Phase-locked magnetoconductance oscillations as a probe of Majorana edge states

We calculate the Andreev conductance of a superconducting ring interrupted by a flux-biased Josephson junction, searching for electrical signatures of circulating edge states. Two-dimensional pair potentials of spin-singlet d-wave and spin-triplet p-wave symmetry support, respectively, (chiral) Dirac modes and (chiral or helical) Majorana modes. These produce h/e-periodic magnetoconductance oscillations of amplitude \simeq (e^{2}/h)N^{-1/2}, measured via an N-mode point contact at the inner or outer perimeter of the grounded ring. For Dirac modes the oscillations in the two contacts are independent, while for an unpaired Majorana mode they are phase locked by a topological phase transition at the Josephson junction.Comment: 10 pages, 6 figures. New appendix on the gauge invariant discretization of the Bogoliubov-De Gennes equation. Accepted for publication in PR

The "Coulomb phase" in frustrated systems

The "Coulomb phase" is an emergent state for lattice models (particularly highly frustrated antiferromagnets) which have local constraints that can be mapped to a divergence-free "flux". The coarse-grained version of this flux or polarization behave analogously to electric or magnetic fields; in particular, defects at which the local constraint is violated behave as effective charges with Coulomb interactions. I survey the derivation of the characteristic power-law correlation functions and the pinch-points in reciprocal space plots of diffuse scattering, as well as applications to magnetic relaxation, quantum-mechanical generalizations, phase transitions to long-range-ordered states, and the effects of disorder.Comment: 30 pp, 5 figures (Sub. to Annual Reviews of Condensed Matter Physics