Broken symmetry of two-component nu =1/2 quantum Hall states

Majorana fermions in spin-singlet nodal superconductors with coexisting noncollinear magnetic order

Realizations of Majorana fermions in solid state materials have attracted great interest recently in connection to topological order and quantum information processing. We propose a novel way to create Majorana fermions in superconductors. We show that an incipient noncollinear magnetic order turns a spin-singlet superconductor with nodes into a topological superconductor with a stable Majorana bound state in the vortex core, at a topologically stable magnetic point defect, and on the edge. We argue that such an exotic non-Abelian phase can be realized in extended t-J models on the triangular and square lattices. It is promising to search for Majorana fermions in correlated electron materials where nodal superconductivity and magnetism are two common caricatures.

Spontaneous particle-hole symmetry breaking in the nu=5/2 fractional quantum Hall effect

The essence of the nu=5/2 fractional quantum Hall effect is believed to be captured by the Moore-Read Pfaffian (or anti-Pfaffian) description. However, a mystery regarding the formation of the Pfaffian state is the role of the three-body interaction Hamiltonian H3 that produces it as an exact ground state and the concomitant particle-hole symmetry breaking. We show that a two-body interaction Hamiltonian H2 constructed via particle-hole symmetrization of H3 produces a ground state nearly exactly approximating the Pfaffian and anti-Pfaffian states, respectively, in the spherical geometry. Importantly, the ground state energy of H2 exhibits a "Mexican-hat" structure as a function of particle number in the vicinity of half filling for a given flux indicating spontaneous particle-hole symmetry breaking. This signature is absent for the second Landau level Coulomb interaction at 5/2.

Halperin (m,m',n) bilayer quantum Hall states on thin cylinders

The Halperin (m,m',n) bilayer quantum Hall states are studied on thin cylinders. In this limit, charge-density-wave patterns emerge that are characteristic of the underlying quantum Hall state. The general patterns are worked out from a variant of the plasma analogy. Torus degeneracies are recovered, and for some important special cases a connection to well-known spin chain physics is made. By including interlayer tunneling, we also work out the critical behavior of a possible phase transition between the (331) state and the non-Abelian Moore-Read state in the thin cylinder limit.

Spin order in paired quantum Hall states

We consider quantum Hall states at even-denominator filling fractions, especially nu=5/2, in the limit of small Zeeman energy. Assuming that a paired quantum Hall state forms, we study spin ordering and its interplay with pairing. We give numerical evidence that at nu=5/2 an incompressible ground state will exhibit spontaneous ferromagnetism. The Ginzburg-Landau (GL) theory for the spin degrees of freedom of paired Hall states is a perturbed CP2 model. We compute the coefficients in the GL theory by a BCS Stoner mean-field theory for coexisting order parameters, and show that even if repulsion is smaller than that required for a Stoner instability, ferromagnetic fluctuations can induce a partially or fully polarized superconducting state.

Nature of excitations of the 5/2 fractional quantum Hall effect

It is shown, with the help of exact diagonalization studies on systems with up to 16 electrons, in the presence of up to two delta function impurities, that the Pfaffian model is not accurate for the actual quasiholes and quasiparticles of the 5/2 fractional quantum Hall effect. Implications for non-Abelian statistics are discussed.

Possible spin triplet superconductivity in NaxCoO2.yH2O

Symmetry-based considerations are combined with inputs from available experimental results to make the case that a novel spin-triplet superconductivity triggered by antiferromagnetic fluctuations may be realized in the newly discovered layered cobaltide NaxCoO2.yH(2)O. In the proposed picture, inaccessible via resonating-valence-bond physics extrapolated from half-filling, the pairing process is similar to that advanced for Sr2RuO4, but enjoys a further advantage coming from the hexagonal structure of the Fermi surface which gives a stronger pairing tendency.