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Register a new userSuppression of odd-frequency pairing by phase-disorder in a nanowire coupled to Majorana zero modes
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Odd-frequency superconductivity is an exotic phase of matter in which Cooper pairing between electrons is entirely dynamical in nature. Majorana zero modes exhibit pure odd-frequency superconducting correlations due to their specific properties. Thus, by tunnel-coupling an array of Majorana zero modes to a spin-polarized wire, it is in principle possible to engineer a bulk one-dimensional odd-frequency spinless $s$-wave superconductor. We here point out that each tunnel coupling element, being dependent on a large number of material-specific parameters, is generically complex with sample variability in both its magnitude and phase. Using this, we demonstrate that, upon averaging over phase-disorder, the induced superconducting, including odd-frequency, correlations in the spin-polarized wire are significantly suppressed. We perform both a rigorous analytical evaluation of the disorder-averaged $T$-matrix in the wire, as well as numerical calculations based on a tight-binding model, and find that the anomalous, i.e. superconducting, part of the $T$-matrix is highly suppressed with phase disorder. We also demonstrate that this suppression is concurrent with the filling of the single-particle excitation gap by smearing the near-zero frequency peaks, due to formation of bound states that satisfy phase-matching conditions between spatially separated Majorana zero modes. Our results convey important constraints on the parameter control needed in practical realizations of Majorana zero mode structures and suggest that the achievement of a bulk 1D odd-$omega$ superconductivity from MZMs demand full control of the system parameters.
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Majorana fermions are rising as a promising key component in quantum computation. While the prevalent approach is to use a quadratic (i.e. non-interacting) Majorana Hamiltonian, when expressed in terms of Dirac fermions, generically the Hamiltonian involves interaction terms. Here we focus on the possible pair correlations in a simple model system. We study a model of Majorana fermions coupled to a boson mode and show that the anomalous correlator between different Majorana fermions, located at opposite ends of a topological wire, exhibits odd frequency behavior. It is stabilized when the coupling strength $g$ is above a critical value $g_c$. We use both, conventional diagrammatic theory and a functional integral approach, to derive the gap equation, the critical temperature, the gap function, the critical coupling, and a Ginzburg-Landau theory allowing to discuss a possible subleading admixture of even-frequency pairing.
We investigate the effect of correlated disorder on Majorana zero modes (MZMs) bound to magnetic vortices in two-dimensional topological superconductors. By starting from a lattice model of interacting fermions with a $p_x pm i p_y$ superconducting ground state in the disorder-free limit, we use perturbation theory to describe the enhancement of the Majorana localization length at weak disorder and a self-consistent numerical solution to understand the breakdown of the MZMs at strong disorder. We find that correlated disorder has a much stronger effect on the MZMs than uncorrelated disorder and that it is most detrimental if the disorder correlation length $ell$ is on the same order as the superconducting coherence length $xi$. In contrast, MZMs can survive stronger disorder for $ell ll xi$ as random variations cancel each other within the length scale of $xi$, while an MZM may survive up to very strong disorder for $ell gg xi$ if it is located in a favorable domain of the given disorder realization.
Majorana zero modes in a superconductor-semiconductor nanowire have been extensively studied during the past decade. Disorder remains a serious problem, preventing the definitive observation of topological Majorana bound states. Thus, it is worthwhile to revisit the simple model, the Kitaev chain, and study the effects of weak and strong disorder on the Kitaev chain. By comparing the role of disorder in a Kitaev chain with that in a nanowire, we find that disorder affects both systems but in a nonuniversal manner. In general, disorder has a much stronger effect on the nanowire than the Kitaev chain, particularly for weak to intermediate disorder. For strong disorder, both the Kitaev chain and nanowire manifest random featureless behavior due to universal Anderson localization. Only the vanishing and strong disorder regimes are thus universal, manifesting respectively topological superconductivity and Anderson localization, but the experimentally relevant intermediate disorder regime is nonuniversal with the details dependent on the disorder realization in the system.
Since the proposal of monopole Cooper pairing in Ref. [1], considerable research efforts have been dedicated to the study of Copper pair order parameters constrained (or obstructed) by the nontrivial normal-state band topology at Fermi surfaces. In the current work, we propose a new type of topologically obstructed Cooper pairing, which we call Euler obstructed Cooper pairing. The Euler obstructed Cooper pairing widely exists between two Fermi surfaces with nontrivial band topology characterized by nonzero Euler numbers; such Fermi surfaces can exist in the $PT$-protected spinless-Dirac/nodal-line semimetals with negligible spin-orbit coupling, where $PT$ is the space-time inversion symmetry. An Euler obstructed pairing channel must have pairing nodes on the pairing-relevant Fermi surfaces, and the total winding number of the pairing nodes is determined by the sum or difference of the Euler numbers on the Fermi surfaces. In particular, we find that when the normal state is nonmagnetic and the pairing is weak, a sufficiently-dominant Euler obstructed pairing channel with zero total momentum leads to nodal superconductivity. If the Fermi surface splitting is small, the resultant nodal superconductor hosts hinge Majorana zero modes, featuring the first class of higher-order nodal superconductivity originating from the topologically obstructed Cooper pairing. The possible dominance of the Euler obstructed pairing channel near the superconducting transition and the robustness of the hinge Majorana zero modes against disorder are explicitly demonstrated using effective or tight-binding models.
We study the low-energy transport properties of a hybrid device composed by a native quantum dot coupled to both ends of a topological superconducting nanowire section hosting Majorana zero-modes. The account of the coupling between the dot and the farthest Majorana zero-mode allows to introduce the topological quality factor, characterizing the level of topological protection in the system. We demonstrate that Coulomb interaction between the dot and the topological superconducting section leads to the onset of the additional overlap of the wavefunctions describing the Majorana zero-modes, leading to the formation of trivial Andreev bound states even for spatially well-separated Majoranas. This leads to the spoiling of the quality factor and introduces a constraint for the braiding process required to perform topological quantum computing operations.
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