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Register a new userMicrowave resonances of the bubble phases in 1/4 and 3/4 filled higher Landau levels
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We have measured the diagonal conductivity in the microwave regime of an ultrahigh mobility two dimensional electron system. We find a sharp resonance in Re[sigma_{xx}] versus frequency when nu > 4 and the partial filling of the highest Landau level, nu^*, is ~ 1/4 or 3/4 and temperatures < 0.1 K. The resonance appears for a range of nu^* from 0.20 to 0.37 and again from 0.62 to 0.82. the peak frequency, f_{pk} changes from ~ 500 to ~ 150 as nu^* = 1/2 is approached. This range of f_{pk} shows no dependence on nu where the resonance is observed. The quality factor, Q, of the resonance is maximum at ~ nu^* = 0.25 and 0.74. We interpret the resonance as due to a pinning mode of the bubble phase crystal.
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For filling factors $ u$ in the range between 4.16 and 4.28, we simultaneously detect {it two} resonances in the real diagonal microwave conductivity of a two--dimensional electron system (2DES) at low temperature $T approx 35$ mK. We attribute the resonances to Wigner crystal and Bubble phases of the 2DES in higher Landau Levels. For $ u$ below and above this range, only single resonances are observed. The coexistence of both phases is taken as evidence of a first order phase transition. We estimate the transition point as $ u=4.22$.
We describe an experimental technique to measure the chemical potential, $mu$, in atomically thin layered materials with high sensitivity and in the static limit. We apply the technique to a high quality graphene monolayer to map out the evolution of $mu$ with carrier density throughout the N=0 and N=1 Landau levels at high magnetic field. By integrating $mu$ over filling factor, $ u$, we obtain the ground state energy per particle, which can be directly compared with numerical calculations. In the N=0 Landau level, our data show exceptional agreement with numerical calculations over the whole Landau level without adjustable parameters, as long as the screening of the Coulomb interaction by the filled Landau levels is accounted for. In the N=1 Landau level, comparison between experimental and numerical data reveals the importance of valley anisotropic interactions and the presence of valley-textured electron solids near odd filling.
A low-disorder, two-dimensional electron system (2DES) subjected to a large perpendicular magnetic field and cooled to very low temperatures provides a rich platform for studies of many-body quantum phases. The magnetic field quenches the electrons kinetic energy and quantizes the energy into a set of Landau levels, allowing the Coulomb interaction to dominate. In excited Landau levels, the fine interplay between short- and long-range interactions stabilizes bubble phases, Wigner crystals with more than one electron per unit cell. Here we present the screening properties of bubble phases, probed via a simple capacitance technique where the 2DES is placed between a top and a bottom gate and the electric field penetrating through the 2DES is measured. The bubbles formed at very low temperatures screen the electric field poorly as they are pinned by the residual disorder potential, allowing a large electric field to reach the top gate. As the temperature is increased, the penetrating electric field decreases and, surprisingly, exhibits a pronounced minimum at a temperature that appears to coincide with the melting temperature of the bubble phase. We deduce a quantitative phase diagram for the transition from bubble to liquid phases for Landau level filling factors $4leq uleq5$.
We consider graphene in a strong perpendicular magnetic field at zero temperature with an integral number of filled Landau levels and study the dispersion of single particle-hole excitations. We first analyze the two-body problem of a single Dirac electron and hole in a magnetic field interacting via Coulomb forces. We then turn to the many-body problem, where particle-hole symmetry and the existence of two valleys lead to a number of effects peculiar to graphene. We find that the coupling together of a large number of low-lying excitations leads to strong many-body corrections, which could be observed in inelastic light scattering or optical absorption. We also discuss in detail how the appearance of different branches in the exciton dispersion is sensitive to the number of filled spin and valley sublevels.
We present measurements of the real diagonal microwave conductivity of the reentrant insulating quantum Hall phases in the first excited Landau level at temperatures below 50 mK. A resonance is detected around filling factor $ u=2.58$ and weaker frequency dependence is seen at $ u=2.42$ and 2.28. These measurements are consistent with the formation of a bubble phase crystal centered around these $ u$ at very low temperatures.
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