A quasi-exciton condensate is a phase characterized by quasi-long range order of an exciton (electron-hole pair) order parameter. Such a phase can arise naturally in a system of two parallel oppositely doped quantum wires, coupled by repulsive Coulomb interactions. We show that the quasi-exciton condensate phase can be stabilized in an extended range of parameters, in both spinless and spinful systems. For spinful electrons, the exciton phase is shown to be distinct from the usual quasi-long range ordered Wigner crystal phase characterized by power-law density wave correlations. The two phases can be clearly distinguished through their inter-wire tunneling current-voltage characteristics. In the quasi-exciton condensate phase the tunneling conductivity diverges at low temperatures and voltages, whereas in the Wigner crystal it is strongly suppressed. Both phases are characterized by a divergent Coulomb drag at low temperature. Finally, metallic carbon nanotubes are considered as a special case of such a one dimensional setup, and it is shown that exciton condensation is favorable due to the additional valley degree of freedom.
Recently, it has been proposed that exotic one-dimensional phases can be realized by gapping out the edge states of a fractional topological insulator. The low-energy edge degrees of freedom are described by a chain of coupled parafermions. We introduce a classification scheme for the phases that can occur in parafermionic chains. We find that the parafermions support both topological symmetry fractionalized phases as well as phases in which the parafermions condense. In the presence of additional symmetries, the phases form a non-Abelian group. As a concrete example of the classification, we consider the effective edge model for a $ u= 1/3$ fractional topological insulator for which we calculate the entanglement spectra numerically and show that all possible predicted phases can be realized.
Topological superconductors supporting Majorana Fermions with non-abelian statistics are presently a subject of intense theoretical and experimental effort. It has been proposed that the observation of a half-frequency or a fractional Josephson effect is a more reliable test for topological superconductivity than the search for end zero modes. Low-energy end modes can occur accidentally due to impurities. In fact, the fractional Josephson effect has been observed for the semiconductor nanowire system. Here we consider the ac Josephson effect in a conventional s-wave superconductor-normal metal-superconductor junction at a finite voltage. Using a Floquet-Keldysh treatment of the finite voltage junction, we show that the power dissipated from the junction, which measures the ac Josephson effect, can show a peak at half (or even incommensurate fractions) of the Josephson frequency. A similar conclusion is shown to hold for the Shapiro step measurement. The ac fractional Josephson peak can also be understood simply in terms of Landau-Zener processes associated with the Andreev bound state spectrum of the junction.
Superconductivity has recently been discovered in Pr$_{2}$Ba$_{4}$Cu$_{7}$O$_{15-delta}$ with a maximum $T_c$ of about 15K. Since the CuO planes in this material are believed to be insulating, it has been proposed that the superconductivity occurs in the double (or zigzag) CuO chain layer. On phenomenological grounds, we propose a theoretical interpretation of the experimental results in terms of a new phase for the zigzag chain, labelled by C$_1$S$_{3/2}$. This phase has a gap for some of the relative spin and charge modes but no total spin gap, and can have a divergent superconducting susceptibility for repulsive interactions. A microscopic model for the zigzag CuO chain is proposed, and on the basis of density matrix renormalization group (DMRG) and bosonization studies of this model, we adduce evidence that supports our proposal.
In the stripe-ordered state of a strongly-correlated two-dimensional electronic system, under a set of special circumstances, the superconducting condensate, like the magnetic order, can occur at a non-zero wave-vector corresponding to a spatial period double that of the charge order. In this case, the Josephson coupling between near neighbor planes, especially in a crystal with the special structure of La_{2-x}Ba_xCuO_4, vanishes identically. We propose that this is the underlying cause of the dynamical decoupling of the layers recently observed in transport measurements at x=1/8.
