Session D2: Quantum Hall Effect in Graphene

Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene

When electrons are confined in two-dimensional (2D) materials, quantum mechanically enhanced transport phenomena, as exemplified by the quantum Hall effects (QHE), can be observed. Graphene, an isolated single atomic layer of graphite, is an ideal realization of such a 2D system. Its behavior is, however, expected to differ dramatically from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron-hole degeneracy and vanishing carrier mass near the point of charge neutrality. In this talk I will present an experimental investigation of magneto transport in a high mobility single layer of graphene. Adjusting the chemical potential using the electric field effect, we discovered an unusual half integer QHE for both electron and hole carriers in graphene, which originates from the quantum mechanical phase associated with the topologically unique graphene Fermi surface. The existence of a non-zero Berry's phase in magneto-oscillations will be discussed in the connection to Dirac Fermion description in graphitic systems. In addition, I will discuss our recent results in transport measurement in strong quantum limit and spin transport in graphene samples.   

QED in Graphene

Electronic properties of materials are commonly described by quasiparticles that behave as non-relativistic electrons with a finite mass and obey the Schr\"{o}dinger equation. I will describe our experimental studies of graphene (a free-standing single layer of carbon atoms) in which electron transport is essentially governed by Dirac's (relativistic) equation and charge carriers mimic relativistic particles with zero rest mass and an effective ``speed of light'' of $\approx $10$^{6}$m/s. We have found a variety of unusual quantum phenomena characteristic of two-dimensional Dirac fermions. In particular, we have observed that a) the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; b) graphene's conductivity never falls below a minimum value corresponding to the conductance quantum, even when carrier concentrations tend to zero; c) the cyclotron mass of massless carriers in graphene is described by Einstein's equation $E $=\textit{mc}$^{2}$; and d) Shubnikov-de Haas oscillations in graphene exhibit a phase shift of $\pi $ due to Berry's phase. I will also explain another, third type of the integer quantum Hall effect that happens in bilayer graphene and accompanied by Berry's phase of 2$\pi $.   

Dirac fermions as a cause of unusual Quantum Hall Effect in Graphene

The graphite films with a single atomic layer of carbon (graphene) have the low-energy "relativistic-like" quasiparticle excitations which can be described by two-dimensional Dirac equation. It is demonstrated that due to the Dirac-like character of carriers the quantization of the Hall conductivity is unusual: it occurs at half-integer filling factors. In addition, the phases and amplitudes of the de Haas - van Alphen and Shubnikov de Haas quantum magnetic oscillations in graphene differ drastically from the patterns observed in a more conventional materials with a parabolic dispersion.   

Electronic coherence and confinement in patterned epitaxial graphene

I will present very recent results from our studies of ultrathin graphite films that are epitaxially grown on single crystal silicon carbide. The quasi-two dimensional films consisting of a few to a few dozen graphene layers are patterned ($\ge $0.1$\mu$m) using standard e-beam lithography methods. Relatively high mobilities ($\mu$ up to 10,000 cm$^2$/Vs) are deduced from transport measurements. Patterned structures reveal a variety of mesoscopic effects (i.e. universal conductance fluctuations and anomalous Shubnikov de Haas oscillations) from which coherence lengths of the order, or greater than 1$\mu$m at cryogenic temperatures are deduced. Evidence for size dependent resistivities even at room temperature is observed. Changes the magnetoresistive properties at about 2K provide evidence for an unusual, first order phase transition. The properties of this new patternable quasi-2D material are promising for sub-micron electronics applications.