243 research outputs found

### Odd-Parity Topological Superconductors: Theory and Application to Cu$_x$Bi$_2$Se$_3$

Topological superconductors have been theoretically predicted as a new class
of time-reversal-invariant superconductors which are fully gapped in the bulk
but have protected gapless surface Andreev bound states. In this work, we
provide a simple criterion that directly identifies this topological phase in
\textit{odd-parity} superconductors. We next propose a two-orbital $U-V$
pairing model for the newly discovered superconductor Cu$_x$Bi$_2$Se$_3$%. Due
to its peculiar three-dimensional Dirac band structure, we find that an
inter-orbital triplet pairing with odd-parity is favored in a significant part
of the phase diagram, and therefore gives rise to a topological superconductor
phase. Finally we propose sharp experimental tests of such a pairing symmetry.Comment: 4.1 pages, 2 figure

### Strongly coupled quantum phonon fluid in a solvable model

We study a model of a large number of strongly coupled phonons that can be
viewed as a bosonic variant of the Sachdev-Ye-Kitaev model. We determine the
phase diagram of the model which consists of a glass phase and a disordered
phase, with a first-order phase transition separating them. We compute the
specific heat of the disordered phase, with which we diagnose the
high-temperature crossover to the classical limit. We further study the
real-time dynamics of the disordered phase, where we identify three dynamical
regimes as a function of temperature. Low temperatures are associated with a
semiclassical regime, where the phonons can be described as long-lived normal
modes. High temperatures are associated with the classical limit of the model.
For a large region in parameter space, we identify an intermediate-temperatures
regime, where the phonon lifetime is of the order of the Planckian time scale
$\hbar/k_B T$.Comment: Typos corrected, references added, discussion improve

### From one-dimensional charge conserving superconductors to the gapless Haldane phase

We develop a framework to analyze one-dimensional topological superconductors
with charge conservation. In particular, we consider models with $N$ flavors of
fermions and $(\mathbb{Z}_2)^N$ symmetry, associated with the conservation of
the fermionic parity of each flavor. For a single flavor, we recover the result
that a distinct topological phase with exponentially localized zero modes does
not exist due to absence of a gap to single particles in the bulk. For $N>1$,
however, we show that the ends of the system can host low-energy,
exponentially-localized modes. The analysis can readily be generalized to
systems in other symmetry classes. To illustrate these ideas, we focus on
lattice models with $SO\left(N\right)$ symmetric interactions, and study the
phase transition between the trivial and the topological gapless phases using
bosonization and a weak-coupling renormalization group analysis. As a concrete
example, we study in detail the case of $N=3$. We show that in this case, the
topologically non-trivial superconducting phase corresponds to a gapless
analogue of the Haldane phase in spin-1 chains. In this phase, although the
bulk is gapless to single particle excitations, the ends host spin-$1/2$
degrees of freedom which are exponentially localized and protected by the spin
gap in the bulk. We obtain the full phase diagram of the model numerically,
using density matrix renormalization group calculations. Within this model, we
identify the self-dual line studied by Andrei and Destri [Nucl. Phys. B,
231(3), 445-480 (1984)], as a first-order transition line between the gapless
Haldane phase and a trivial gapless phase. This allows us to identify the
propagating spin-$1/2$ kinks in the Andrei-Destri model as the topological
end-modes present at the domain walls between the two phases

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