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Register a new userFragile topology in nodal-line semimetal superconductors with double band inversion
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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.
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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.
We study systematically the scattering processes and the conductance spectra in nodal-line semimetalsuperconductor junctions using the extended Blonder-Tinkham-Klapwijk theory. The coexistence of peculiar quadruple reflections are found, which are the specular normal reflection, the retro-normal reflection, the specular Andreev reflection and the retro-Andreev reflection. The incident angle dependence and the quasiparticle energy dependence of the double normal reflections and the double Andreev reflections are investigated under various values of parameters such as the interfacial barrier height, the chemical potentials, and the orbital coupling strength. It is found that the appearance and the disappearance of the reflections and their magnitudes can be controlled through tuning these parameters. The scattering mechanism for the reflections are analyzed in details from the viewpoint of the band structure. We also investigate the conductance spectra for the junctions, which show distinctive features and strong anisotropy about the orientation relationships of the nodal line and interface. The unique scattering processes and conductance spectra found in the junctions are helpful in designing superconducting electronic devices and searching for the nodal line in materials experimentally.
We observed quantum oscillations in thermoelectric and magnetic torque signals in non-centrosymmetric superconductor PbTaSe$_2$. One oscillatory frequency stems from the orbits formed by magnetic breakdown, while others are from two-dimensional-like Fermi surfaces near the topological nodal rings. Our comprehensive understanding of the Fermi surface topology of PbTaSe$_2$, including nailing down the Fermi level and detecting the Berry phases near the nodal rings, is crucial for searching plausible topological superconductivity in its bulk and surface states.
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.
Dirac states hosted by Sb/Bi square nets are known to exist in the layered antiferromagnetic AMnX$_2$ (A = Ca/Sr/Ba/Eu/Yb, X=Sb/Bi) material family the space group to be P4/nmm or I4/mmm. In this paper, we present a comprehensive study of quantum transport behaviors, angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations on SrZnSb2, a nonmagnetic analogue to AMnX2, which crystallizes in the pnma space group with distorted square nets. From the quantum oscillation measurements up to 35 T, three major frequencies including F$_1$ = 103 T, F$_2$ = 127 T and F$_3$ = 160 T, are identified. The effective masses of the quasiparticles associated with these frequencies are extracted, namely, m*$_1$ = 0.1 m$_e$, m*$_2$ = 0.1 m$_e$ and m*$_3$ = 0.09m$_e$, where m$_e$ is the free electron mass. From the three-band Lifshitz-Kosevich fit, the Berry phases accumulated along the cyclotron orbit of the quasiparticles are 0.06$pi$, 1.2$pi$ and 0.74$pi$ for F$_1$, F$_2$ and F$_3$, respectively. Combined with the ARPES data and the first-principles calculations, we reveal that F2 and F3 are associated with the two nontrivial Fermi pockets at the Brillouin zone edge while F1 is associated with the trivial Fermi pocket at the zone center. In addition, the first-principles calculations further suggest the existence of Dirac nodal line in the band structure of SrZnSb$_2$.
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