For certain orientations of Josephson junctions between two px-wave or two d-wave superconductors, the subgap Andreev bound states produce a 4π-periodic relation between the Josephson current I and the phase difference φ: I ∝ sin(φ/2). Consequently, the ac Josephson current has the fractional frequency eV /h, where V is the dc voltage. In the tunneling limit, the Josephson current is proportional to the first power (not square) of the electron tunneling amplitude. Thus, the Josephson current between unconventional superconductors is carried by single electrons, rather than by Cooper pairs. The fractional ac Josephson effect can be observed experimentally by measuring frequency spectrum of microwave radiation from the junction. We also study junctions between singlet s-wave and triplet px-wave, as well as between chiral px ± ipy-wave superconductors.

The singlet s-, d-and triplet p-wave pairing symmetries in quasi-one-dimensional organic superconductors can be experimentally discriminated by probing the Andreev bound states at the sample edges. These states have the energy in the middle of the superconducting gap and manifest themselves as a zero-bias peak in tunneling conductance into the corresponding edge. Their existence is related to the sign change of the pairing potential around the Fermi surface. We present an exact self-consistent solution of the edge problem showing the presence of the midgap states for px-wave superconductivity. The spins of the edge state respond paramagnetically to a magnetic field parallel to the vector d that characterizes triplet pairing.

We study the effect of order parameter phase fluctuations on the single-particle properties of fermions in the underdoped cuprate superconductors using a phenomenological low-energy theory. We identify the fermion-phase field coupling as the Doppler-shift of the quasiparticle spectrum induced by the fluctuating superfluid velocity and we calculate the effect of these fluctuations on the fermion selfenergy. We show that the vortex pair unbinding near the superconducting transition causes a significant broadening in the fermion spectral function, producing a pseudogap-like feature. We also discuss the specific heat and show that the phase fluctuation effect is visible due to the short coherence length.

For certain orientations of Josephson junctions between two p_x-wave or two d-wave superconductors, the subgap Andreev bound states produce a 4pi-periodic relation between the Josephson current I and the phase difference phi: I ~ sin(phi/2). Consequently, the ac Josephson current has the fractional frequency eV/h, where V is the dc voltage. In the tunneling limit, the Josephson current is proportional to the first power (not square) of the electron tunneling amplitude. Thus, the Josephson current between unconventional superconductors is carried by single electrons, rather than by Cooper pairs. The fractional ac Josephson effect can be observed experimentally by measuring frequency spectrum of microwave radiation from the junction.Comment: 8 pages, 3 figures, RevTEX 4; v2. - minor typos corrected in proof

Bosonization of degenerate fermions yields insight both into Landau Fermi liquids, and into non-Fermi liquids. We begin our review with a pedagogical introduction to bosonization, emphasizing its applicability in spatial dimensions greater than one. After a brief historical overview, we present the essentials of the method. Well known results of Landau theory are recovered, demonstrating that this new tool of many-body theory is robust. Limits of multidimensional bosonization are tested by considering several examples of non-Fermi liquids, in particular the composite fermion theory of the half-filled Landau level. Nested Fermi surfaces present a different challenge, and these may be relevant in the cuprate superconductors. We conclude by discussing the future of multidimensional bosonization.