arXiv subjects

Matthew P. A. Fisher

Publications and source records attributed to Matthew P. A. Fisher.

147 records · Page 9Linked to original sources

arXiv1993

Cooper pair tunnelling into a Quantum Hall fluid

Transport through a tunnel junction connecting a superconductor to a spin-aligned quantum Hall fluid at filling $ν$ is studied theoretically. The dominant transport channel at low temperatures is the tunnelling of Cooper pairs into edge states of the quantum Hall fluid. This process, which is greatly suppressed at low energies due to both Coulomb and Pauli exclusion effects, leads to a tunnelling conductance which vanishes with temperature as $T^{4/ν-2}$, for $ν^{-1}$ an odd integer. For integer fillings with $ν>1$ the "Pauli blockade" is circumvented and a non-vanishing conductance is predicted.

cond-mat↗

arXiv1993

Resonant Tunneling Between Quantum Hall Edge States

Resonant tunneling between fractional quantum Hall edge states is studied in the Luttinger liquid picture. For the Laughlin parent states, the resonance line shape is a universal function whose width scales to zero at zero temperature. Extensive quantum Monte Carlo simulations are presented for $ν= 1/3$ which confirm this picture and provide a parameter-free prediction for the line shape.

cond-mat↗

arXiv1993

Mott Transition in An Anyon Gas

We introduce and analyze a lattice model of anyons in a periodic potential and an external magnetic field which exhibits a transition from a Mott insulator to a quantum Hall fluid. The transition is characterized by the anyon statistics, $α$, which can vary between Fermions, $α=0$, and Bosons, $α=1$. For bosons the transition is in the universality class of the classical three-dimensional XY model. Near the Fermion limit, the transition is described by a massless $2+1$ Dirac theory coupled to a Chern-Simons gauge field. Analytic calculations perturbative in $α$, and also a large N-expansion, show that due to gauge fluctuations, the critical properties of the transition are dependent on the anyon statistics. Comparison with previous calcualations at and near the Boson limit, strongly suggest that our lattice model exhibits a fixed line of critical points, with universal critical properties which vary continuosly and monotonically as one passes from Fermions to Bosons. Possible relevance to experiments on the transitions between plateaus in the fractional quantum Hall effect and the magnetic field-tuned superconductor-insulator transition are briefly discussed.

cond-mat↗