Conductance Fluctuations in High-mobility Graphene Field Effect Transistors

Abstract

In the past decade, a major fraction of the research carried out in condensed matter physics has been dedicated to address the unique physical properties of single layer graphene (SLG). Different properties of Dirac fermions in SLG have been explored, both from an academic point of view as well as with an eye towards their possible technological applications [1, 2]. Despite this, several aspects remain unexplored and unanswered till date. In this thesis, we attempt to address some of these by probing the conductance fluctuations in high-mobility graphene. Several unique properties, like large surface to volume ratio, low intrinsic charge carrier concentration, high charge carrier mobility and large electrical signal to noise ratio make graphene a suitable choice for chemical vapour sensors [1, 3]. Indeed, the resistance of graphene is very sensitive to the presence of a wide variety of chemicals present its ambient. However, the response and reset times of a graphene sensor device are very large (ranging few tens of minutes to several hours), which is a bottleneck for its commercial realization [3–5]. To address this issue, we have studied the effect of ambient on the resistance fluctuations (noise) of single-layer graphene field effect transistors (SLG-FET). We observed that, in the presence of chemical vapour, noise increased by orders of magnitude. The shape of the power spectral density of noise was found to be determined by the energetics of the adsorption-desorption of molecules from the graphene surface. This change in noise takes place over time scales much smaller than that required for the resistance to change. We showed that a dynamic adsorption-desorption induced charge carrier density fluctuations is the origin of the excess noise. We find that a detection scheme based on measurements of the resistance fluctuations is far superior to the traditional method of measuring the change in average resistance in terms of the sensitivity, specificity, and response time of the detector. SLG is a weakly interacting, perfect two dimensional system, with a vanishingly small density of states near the Dirac point [1]. Since the screening is weak near the Dirac point, even a small amount of disorder present in the system would localize the charge carriers, resulting in a diverging resistance near the Dirac point [6, 7]. However, this Anderson localizationdelocalization transition has never been observed in SLG. This has been attributed to the presence of charge puddles near the Dirac point [6, 8]. In the absence of a direct transport probe for Anderson localization in SLG, we looked for alternate experimental proof. It is known that at the critical localization-delocalization transition point, large fluctuations appear in physical observables, e.g. spatial distribution of amplitude of critical wavefunctions, which obey a multifractal scaling [9– 11]. Motivated by this, we have explored the possibility of finding signatures of Anderson localization in SLG, by studying multifractality of conductance fluctuations. We observed a large multifractality in Universal conductance fluctuations (UCF) near the Dirac point. This multifractality decreased as temperature was increased, or when screening increased while moving away from the Dirac point. We conjecture that the origin of this multifractality is an incipient Anderson localization transition occurring close to the Dirac point in SLG. As supporting evidences, we studied the statistics of mesoscopic fluctuations at the critical points in the quantum Hall regime, which are known to be Anderson localization-delocalization transition points. A large multifractality was observed near the critical transition points, which decreased as the chemical potential moved away from the critical points. We have studied the effect of temperature and electric field on the quantum Hall plateau-to-plateau transitions, from which we have obtained the critical exponents, and Landau level energy gaps between broken-symmetry integer quantum Hall states in bilayer graphene. The temperature exponent governing the slope of Hall conductance versus Landau level filling factor was found to match very well with the predictions of Anderson localization transitions at the quantum Hall critical points