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Register a new userTopology and symmetry of surface Majorana arcs in cyclic superconductors
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We study the topology and symmetry of surface Majorana arcs in superconductors with nonunitary cyclic pairing. Cyclic $p$-wave pairing may be realized in a cubic or tetrahedral crystal, while it is a candidate for the interior $^3P_2$ superfluids of neutron stars. The cyclic state is an admixture of full gap and nodal gap with eight Weyl points and the low-energy physics is governed by itinerant Majorana fermions. We here show the evolution of surface states from Majorana cone to Majorana arcs under rotation of surface orientation. The Majorana cone is protected solely by an accidental spin rotation symmetry and fragile against spin-orbit coupling, while the arcs are attributed to two topological invariants: the first Chern number and one-dimensional winding number. Lastly, we discuss how topologically protected surface states inherent to the nonunitary cyclic pairing can be captured from surface probes in candidate compounds, such as U$_{1-x}$Th$_{x}$Be$_{13}$. We examine tunneling conductance spectra for two competitive scenarios in U$_{1-x}$Th$_{x}$Be$_{13}$---the degenerate $E_u$ scenario and the accidental scenario.
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Superconductivity is a phenomenon where the macroscopic quantum coherence appears due to the pairing of electrons. This offers a fascinating arena to study the physics of broken gauge symmetry. However, the important symmetries in superconductors are not only the gauge invariance. Especially, the symmetry properties of the pairing, i.e., the parity and spin-singlet/spin-triplet, determine the physical properties of the superconducting state. Recently it has been recognized that there is the important third symmetry of the pair amplitude, i.e., even or odd parity with respect to the frequency. The conventional uniform superconducting states correspond to the even-frequency pairing, but the recent finding is that the odd-frequency pair amplitude arises in the spatially non-uniform situation quite ubiquitously. Especially, this is the case in the Andreev bound state (ABS) appearing at the surface/interface of the sample. The other important recent development is on the nontrivial topological aspects of superconductors. As the band insulators are classified by topological indices into (i) conventional insulator, (ii) quantum Hall insulator, and (iii) topological insulator, also are the gapped superconductors. The influence of the nontrivial topology of the bulk states appears as the edge or surface of the sample. In the superconductors, this leads to the formation of zero energy ABS (ZEABS). Therefore, the ABSs of the superconductors are the place where the symmetry and topology meet each other which offer the stage of rich physics. In this review, we discuss the physics of ABS from the viewpoint of the odd-frequency pairing, the topological bulk-edge correspondence, and the interplay of these two issues. It is described how the symmetry of the pairing and topological indices determines the absence/presence of the ZEABS, its energy dispersion, and properties as the Majorana fermions.
The symmetries of superconducting gap functions remain an important question of iron-based superconductivity. Motivated by the recent angle-resolved photoemission spectroscopic measurements on iron-chalcogenide superconductors, we investigate the influence of pairing symmetries on the topological surface state. If the surface Dirac cone becomes gapped in the superconducting phase, it implies magnetization induced from time-reversal symmetry breaking pairing via spin-orbit coupling. Based on the crystalline symmetry constraints on the Ginzburg-Landau free energy, the gap function symmetries are among the possibilities of $A_{1g(u)}pm iA_{2g(u)}$, $B_{1g(u)}pm iB_{2g(u)}$, or, $E_{g(u)}pm i E_{g(u)}$. This time-reversal symmetry breaking effect can exist in the normal state very close to $T_c$ with the relative phase between two gap functions locked at $pm frac{pi}{2}$. The coupling between magnetization and superconducting gap functions is calculated based on a three-orbital model for the band structure of iron-chalcogenides. This study provides the connection between the gap function symmetries and topological properties of the surface state.
Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c-axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified.
The study of topological superconductivity is largely based on the analysis of mean-field Hamiltonians that violate particle number conservation and have only short-range interactions. Although this approach has been very successful, it is not clear that it captures the topological properties of real superconductors, which are described by number-conserving Hamiltonians with long-range interactions. To address this issue, we study topological superconductivity directly in the number-conserving setting. We focus on a diagnostic for topological superconductivity that compares the fermion parity $mathcal{P}$ of the ground state of a system in a ring geometry and in the presence of zero vs. $Phi_{text{sc}}=frac{h}{2e} equiv pi$ flux of an external magnetic field. A version of this diagnostic exists in any dimension and provides a $mathbb{Z}_2$ invariant $ u=mathcal{P}_0mathcal{P}_{pi}$ for topological superconductivity. In this paper we prove that the mean-field approximation correctly predicts the value of $ u$ for a large family of number-conserving models of spinless superconductors. Our result applies directly to the cases of greatest physical interest, including $p$-wave and $p_x+ip_y$ superconductors in one and two dimensions, and gives strong evidence for the validity of the mean-field approximation in the study of (at least some aspects of) topological superconductivity.
We report on the results of directional point-contact Andreev-reflection (PCAR) measurements in Ba(Fe_{1-x}Co_x)2As2 single crystals and epitaxial c-axis oriented films with x = 0.08 as well as in Ca(Fe_{1-x}Co_x)2As2 single crystals with x = 0.06. The PCAR spectra are analyzed within the two-band 3D version of the Blonder-Tinkham-Klapwijk model for Andreev reflection we recently developed, and that makes use of an analytical expression for the Fermi surface that mimics the one calculated within the density-functional theory (DFT). The spectra in Ca(Fe_{0.94}Co_{0.06})2As2 unambiguously demonstrate the presence of nodes or zeros in the small gap. In Ba(Fe_{0.92}Co_{0.08})2As2, the ab-plane spectra in single crystals can be fitted by assuming two nodeless gaps, but this model fails to fit the c-axis ones in epitaxial films. All these results are discussed in comparison with recent theoretical predictions about the occurrence of accidental 3D nodes and the presence of hot spots in the gaps of 122 compounds.
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