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Register a new userExperimental determination of the energy per particle in partially filled Landau levels
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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.
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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.
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.
The intense search for topological superconductivity is inspired by the prospect that it hosts Majorana quasiparticles. We explore in this work the optimal design for producing topological superconductivity by combining a quantum Hall state with an ordinary superconductor. To this end, we consider a microscopic model for a topologically trivial two-dimensional p-wave superconductor exposed to a magnetic field, and find that the interplay of superconductivity and Landau level physics yields a rich phase diagram of states as a function of $mu/t$ and $Delta/t$, where $mu$, $t$ and $Delta$ are the chemical potential, hopping strength, and the amplitude of the superconducting gap. In addition to quantum Hall states and topologically trivial p-wave superconductor, the phase diagram also accommodates regions of topological superconductivity. Most importantly, we find that application of a non-uniform, periodic magnetic field produced by a square or a hexagonal lattice of $h/e$ fluxoids greatly facilitates regions of topological superconductivity in the limit of $Delta/trightarrow 0$. In contrast, a uniform magnetic field, a hexagonal Abrikosov lattice of $h/2e$ fluxoids, or a one dimensional lattice of stripes produces topological superconductivity only for sufficiently large $Delta/t$.
We study RKKY interactions for magnetic impurities on graphene in situations where the electronic spectrum is in the form of Landau levels. Two such situations are considered: non-uniformly strained graphene, and graphene in a real magnetic field. RKKY interactions are enhanced by the lowest Landau level, which is shown to form electron states binding with the spin impurities and add a strong non-perturbative contribution to pairwise impurity spin interactions when their separation $R$ no more than the magnetic length. Beyond this interactions are found to fall off as $1/R^3$ due to perturbative effects of the negative energy Landau levels. Based on these results, we develop simple mean-field theories for both systems, taking into account the fact that typically the density of states in the lowest Landau level is much smaller than the density of spin impurities. For the strain field case, we find that the system is formally ferrimagnetic, but with very small net moment due to the relatively low density of impurities binding electrons. The transition temperature is nevertheless enhanced by them. For real fields, the system forms a canted antiferromagnet if the field is not so strong as to pin the impurity spins along the field. The possibility that the system in this latter case supports a Kosterlitz-Thouless transition is discussed.
It is well established that the ground states of a two-dimensional electron gas with half-filled high ($N ge 2$) Landau levels are compressible charge-ordered states, known as quantum Hall stripe (QHS) phases. The generic features of QHSs are a maximum (minimum) in a longitudinal resistance $R_{xx}$ ($R_{yy}$) and a non-quantized Hall resistance $R_H$. Here, we report on emergent minima (maxima) in $R_{xx}$ ($R_{yy}$) and plateau-like features in $R_H$ in half-filled $N ge 3$ Landau levels. Remarkably, these unexpected features develop at temperatures considerably lower than the onset temperature of QHSs, suggesting a new ground state.
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