We show that the manifestation of quantum interference in graphene is very different from that in conventional two-dimensional systems. Due to the chiral nature of charge carriers, it is sensitive not only to inelastic, phase-breaking scattering, but also to a number of elastic scattering processes. We study weak localization in different samples and at different carrier densities, including the Dirac region, and find the characteristic rates that determine it. We show how the shape and quality of graphene flakes affect the values of the elastic and inelastic rates and discuss their physical origin.

We show that quantum interference in graphene can result in antilocalization of charge carriers--an increase of the conductance, which is detected by a negative magnetoconductance. We demonstrate that depending on experimental conditions one can observe either weak localization or antilocalization of carriers in graphene. A transition from localization to antilocalization occurs when the carrier density is decreased and the temperature is increased. We show that quantum interference in graphene can survive at high temperatures, up to T approximately 200 K, due to weak electron-phonon scattering.

We have performed the first experimental investigation of quantum interference corrections to the conductivity of a bilayer graphene structure. A negative magnetoresistance--a signature of weak localization--is observed at different carrier densities, including the electroneutrality region. It is very different, however, from the weak localization in conventional two-dimensional systems. We show that it is controlled not only by the dephasing time, but also by different elastic processes that break the effective time-reversal symmetry and provide intervalley scattering.

We propose a method of measuring the electron temperature Te in mesoscopic conductors and demonstrate experimentally its applicability to micron-size graphene devices in the linear-response regime (Te ≈ T , the bath temperature). The method can be especially useful in case of overheating, Te > T . It is based on analysis of the correlation function of mesoscopic conductance fluctuations. Although the fluctuation amplitude strongly depends on the details of electron scattering in graphene, we show that Te extracted from the correlation function is insensitive to these details. Graphene is an atomically thin graphite layer [1,2] recently used in field-effect transistors [3]. In graphenebased semiconductor devices phonons are poorly coupled to the environment since the mass of carbon atoms is typically smaller than that of atoms in the underlying substrate, making the overheating of graphene structures a likely event at high currents. This raises a question of how to measure the temperature of electrons in graphene. Since classical conductivity in graphene has a very weak temperature dependence at low and intermediate temperatures [4], extracting the electron temperature from transport measurements requires analyzing more subtle quantum effects. One possibility would be to analyze the decoherence rate τ −1 ϕ using the weak-localization (WL) effects in magneto-resistance [5,6]. However, it was shown theoretically [7] and confirmed experimentally [8] that the WL in graphene reveals itself in a rather complicated way due to the influence of inter-valley scattering and the disorder which breaks the sublattice symmetry. Thus WL does not offer an easy way of measuring the electron temperature T e . Another possibility would be to exploit the temperature dependence of the amplitude of universal conductance fluctuations (UCF) [5,9,10]. Unfortunately, a quantitative implementation of such analysis is hindered by the necessity to both account for the temperature dependence of τ −1 ϕ and attribute a definite symmetry class to a particular graphene-based device [8, 11, 12, 13]. However, it has been noticed that the correlation functions of random UCF dependence on magnetic field B and the Fermi energy ε F provide useful information about subtle spectral characteristics of a disordered conductor [14].

We study fluctuations of the conductance of micron-sized graphene devices as a function of the Fermi energy and magnetic field. The fluctuations are studied in combination with analysis of weak localization which is determined by the same scattering mechanisms. It is shown that the variance of conductance fluctuations depends not only on inelastic scattering that controls dephasing but also on elastic scattering. In particular, contrary to its effect on weak localization, strong intervalley scattering suppresses conductance fluctuations in graphene. The correlation energy, however, is independent of the details of elastic scattering and can be used to determine the electron temperature of graphene structures.