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Register a new userTuning the topology of $p$-wave superconductivity in an analytically solvable two-band model
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We introduce and solve a two-band model of spinless fermions with $p_x$-wave pairing on a square lattice. The model reduces to the well-known extended Harper-Hofstadter model with half-flux quanta per plaquette and weakly coupled Kitaev chains in two respective limits. We show that its phase diagram contains a topologically nontrivial weak pairing phase as well as a trivial strong pairing phase as the ratio of the pairing amplitude and hopping is tuned. Introducing periodic driving to the model, we observe a cascade of Floquet phases with well defined quasienergy gaps and featuring chiral Majorana edge modes at the zero- or $pi$-gap, or both. Dynamical topological invariants are obtained to characterize each phase and to explain the emergence of edge modes in the anomalous phase where all the quasienergy bands have zero Chern number. Analytical solution is achieved by exploiting a generalized mirror symmetry of the model, so that the effective Hamiltonian is decomposed into that of spin-$1/2$ in magnetic field, and the loop unitary operator becomes spin rotations. We further show the dynamical invariants manifest as the Hopf linking numbers.
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In this paper we study the effects of hybridization in the superconducting properties of a two-band system. We consider the cases that these bands are formed by electronic orbitals with angular momentum, such that, the hybridization $V(mathbf{k})$ among them can be symmetric or antisymmetric under inversion symmetry. We take into account only intra-band attractive interactions in the two bands and investigate the appearance of an induced inter-band pairing gap. We show that (inter-band) superconducting orderings are induced in the total absence of attractive interaction between the two bands, which turns out to be completely dependent on the hybridization between them. For the case of antisymmetric hybridization we show that the induced inter-band superconductivity has a p-wave symmetry.
In flat bands, superconductivity can lead to surprising transport effects. The superfluid mobility, in the form of the superfluid weight $D_s$, does not draw from the curvature of the band but has a purely band-geometric origin. In a mean-field description, a non-zero Chern number or fragile topology sets a lower bound for $D_s$, which, via the Berezinskii-Kosterlitz-Thouless mechanism, might explain the relatively high superconducting transition temperature measured in magic-angle twisted bilayer graphene (MATBG). For fragile topology, relevant for the bilayer system, the fate of this bound for finite temperature and beyond the mean-field approximation remained, however, unclear. Here, we use numerically exact Monte Carlo simulations to study an attractive Hubbard model in flat bands with topological properties akin to those of MATBG. We find a superconducting phase transition with a critical temperature that scales linearly with the interaction strength. We then investigate the robustness of the superconducting state to the addition of trivial bands that may or may not trivialize the fragile topology. Our results substantiate the validity of the topological bound beyond the mean-field regime and further stress the importance of fragile topology for flat-band superconductivity.
The possibility of p-wave pairing in superconductors has been proposed more than five decades ago, but has not yet been convincingly demonstrated. One difficulty is that some p-wave states are thermodynamically indistinguishable from s-wave, while others are very similar to d-wave states. Here we studied the self-field critical current of NdFeAs(O,F) thin films in order to extract absolute values of the London penetration depth, the superconducting energy gap, and the relative jump in specific heat at the superconducting transition temperature, and find that all the deduced physical parameters strongly indicate that NdFeAs(O,F) is a bulk p-wave superconductor. Further investigation revealed that single atomic layer FeSe also shows p-wave pairing. In an attempt to generalize these findings, we re-examined the whole inventory of superfluid density measurements in iron-based superconductors show quite generally that most of the iron-based superconductors are p-wave superconductors.
We study the topological properties of the nodal-line semimetal superconductor. The single band inversion and the double band inversion coexist in an $s$-wave nodal-line semimetal superconductor. In the single/double band inversion region, the system is in a stable/fragile topological state. The two topological invariants describing these two topological states are coupled to each other, leading to the coupled edge states. The stable topological state is indexed by ${mathrm Z}$(d=1), while the fragile topological state is characterized to be ${mathrm Z}otimes {mathrm Z}(d=1)$. In addition, the $s$-wave nodal-line semimetal superconductor has a nontrivial ${mathrm Z_{4}=2}$ topological invariant, indicating that it is a inversion symmetry protected second order topological crystalline superconductor. While the $p$-wave nodal-line semimetal belongs to a pure fragile topological superconductor due to the double band inversion. The vortex bound states and the surface impurity effects are studied and they can be used to distinguish the different pairing states and identify the fragile topology of the system. Remarkably, we propose that vortex line in the nodal-line semimetal superconductor is a one dimensional fragile topological state protected by the spatial symmetry.
A superconductor with $p_x+ip_y$ order has long fascinated the physics community because vortex defects in such a system host Majorana zero modes. Here we propose a simple construction of a chiral superconductor using proximitized quantum wires and twist angle engineering as basic ingredients. We show that a weakly coupled parallel array of such wires forms a gapless $p$-wave superconductor. Two such arrays, stacked on top of one another with a twist angle close to $90^circ$, spontaneously break time reversal symmetry and form a robust, fully gapped $p_x+ip_y$ superconductor. We map out topological phases of the proposed system, demonstrate existence of Majorana zero modes in vortices, and discuss prospects for experimental realization.
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