Conductivity predictions for the 5/2 fractional quantum Hall state using the composite fermion superconductor model.

摘要

The fractional quantum Hall effect (FQHE) occurs when a two-dimensional electron gas is placed in a strong magnetic field at low temperatures. When this effect occurs the Hall resistance, R_H, defined to be the Hall voltage divided by the current, is quantized, with R_H = (1/ν)h/ e2 where ν = p/q is the Landau level filling fraction; and p and q are relatively prime integers. For almost all observed FQHE states, q is odd with one notable exception: the ν = 5/2 FQHE state. Understanding the nature of this incompressible even-denominator state is one of the central questions in the theory of the FQHE and is the subject of this Dissertation.; We use a powerful theoretical tool for studying the FQHE: composite fermion theory. Composite fermions can be viewed as electrons bound to an even number of magnetic flux quanta. Jain has shown that the FQHE for electrons can be viewed as an integer quantum Hall effect (p = 1) for composite fermions. More recently, Halperin, Lee and Read developed a successful theory of the compressible ν = 1/2 state using composite fermions.; There is now compelling theoretical evidence that the 5/2 state is a so-called Moore-Read state—a state which can be viewed as a spin-polarized p-wave superconductor of composite fermions. We have developed a semi-phenomenological description of this state by modifying the Halperin-Lee-Read theory, adding a p-wave pairing interaction between composite fermions by hand. The electromagnetic response functions for the resulting superconducting state of composite fermions are then calculated. We show that these response functions exhibit the expected BCS ‘coherence factor’ effects, such as the Hebel-Slichter peak.; Using the composite fermion response functions, we then calculate the corresponding electronic response functions using Chern-Simons theory. We find that in the electronic response, the most striking coherence factor effects (e.g., the Hebel-Slichter peak) are strongly suppressed. However, the low-temperature ω = 2Δ threshold behavior does show clear coherence factor effects.; Finally, we use our model to predict the wave-vector and frequency dependence of the longitudinal conductivity, σ_xx( q, ω), which can be measured in surface-acoustic-wave propagation experiments.