Evidence of a first-order phase transition between Wigner-crystal and bubble phases of 2D electrons in higher Landau Levels

Competing Fractional Quantum Hall and Electron Solid Phases in Graphene

We report experimental observation of the reentrant integer quantum Hall effect in graphene, appearing in the N=2 Landau level. Similar to high-mobility GaAs/AlGaAs heterostructures, the effect is due to a competition between incompressible fractional quantum Hall states, and electron solid phases. The tunability of graphene allows us to measure the B-T phase diagram of the electron solid phase. The hierarchy of reentrant states suggests spin and valley degrees of freedom play a role in determining the ground state energy. We find that the melting temperature scales with magnetic field, and construct a phase diagram of the electron liquid-solid transition.

Current Flow in the Bubble and Stripe Phases

The spontaneous ordering of spins and charges in geometric patterns is currently under scrutiny in a number of different material systems. A topic of particular interest is the interaction of such ordered phases with itinerant electrons driven by an externally imposed current. It not only provides important information on the charge ordering itself but potentially also allows manipulating the shape and symmetry of the underlying pattern if current flow is strong enough. Unfortunately, conventional transport methods probing the macroscopic resistance suffer from the fact that the voltage drop along the sample edges provides only indirect information on the bulk properties because a complex current distribution is elicited by the inhomogeneous ground state. Here, we promote the use of surface acoustic waves to study these broken-symmetry phases and specifically address the bubble and stripe phases emerging in high-quality two-dimensional electron systems in GaAs/AlGaAs heterostructures as prototypical examples. When driving a unidirectional current, we find a surprising discrepancy between the sound propagation probing the bulk of the sample and the voltage drop along the sample edges. Our results prove that the current-induced modifications observed in resistive transport measurements are in fact a local phenomenon only, leaving the majority of the sample unaltered. More generally, our findings shed new light on the extent to which these ordered electron phases are impacted by an external current and underline the intrinsic advantages of acoustic measurements for the study of such inhomogeneous phases.

Observation of pinning mode of stripe phases of 2D systems in high Landau levels

We study the radio-frequency diagonal conductivities of the anisotropic stripe phases of higher Landau levels near half-integer fillings. In the hard direction, in which larger dc resistivity occurs, the spectrum exhibits a striking resonance, while in the orthogonal, easy direction, no resonance is discernible. The resonance is interpreted as a pinning mode of the stripe phase.

Phase coexistence of cluster crystals: beyond the Gibbs phase rule

We report a study of the phase behavior of multiple-occupancy crystals through simulation. We argue that in order to reproduce the equilibrium behavior of such crystals, it is essential to treat the number of lattice sites as a constraining thermodynamic variable. The resulting free-energy calculations thus differ considerably from schemes used for single-occupancy lattices. Using our approach, we obtain the phase diagram and the bulk modulus for a generalized exponential model that forms cluster crystals at high densities. We compare the simulation results with existing theoretical predictions. We also identify two types of density fluctuations that can lead to two sound modes and evaluate the corresponding elastic constants.

Competition between a fractional quantum hall liquid and bubble and Wigner crystal phases in the third Landau level

Magnetotransport measurements were performed in an ultrahigh mobility GaAs/AlGaAs quantum well of density approximately 3.0 x 10(11) cm(-2). The temperature dependence of the magnetoresistance Rxx was studied in detail in the vicinity of nu=9/2. In particular, we discovered new minima in Rxx at a filling factor nu approximately 41/5 and 44/5, but only at intermediate temperatures 80 approximately less than T approximately less than 120 mK. We interpret these as evidence for a fractional quantum Hall liquid forming in the N=2 Landau level and competing with bubble and Wigner crystal phases favored at lower temperatures. Our data suggest that a magnetically driven insulator-insulator quantum phase transition occurs between the bubble and Wigner crystal phases at T=0.