Experimental evidence for s-wave pairing symmetry in superconducting Cu(x)Bi2Se3 single crystals using a scanning tunneling microscope

Dirac and Weyl superconductors in three dimensions

We introduce the concept of three-dimensional Dirac (Weyl) superconductors (SC), which have protected bulk fourfold (twofold) nodal points and surface Majorana arcs at zero energy. We provide a sufficient criterion for realizing them in centrosymmetric SCs with odd-parity pairing and mirror symmetry. Pairs of Dirac nodes appear in a mirror-invariant plane when the mirror winding number is nontrivial. Breaking mirror symmetry may gap Dirac nodes producing a topological SC. Each Dirac node evolves to a nodal ring when inversion-gauge symmetry is broken, whereas it splits into a pair of Weyl nodes when, and only when, time-reversal symmetry is broken.

Turning a band insulator into an exotic superconductor

Understanding exotic, non-s-wave-like states of Cooper pairs is important and may lead to new superconductors with higher critical temperatures and novel properties. Their existence is known to be possible but has always been thought to be associated with non-traditional mechanisms of superconductivity where electronic correlations play an important role. Here we use a first principles linear response calculation to show that in doped Bi₂Se₃ an unconventional p-wave-like state can be favoured via a conventional phonon-mediated mechanism, as driven by an unusual, almost singular behaviour of the electron–phonon interaction at long wavelengths. This may provide a new platform for our understanding of superconductivity phenomena in doped band insulators.

Most superconductors that exhibit exotic pairing symmetries are derived from host materials that are Mott insulators. Xiangang Wan and Sergey Savrasov show that it may be possible to realize an exotic p-wave superconductor in doped Bi₂Se₃, which is a topological band insulator.

First-order chiral to non-chiral transition in the angular dependence of the upper critical induction of the Scharnberg-Klemm p-wave pair state

We calculate the temperature T and angular (θ, ϕ) dependencies of the upper critical induction Bc2(θ, ϕ, T) for parallel-spin superconductors with an axially symmetric p-wave pairing interaction pinned to the lattice and a dominant ellipsoidal Fermi surface (FS). For all FS anisotropies, the chiral Scharnberg-Klemm (SK) state Bc2(θ, ϕ, T) exceeds that of the chiral Anderson-Brinkman-Morel (ABM) state and exhibits a kink at θ = θ*(T, ϕ), indicative of a first-order transition from its chiral, nodal-direction behavior to its non-chiral, antinodal-direction behavior. Applicabilities to Sr2RuO4, UCoGe and the candidate topological superconductor CuxBi2Se3 are discussed.

Dissipation in a simple model of a topological Josephson junction

The topological features of low-dimensional superconductors have created a lot of excitement recently because of their broad range of applications in quantum information and their potential to reveal novel phases of quantum matter. A potential problem for practical applications is the presence of phase slips that break phase coherence. Dissipation in nontopological superconductors suppresses phase slips and can restore long-range order. Here, we investigate the role of dissipation in a topological Josephson junction. We show that the combined effects of topology and dissipation keep phase and antiphase slips strongly correlated so that the device is superconducting even under conditions where a nontopological device would be resistive. The resistive transition occurs at a critical value of the dissipation that is 4 times smaller than that expected for a conventional Josephson junction. We propose that this difference could be employed as a robust experimental signature of topological superconductivity.

Surface-induced order parameter distortion in superfluid ³He-B measured by nonlinear NMR

The B phase of superfluid 3He is a three-dimensional time-reversal invariant topological superfluid, predicted to support gapless Majorana surface states. We confine superfluid 3He into a thin nanofluidic slab geometry. In the presence of a weak symmetry-breaking magnetic field, we have observed two possible states of the confined 3He-B phase manifold, through the small tipping angle NMR response. Large tipping angle nonlinear NMR has allowed the identification of the order parameter of these states and enabled a measurement of the surface-induced gap distortion. The results for two different quasiparticle surface scattering boundary conditions are compared with the predictions of weak-coupling quasiclassical theory. We identify a textural domain wall between the two B phase states, the edge of which at the cavity surface is predicted to host gapless states, protected in the magnetic field.

Pressure-induced unconventional superconducting phase in the topological insulator Bi2Se3

Simultaneous low-temperature electrical resistivity and Hall effect measurements were performed on single-crystalline Bi2Se3 under applied pressures up to 50 GPa. As a function of pressure, superconductivity is observed to onset above 11 GPa with a transition temperature Tc and upper critical field Hc2 that both increase with pressure up to 30 GPa, where they reach maximum values of 7 K and 4 T, respectively. Upon further pressure increase, Tc remains anomalously constant up to the highest achieved pressure. Conversely, the carrier concentration increases continuously with pressure, including a tenfold increase over the pressure range where Tc remains constant. Together with a quasilinear temperature dependence of Hc2 that exceeds the orbital and Pauli limits, the anomalously stagnant pressure dependence of Tc points to an unconventional pressure-induced pairing state in Bi2Se3 that is unique among the superconducting topological insulators.

Time-reversal-invariant topological superconductivity and Majorana Kramers pairs

We propose a feasible route to engineer one- and two-dimensional time-reversal-invariant topological superconductors (SCs) via proximity effects between nodeless s(±) wave iron-based SCs and semiconductors with large Rashba spin-orbit interactions. At the boundary of a time-reversal-invariant topological SC, there emerges a Kramers pair of Majorana edge (bound) states. For a Josephson π junction, we predict a Majorana quartet that is protected by mirror symmetry and leads to a mirror fractional Josephson effect. We analyze the evolution of the Majorana pair in Zeeman fields, as the SC undergoes a symmetry class change as well as topological phase transitions, providing an experimental signature in tunneling spectroscopy. We briefly discuss the realization of this mechanism in candidate materials and the possibility of using s and d wave SCs and weak topological insulators.