigate experimentally transport through ring-shaped devices etched in graphene and observe clear Aharonov-Bohm conductance oscillations. The temperature dependence of the oscillation amplitude indicates that below 1 K, the phase coherence length is comparable to or larger than the size of the ring. An increase in the amplitude is observed at high magnetic field, when the cyclotron diameter becomes comparable to the width of the arms of the ring. By measuring the dependence on gate voltage, we find that the Aharonov-Bohm effect vanishes at the charge neutrality point, and we observe an unexpected linear dependence of the oscillation amplitude on the ring conductance. DOI: 10.1103/PhysRevB.77.085413 PACS number͑s͒: 73.23.Ϫb, 73.20.Ϫr, 73.22.Ϫf, 73.61.Wp The investigation of transport phenomena originating from quantum interference of electronic waves has proven to be a very effective probe of the electronic properties of conducting materials. Recent work has shown that this is also the case for graphene, a novel material consisting of an individual layer of carbon atoms, in which the electron dynamics is governed by the Dirac equation.1 The anomalous behavior of the weak-localization correction to the conductivity that is observed in the experiments, 2 for instance, is directly related to the presence of two independent valleys in the band structure of graphene 3,4 and can be used to extract the intervalley scattering time.5 Another example is provided by the observation of a Josephson supercurrent in graphene superconducting junctions, which permits to conclude that transport through graphene is phase coherent even when the material is biased at the charge neutrality point ͑i.e., where nominally no charge carriers are present͒. 6 Possibly, the phenomenon that most directly illustrates electronic interference in solid-state devices is the occurrence of periodic oscillations in the conductance of ringshaped devices, measured as a function of magnetic field. 7 This phenomenon, which is a direct consequence of the Aharonov-Bohm ͑AB͒ effect, has been investigated extensively in the past in rings made with metallic films or with semiconducting heterostructures, and its study has contributed significantly to our understanding of mesoscopic physics. For example, the analysis of h/e and h/2e AB conductance oscillations has clarified the difference between sample-specific and ensemble-averaged phenomena.7 The investigation of the temperature and magnetic field dependences of the oscillation amplitudes has been used to investigate processes leading to decoherence of electron waves, such as electron-electron interaction, 7,8 or the interaction with magnetic impurities. 9 In graphene, however, no experimental observation of AB conductance oscillations has been reported so far, although there is an emerging interest in the problem from the theoretical side. 10,11 In the course of recent experiments, we have observed AB conductance oscillations experimentally in several rings fabricated on few-layer graphene. In thi...

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