Observing a scale anomaly and a universal quantum phase transition in graphene.

One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale-free quantum system is broken into a discrete scale symmetry for a critical value of a control parameter. This is an example of a (zero temperature) quantum phase transition. Such an anomaly takes place for the quantum inverse square potential known to describe 'Efimov physics'. Broken continuous scale symmetry into discrete scale symmetry also appears for a charged and massless Dirac fermion in an attractive 1/r Coulomb potential. The purpose of this article is to demonstrate the universality of this quantum phase transition and to present convincing experimental evidence of its existence for a charged and massless fermion in an attractive Coulomb potential as realized in graphene.When the continuous scale symmetry of a quantum system is broken, anomalies occur which may lead to quantum phase transitions. Here, the authors provide evidence for such a quantum phase transition in the attractive Coulomb potential of vacancies in graphene, and further envision its universality for diverse physical systems.

Single-layer behavior and its breakdown in twisted graphene layers.

We report high magnetic field scanning tunneling microscopy and Landau level spectroscopy of twisted graphene layers grown by chemical vapor deposition. For twist angles exceeding ~3° the low energy carriers exhibit Landau level spectra characteristic of massless Dirac fermions. Above 20° the layers effectively decouple and the electronic properties are indistinguishable from those in single-layer graphene, while for smaller angles we observe a slowdown of the carrier velocity which is strongly angle dependent. At the smallest angles the spectra are dominated by twist-induced van Hove singularities and the Dirac fermions eventually become localized. An unexpected electron-hole asymmetry is observed which is substantially larger than the asymmetry in either single or untwisted bilayer graphene.

Fractional quantum Hall effect in suspended graphene probed with two-terminal measurements.

Recently, fractional quantization of two-terminal conductance was reported in suspended graphene. The quantization, which was clearly visible in fields as low as 2 T and persistent up to 20 K in 12 T, was attributed to the formation of an incompressible fractional quantum Hall state. Here, we argue that the failure of earlier experiments to detect the integer and fractional quantum Hall effect with a Hall-bar lead geometry is a consequence of the invasive character of voltage probes in mesoscopic samples, which are easily shorted out owing to the formation of hot spots near the edges of the sample. This conclusion is supported by a detailed comparison with a solvable transport model. We also consider, and rule out, an alternative interpretation of the quantization in terms of the formation of a p-n-p junction, which could result from contact doping or density inhomogeneity. Finally, we discuss the estimate of the quasi-particle gap of the quantum Hall state. The gap value, obtained from the transport data using a conformal mapping technique, is considerably larger than in GaAs-based two-dimensional electron systems, reflecting the stronger Coulomb interactions in graphene.

Modification of electronic properties of graphene with self-assembled monolayers.

Integration of organic and inorganic electronic materials is one of the emerging approaches to achieve novel material functionalities. Here, we demonstrate a stable self-assembled monolayer of an alkylsilane grown at the surface of graphite and graphene. Detailed characterization of the system using scanning probe microscopy, X-ray photoelectron spectroscopy, and transport measurements reveals the monolayer structure and its effect on the electronic properties of graphene. The monolayer induces a strong surface doping with a high density of mobile holes (n > 10(13) cm(-2)). The ability to tune electronic properties of graphene via stable molecular self-assembly, including selective doping of steps, edges, and other defects, may have important implications in future graphene electronics.

Percolation transition in the heterogeneous vortex state of NbSe2.

A percolation transition in the vortex state of a superconducting 2H-NbSe2 crystal is observed in the regime where vortices form a heterogeneous phase consisting of ordered and disordered domains. The transition is signaled by a sharp increase in critical current that occurs when the volume fraction of disordered domains reaches the value P(c) = 0.26 +/- 0.04. Measurements on different vortex states show that, while the temperature of the transition depends on history and measurement speed, the value of P(c) and the critical exponent characterizing the approach to it, r = 1.97 +/- 0.66, are universal.

Observation of the vortex lattice spinodal in NbSe2.

Metastable superheated and supercooled vortex states in NbSe2 crystals were probed with fast transport measurements over a wide range of field and temperature. The limit of metastability of the superheated vortex lattice defines a line in the phase diagram that lies below the superconducting transition and is clearly separated from it. This line is identified as the vortex lattice spinodal, and is in good agreement with recent theoretical predictions by Li and Rosenstein [Phys. Rev. B 65, 220504 (2002)]; cond-mat/0305258]. By contrast, no limit of metastability is observed for the supercooled disordered state.

Quasiparticle spectra, charge-density waves, superconductivity, and electron-phonon coupling in 2H-NbSe2.

High-resolution photoemission has been used to study the electronic structure of the charge-density wave (CDW) and superconducting dichalcogenide, 2H-NbSe2. From the extracted self-energies, important components of the quasiparticle interactions have been identified. In contrast to previously studied TaSe2, the CDW transition does not affect the electronic properties significantly. The electron-phonon coupling is identified as a dominant contribution to the quasiparticle self-energy and is shown to be very anisotropic (k dependent) and much stronger than in TaSe2.

Depinning of a metastable disordered vortex lattice.

We report on experiments investigating the depinning dynamics of a strongly pinned vortex lattice in 2H-NbSe2. We find that the depinning process starts at currents that are well below the critical current of the entire lattice and that it is governed by the formation of contiguous channels of mobile vortices connecting the sample edges. We obtain the formation time of the first channel by monitoring the delayed voltage response to a driving current step and by measuring the ramping rate dependence of the critical current. The subsequent increase in the number of moving vortices is determined from the temporal evolution of the voltage response and the critical current.

Equilibration and dynamic phase transitions of a driven vortex lattice.

We report on the observation of two types of current driven transitions in metastable vortex lattices. The metastable states, which are missed in usual slow transport measurements, are detected with a fast transport technique in the vortex lattice of undoped 2H-NbSe2. The transitions are seen by following the evolution of these states when driven by a current. At low currents we observe an equilibration transition from a metastable to a stable state, followed by a dynamic crystallization transition at high currents.