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Register a new userCoherence Effects of Caroli-de Gennes-Matricon Modes in Nodal Topological Superconductors
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Coherence effects by the impurity scattering of Caroli--de Gennes--Matricon (CdGM) modes in a vortex for nodal topological superconductors have been studied. The coherence effects reflect a topological number defined on a particular momentum space avoiding the superconducting gap nodes. First, we analytically derived the eigenvalue and eigenfunction of the CdGM modes, including the zero-energy modes, in a nodal topological superconducting state without impurities, where we focused on a possible superconducting state of UPt$_3$ as an example. Then, we studied impurity effects on the CdGM modes by introducing the impurity self-energy, which are dominated by the coherence factor depending on the eigenfunction of the CdGM modes. For the zero-energy CdGM modes, the coherence factor vanishes in a certain momentum range, which is guaranteed by topological invariance characterized by the one-dimensional winding number.
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Using low-temperature scanning tunneling microscopy (STM), we studied the vortex states of single-layer FeSe film on SrTiO3 (100) substrate, and the local behaviors of superconductivity at sample boundaries. We clearly observed multiple discrete Caroli-de Gennes-Matricon (CdGM) states in the vortex core, and quantitative analysis shows their energies well follow the formula: E = {mu}{Delta}^2/E_F, where {mu} is a half integer and {Delta} is the mean superconducting gap over the Fermi surface. Meanwhile, a fully gapped spectrum without states near zero bias is observed at [110](Fe) oriented boundary of 1 ML and 2 ML FeSe films, and atomic step edge of 1 ML FeSe. Accompanied with theoretical calculations, our results indicate a s-wave pairing without sign-change in the high-TC FeSe_SrTiO3 superconductor.
Motivated by the recent proposals for unconventional emergent physics in twisted bilayers of nodal superconductors, we study the peculiarities of the Josephson effect at the twisted interface between $d$-wave superconductors. We demonstrate that for clean interfaces with a twist angle $theta_0$ in the range $0^circ<theta_0<45^circ$ the critical current can exhibit nonmonotonic temperature dependence with a maximum at a nonzero temperature as well as a complex dependence on the twist angle at low temperatures. The former is shown to arise quite generically due to the contributions of the momenta around the gap nodes, which are negative for nonzero twist angles. It is demonstrated that these features reflect the geometry of the Fermi surface and are sensitive to the form of the momentum dependence of the tunneling at the twisted interface. Close to $theta_0=45^circ$ we find that the critical current does not vanish due to Cooper pair cotunneling, which leads to a transition to a time-reversal breaking topological superconducting $d+id$ phase. Weak interface roughness, quasiperiodicity, and inhomogeneity broaden the momentum dependence of the interlayer tunneling leading to a critical current $I_csim cos(2theta_0)$ with $cos(6theta_0)$ corrections. Furthermore, strong disorder at the interface is demonstrated to suppress the time-reversal breaking superconducting phase near $theta_0=45^circ$. Last, we provide a comprehensive theoretical analysis of experiments that can reveal the full current-phase relation for twisted superconductors close to $theta_0=45^circ$. In particular, we demonstrate the emergence of the Fraunhofer interference pattern near $theta_0=45^circ$, while accounting for realistic sample geometries, and show that its temperature dependence can yield unambiguous evidence of Cooper pair cotunneling, necessary for topological superconductivity.
Caroli-de Gennes-Martricon (CdGM) states were predicted in 1964 as low energy excitations within vortex cores of type-II superconductors. In the quantum limit, namely $T/T_mathrm{c} ll Delta/E_mathrm{F}$, the energy levels of these states were predicted to be discrete with the basic levels at $E_mu = pm mu Delta^2/E_mathrm{F}$ ($mu = 1/2$, $3/2$, $5/2$, ...). However, due to the small ratio of $Delta/E_mathrm{F}$ in most type-II superconductors, it is very difficult to observe the discrete CdGM states, but rather a symmetric peak appears at zero-bias at the vortex center. Here we report the clear observation of these discrete energy levels of CdGM states in FeTe$_{0.55}$Se$_{0.45}$. The rather stable energies of these states versus space clearly validates our conclusion. Analysis based on the energies of these CdGM states indicates that the Fermi energy in the present system is very small.
The theory of symmetry indicators has enabled database searches for topological materials in normal conducting phases, which has led to several encyclopedic topological material databases. Here, based on recently developed symmetry indicators for superconductors, we report our comprehensive search for topological and nodal superconductors among nonmagnetic materials in Inorganic Crystal Structure Database. A myriad of topological superconductors with exotic boundary states are discovered. When materials are symmetry-enforced nodal superconductors, positions and shapes of the nodes are also identified. These data are aggregated at Database of Topological and Nodal Supercoductors. We also provide a subroutine Topological Supercon, which allows users to examine the topological nature in the superconducting phase of any material themselves by uploading the result of first-principles calculations as an input. Our database and subroutine, when combined with experiments, will help us understand the unconventional pairing mechanism and facilitate realizations of the long-sought Majorana fermions promising for topological quantum computations.
Collective modes in two dimensional topological superconductors are studied by an extended random phase approximation theory while considering the influence of vector field of light. In two situations, the s-wave superconductors without spin-orbit-coupling (SOC), and the hybrid semiconductor and s-wave superconductor layers with strong SOC, we get the analytical results for longitudinal modes which are found to be indeed gapless. Further more, the effective modes volumes can be calculated, the electric and magnetic fields can be expressed as the creation and annihilation operators of such modes. So, one can study the interaction of them with other quasi-particles through fields.
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