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Register a new userMagic angles and current-induced topology in twisted nodal superconductors
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Pavel Volkov Andreevich
Publication date
2020
fields
Physics
and research's language is
English
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Motivated by the recent achievements in the realization of strongly correlated and topological phases in twisted van der Waals heterostructures, we study the low-energy properties of a twisted bilayer of nodal superconductors. It is demonstrated that the spectrum of the superconducting Dirac quasiparticles close to the gap nodes is strongly renormalized by twisting and can be controlled with magnetic fields, current, or interlayer voltage. In particular, the application of an interlayer current transforms the system into a topological superconductor, opening a topological gap and resulting in a quantized thermal Hall effect with gapless, neutral edge modes. Close to the magic angle, where the Dirac velocity of the quasiparticles is found to vanish, a correlated superconducting state breaking time-reversal symmetry is shown to emerge. Estimates for a number of superconducting materials, such as cuprate, heavy fermion, and organic nodal superconductors, show that twisted bilayers of nodal superconductors can be readily realized with current experimental techniques.
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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.
We examine pinning and dynamics of Abrikosov vortices interacting with pinning centers placed in a moire pattern for varied moire lattice angles. We find a series of magic angles at which the critical current shows a pronounced dip corresponding to lattices in which the vortices can flow along quasi-one-dimensional channels. At these magic angles, the vortices move with a finite Hall angle. Additionally, for some lattice angles there are peaks in the critical current produced when the substrate has a quasiperiodic character that strongly reduces the vortex channeling. Our results should be general to a broad class of particle-like assemblies moving on moire patterns.
We investigate the properties of the coexistence phase of itinerant antiferromagnetism and nodal $d$-wave superconductivity (Q-phase) discovered in heavy fermion CeCoIn5 under applied magnetic field. We solve the minimal model that includes $d$-wave superconductivity and underlying magnetic correlations in real space to elucidate the structure of the $Q$-phase in the presence of an externally applied magnetic field. We further focus on the role of magnetic impurities, and show that they nucleate the Q-phase at lower magnetic fields. Our most crucial finding is that, even at zero applied field, dilute magnetic impurities cooperate via RKKY-like exchange interactions to generate a long-range ordered coexistence state identical to the Q-phase. This result is in agreement with recent neutron scattering measurements [S. Raymond et al., J. Phys. Soc. Jpn. {bf 83}, 013707 (2014)].
Landau levels (LL) have been predicted to emerge in systems with Dirac nodal points under applied non-uniform strain. We consider 2D, $d_{xy}$ singlet (2D-S) and 3D $p pm i p$ equal-spin triplet (3D-T) superconductors (SCs). We demonstrate the spinful Majorana nature of the bulk gapless zeroth-LLs. Strain along certain directions can induce two topologically distinct phases in the bulk, with zeroth LLs localized at the the interface. These modes are unstable toward ferromagnetism for 2D-S cases. Emergent real-space Majorana fermions in 3D-T allow for more exotic possibilities.
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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