Theoretical, Unified Derivation of Both the Integer Quantum Hall Effect and Fractional Quantum Hall Effect

In this paper, using the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the balance between the Lorentz force and electrical force, we succeed in deriving the fractional quantum Hall effect and the integer quantum Hall effect; we find that the latter exists as a special case of the former. Moreover, using the derived expression describing the fractional quantum Hall effect, a relationship between the plateau in the resistivity of the sample and the applied magnetic field is obtained. The findings of this model agree well with experimental measurements. Because the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the force balance have concrete physical meanings in this work, we could provide a clear picture of the origin of both the integer quantum Hall effect and the fractional quantum Hall effect.

Particle-hole symmetry and the reentrant integer quantum Hall Wigner solid

The interplay of strong Coulomb interactions and of topology is currently under intense scrutiny in various condensed matter and atomic systems. One example of this interplay is the phase competition of fractional quantum Hall states and the Wigner solid in the two-dimensional electron gas. Here we report a Wigner solid at ν = 1.79 and its melting due to fractional correlations occurring at ν = 9/5. This Wigner solid, that we call the reentrant integer quantum Hall Wigner solid, develops in a range of Landau level filling factors that is related by particle-hole symmetry to the so called reentrant Wigner solid. We thus find that the Wigner solid in the GaAs/AlGaAs system straddles the partial filling factor 1/5 not only at the lowest filling factors, but also near ν = 9/5. Our results highlight the particle-hole symmetry as a fundamental symmetry of the extended family of Wigner solids and paint a complex picture of the competition of the Wigner solid with fractional quantum Hall states.

Universal upper bound for the entropy of superconducting vortices and the quantum Nernst effect

We show that the entropy per quantum vortex per layer in superconductors in external magnetic fields is bounded by the universal value kBln 2, which explains puzzling results of recent experiments on the Nernst effect. The observed plateau of the Nernst signal as a function of the magnetic field is correspondingly attributed to a manifestation of the integer quantum Nernst effect.