Quantum Transport in Graphene Structures

Alexander Savchenko

University of Exeter, UK

We perform a comparative study of weak localisation (WL) in bilayer [1] and monolayer graphene [2]. Although the two systems are different in their energy spectrum (massive fermions in bilayer and massless in monolayer), they have common features, such as the chirality of charge carriers. These makes WL in both systems very different from that in conventional 2D structures. Notably, is becomes controlled not only by inelastic scattering but also by a number of elastic scattering mechanisms. By changing the geometry and quality of samples (obtained by mechanical exfoliation) we demonstrate that WL in graphene can take a variety of forms well described by theory [3]. We show that WL does exist at different carrier densities, including the electro-neutrality region, and determine the dependence of the characteristic times on the density of electrons and holes.
The studies of WL are complemented by the analysis of conductance fluctuations in both systems. They have the same physical origin as WL quantum interference and are controlled by the same scattering mechanisms. Using information obtained from WL, we show that the amplitude of the fluctuations agrees with that expected from the theory of universal conductance fluctuations.
With two-gate control of carrier density we realise ballistic p-n graphene structures and almost ballistic p-n-p structures. Calculating the band-structure profile of the samples allows us to determine unequivocally the expected resistance of graphene p-n junctions and show that p-n junctions have indeed selective transmission for chiral carriers [5]. This is seen as an increase of the resistance of ballistic graphene p-n junctions compared with that of diffusive.
[1] R.V. Gorbachev et al., Phys. Rev. Lett. 98, 176805 (2007).
[2] F.V.Tikhonenko et al., Phys. Rev. Lett. 100, 056802 (2008).
[3] E. McCann et al., Phys. Rev. Lett. 97, 146805 (2006);
K. Kechedzhi et al., Phys. Rev. Lett. 98, 176806 (2007).
[4] R.V. Gorbachev et al., arXiv:0804.2081.
[5] V.V. Cheianov and V. I. Fal'ko, Phys. Rev. B 74, 041403 (2006)