Steve Simon

Abstract:

To investigate Majorana fermionic excitations of a px +i py superconductor, the Bogoliubov-de Gennes equation is solved on a sphere for two cases: (i) a vortex-antivortex pair at opposite poles and (ii) an edge near the south pole and an antivortex at the north pole. The vortex cores support a state of two Majorana fermions, the energy of which decreases exponentially with the radius of the sphere, independently of a moderate disorder potential. The tunneling conductance of an electron into the superconductor near the position of a vortex is computed for finite temperature and is compared to the case of an s -wave superconductor. The zero-bias conductance peak of the antivortex is half that of the vortex. This effect can be used as a probe of the order-parameter symmetry and as a direct measurement of the Majorana fermion. © 2009 The American Physical Society.

Abstract:

Quantum Hall bilayer systems at filling fractions near ν= 1 2 + 1 2 undergo a transition from a compressible phase with strong intralayer correlation to an incompressible phase with strong interlayer correlations as the layer separation d is reduced below some critical value. Deep in the intralayer phase (large separation) the system can be interpreted as a fluid of composite fermions (CFs), whereas deep in the interlayer phase (small separation) the system can be interpreted as a fluid of composite bosons (CBs). The focus of this paper is to understand the states that occur for intermediate layer separation by using trial variational wave functions. We consider two main classes of wave functions. In the first class, previously introduced in Möller [Phys. Rev. Lett. 101, 176803 (2008)], we consider interlayer BCS pairing of two independent CF liquids. We find that these wave functions are exceedingly good for d 0 with 0 as the magnetic length. The second class of wave functions naturally follows the reasoning of Simon [Phys. Rev. Lett. 91, 046803 (2003)] and generalizes the idea of pairing wave functions by allowing the CFs also to be replaced continuously by CBs. This generalization allows us to construct exceedingly good wave functions for interlayer spacings of d 0 as well. The accuracy of the wave functions discussed in this work, compared with exact diagonalization, approaches that of the celebrated Laughlin wave function. © 2009 The American Physical Society.