Electron Solid Phase Research Articles

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.

NMR in the solid phase of two-dimensional electrons at high magnetic fields

We report on a magnetic resonance study in the electron solid phase of a low-disorder $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ sample at very high magnetic fields using a resistively detected NMR technique. An anomalous dispersivelike line shape is observed at the onset of the electron solid in the vicinity of the Landau filling $\ensuremath{\nu}=\frac{2}{9},\frac{1}{5}$ fractional quantum Hall state, reminiscent of the line shape observed near filling factor $\ensuremath{\nu}\ensuremath{\sim}1$. In contrast to this filling factor region, the spin-lattice relaxation time ${T}_{1}$ in the electron solid is found to be very long, and does not correlate with either ${R}_{xx}$ or the Landau filling factor. The dispersivelike line shapes observed in this regime suggests that the intricate interplay between the nuclear spin and the electronic transport may be modified by the formation of the electron solid.

Stiff liquid and solid of electrons in two dimensions

Electrons in two-dimensional (2D) layers at semiconductor interfaces may be driven to a solid phase by reducing their density. Understandmg of this electron liquid-solid transition at mK-temperatures and the origin of the 2D electron solid phase remain challenging. The experimental system under study is subject to strong interactions and disorder. Charge transport in the electron solid phase demonstrates many features anticipated for the pinned crystal, though no direct imaging of a spatial charge- or magnetic-ordering is available by now. Rich information has been recently obtained for dilute electron liquid phase on strong renormalization of the Pauli spin susceptibility, magnetization, and the effective mass. These data provide a set of the Fermi-liquid coupling parameters for densities down to and at the transition. The steep density dependence of the susceptibility is intriguing because it might indicate a developing magnetic transition, though it is more likely reflects a tendency to crystallization.

Magneto-optical determination of the electron-solid phase boundary.

We have obtained a two-dimensional electron-solid phase diagram in the extreme magnetic quantum limit by studying the temperature dependence of the radiative recombination of electrons in a GaAs/AlxGa1-xAs heterojunction with holes bound to a delta-layer, 250 A away in the GaAs, of Be acceptors. The low-energy shoulder to the luminescence line, indicating the presence of the electron solid, is seen to disappear at a filling-factor-dependent critical temperature. We observe no shoulder above a filling factor of 0.25, and the critical temperature falls to below 0.4 K at filling factors 1/5 and 1/7.

Temperature dependence of the luminescence from a two-dimensional electron system in the Wigner solid regime

We have studied the temperature and magnetic field dependence of the luminescence of a two-dimensional electron system in the extreme magnetic quantum limit. Analysis of the intensity variations of the shoulder that appears on the low-energy side of the lowest Landau level luminescence peak, attributed to the formation of a pinned Wigner crystal, has enabled us to construct an electron solid phase diagram. In the fractional quantum Hall regime, we observe clear maxima in the high- and low-energy halfwidths of the luminescence line around fractional occupancies 1 3 , 1 5 and 1 7 . This behaviour is consistent with a transit between two luminescence lines at the shifts.

Optical spectroscopy of GaAs in the extreme quantum limit: integer and fractional quantum Hall effect, and onset of the electron solid

Our recent optical detection of the integer and fractional quantum Hall effects in GaAs, by intrinsic band-gap photoluminescence at dilution refrigerator temperatures, is reviewed. This work has been extended to the extreme quantum limit where a photoluminescence peak develops close to Landau level filling factor v = 1 5 which correlates both with the onset of threshold behaviour in current-voltage characteristics of the two-dimensional electron system and a resonant radio-frequency absorption; the latter are quantitatively accounted for by a model of crystalline electronic structure broken up into domains. Preliminary mK transport experiments in intense, pulsed magnetic fields are also described, which establish a basis to access the electron solid phase transition in a hitherto unattainable region of the ( B, T) plane.