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Register a new userSpin and the Coulomb Gap in the Half-Filled Lowest Landau Level
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James P. Eisenstein
Publication date
2016
fields
Physics
and research's language is
English
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The Coulomb gap observed in tunneling between parallel two-dimensional electron systems, each at half filling of the lowest Landau level, is found to depend sensitively on the presence of an in-plane magnetic field. Especially at low electron density, the width of the Coulomb gap at first increases sharply with in-plane field, but then abruptly levels off. This behavior appears to coincide with the known transition from partial to complete spin polarization of the half-filled lowest Landau level. The tunneling gap therefore opens a new window onto the spin configuration of two-dimensional electron systems at high magnetic field.
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Motivated by recent proposal by Potter et al. [Phys. Rev. X 6, 031026 (2016)] concerning possible thermoelectric signatures of Dirac composite fermions, we perform a systematic experimental study of thermoelectric transport of an ultrahigh-mobility GaAs/AlxGa1-xAs two dimensional electron system at filling factor v = 1/2. We demonstrate that the thermopower Sxx and Nernst Sxy are symmetric and anti-symmetric with respect to B = 0 T, respectively. The measured properties of thermopower Sxx at v = 1/2 are consistent with previous experimental results. The Nernst signals Sxy of v = 1/2, which have not been reported previously, are non-zero and show a power law relation with temperature in the phonon-drag dominant region. In the electron-diffusion dominant region, the Nernst signals Sxy of v = 1/2 are found to be significantly smaller than the linear temperature dependent values predicted by Potter et al., and decreasing with temperature faster than linear dependence.
In this paper we study the relation between the conventional Fermion-Chern-Simons (FCS) theory of the half-filled Landau level (nu=1/2), and alternate descriptions that are based on the notion of neutral quasi-particles that carry electric dipole moments. We have previously argued that these two approaches are equivalent, and that e.g., the finite compressibility obtained in the FCS approach is also obtained from the alternate approach, provided that one properly takes into account a peculiar symmetry of the dipolar quasiparticles --- the invariance of their energy to a shift of their center of mass momentum. Here, we demonstrate the equivalence of these two approaches in detail. We first study a model where the charge and flux of each fermion is smeared over a radius Q^{-1} where results can be calculated to leading order in the small parameter Q/k_f. We study two dipolar-quasiparticle descriptions of the nu=1/2 state in the small-Q model and confirm that they yield the same density response function as in the FCS approach. We also study the single-particle Greens function and the effective mass, for one form of dipolar quasiparticles, and find the effective mass to be infra-red divergent, exactly as in the FCS approach. Finally, we propose a form for a Fermi-liquid theory for the dipolar quasiparticles, which should be valid in the physical case where Q is infinite.
We construct an action for the composite Dirac fermion consistent with symmetries of electrons projected to the lowest Landau level. First we construct a generalization of the $g=2$ electron that gives a smooth massless limit on any curved background. Using the symmetries of the microscopic electron theory in this massless limit we find a number of constraints on any low-energy effective theory. We find that any low-energy description must couple to a geometry which exhibits nontrivial curvature even on flat space-times. Any composite fermion must have an electric dipole moment proportional and orthogonal to the composite fermions wavevector. We construct the effective action for the composite Dirac fermion and calculate the physical stress tensor and current operators for this theory.
Half-filled Landau levels host an emergent Fermi-liquid which displays an instability towards pairing, culminating in a gapped even-denominator fractional quantum Hall ground state. While this pairing may be probed by tuning the polarization of carriers in competing orbital and spin degrees of freedom, sufficiently high quality platforms offering such tunability remain few. Here we explore the ground states at filling factor $ u$ = 5/2 in ZnO-based two-dimensional electron systems through a forced intersection of opposing spin branches of Landau levels taking quantum numbers $N$ = 1 and 0. We reveal a cascade of phases with distinct magnetotransport features including a gapped phase polarized in the $N$ = 1 level and a compressible phase in N = 0, along with an unexpected Fermi-liquid, a second gapped, and a strongly anisotropic nematic-like phase at intermediate polarizations when the levels are near degeneracy. The phase diagram is produced by analyzing the proximity of the intersecting levels and highlights the excellent reproducibility and controllability ZnO offers for exploring exotic fractionalized electronic phases.
We study the effect of electron-electron interaction and spin on electronic and transport properties of gated graphene nanoribbons (GNRs) in a perpendicular magnetic field in the regime of the lowest Landau level (LL). The electron-electron interaction is taken into account using the Hartree and Hubbard approximations, and the conductance of GNRs is calculated on the basis of the recursive Greens function technique within the Landauer formalism. We demonstrate that, in comparison to the one-electron picture, electron-electron interaction leads to the drastic changes in the dispersion relation and structure of propagating states in the regime of the lowest LL showing a formation of the compressible strip and opening of additional conductive channels in the middle of the ribbon. We show that the latter are very sensitive to disorder and get scattered even if the concentration of disorder is moderate. In contrast, the edge states transport is very robust and can not be suppressed even in the presence of a strong spin-flipping.
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