Topological ultranodal pair states in iron-based superconductors

Lifting of Gap Nodes by Disorder in Tetragonal FeSe_{1-x}S_{x} Superconductors

The observation of time-reversal symmetry breaking and large residual density of states in tetragonal FeSe_{1-x}S_{x} suggests a novel type of ultranodal superconducting state with Bogoliubov Fermi surfaces (BFSs). Although such BFSs in centrosymmetric superconductors are expected to be topologically protected, the impurity effect of this exotic superconducting state remains elusive experimentally. Here, we investigate the impact of controlled defects introduced by electron irradiation on the superconducting state of tetragonal FeSe_{1-x}S_{x} (0.18≤x≤0.25). The temperature dependence of magnetic penetration depth is initially consistent with a model with BFSs in the pristine sample. After irradiation, we observe a nonmonotonic evolution of low-energy excitations with impurity concentrations. This nonmonotonic change indicates a transition from nodal to nodeless, culminating in gapless with Andreev bound states, reminiscent of the nodal s_{±} case. This points to the accidental nature of the possible BFSs in tetragonal FeSe_{1-x}S_{x}, which are susceptible to disruption by the disorder.

Magnetisation control of the nematicity direction and nodal points in a superconducting doped topological insulator

We study the effects of magnetisation on the properties of the doped topological insulator of theBi2Se3family with nematic superconductivity. We found that the direction of the in-plane magnetisation fixes the direction of the nematicity in the system. The chiral state is more favourable than the nematic state for large values of out-of-plane magnetisation. Overall, the critical temperature of the nematic superconductivity is robust against magnetisation. We explore in detail the spectrum of the system with the pinned direction of the nematic order parameterΔy. Without magnetisation, there is a full gap in the spectrum because of finite hexagonal warping. At an out-of-planemzor orthogonal in-planemxmagnetisation that is strong enough, the spectrum is closed at the nodal points that are split by the magnetisation. Flat Majorana surface states connect such split bulk nodal points. Parallel magnetisationmylifts the nodal points and opens a full gap in the spectrum. We discuss relevant experiments and propose experimental verifications of our theory.

Electronic stripe patterns near the fermi level of tetragonal Fe(Se,S)

FeSe1-xSx remains one of the most enigmatic systems of Fe-based superconductors. While much is known about the orthorhombic parent compound, FeSe, the tetragonal samples, FeSe1-xSx with x > 0.17, remain relatively unexplored. Here, we provide an in-depth investigation of the electronic states of tetragonal FeSe0.81S0.19, using scanning tunneling microscopy and spectroscopy (STM/S) measurements, supported by angle-resolved photoemission spectroscopy (ARPES) and theoretical modeling. We analyze modulations of the local density of states (LDOS) near and away from Fe vacancy defects separately and identify quasiparticle interference (QPI) signals originating from multiple regions of the Brillouin zone, including the bands at the zone corners. We also observe that QPI signals coexist with a much stronger LDOS modulation for states near the Fermi level whose period is independent of energy. Our measurements further reveal that this strong pattern appears in the STS measurements as short range stripe patterns that are locally two-fold symmetric. Since these stripe patterns coexist with four-fold symmetric QPI around Fe-vacancies, the origin of their local two-fold symmetry must be distinct from that of nematic states in orthorhombic samples. We explore several aspects related to the stripes, such as the role of S and Fe-vacancy defects, and whether they can be explained by QPI. We consider the possibility that the observed stripe patterns may represent incipient charge order correlations, similar to those observed in the cuprates.

Topological nodal line in superfluid 3He and the Anderson theorem

Superconductivity and superfluidity with anisotropic pairing-such as d-wave in cuprates and p-wave in superfluid ³He-are strongly suppressed by impurities. Meanwhile, for applications, the robustness of Cooper pairs to disorder is highly desired. Recently, it has been suggested that unconventional systems become robust if the impurity scattering mixes quasiparticle states only within individual subsystems obeying the Anderson theorem that protects conventional superconductivity. Here, we experimentally verify this conjecture by measuring the temperature dependence of the energy gap in the polar phase of superfluid ³He. We show that oriented columnar non-magnetic defects do not essentially modify the energy spectrum, which has a Dirac nodal line. Although the scattering is strong, it preserves the momentum along the length of the columns and forms robust subsystems according to the conjecture. This finding may stimulate future experiments on the protection of topological superconductivity against disorder and on the nature of topological fermionic flat bands.

Expanded quantum vortex liquid regimes in the electron nematic superconductors FeSe1-xSx and FeSe1-xTex

The quantum vortex liquid (QVL) is an intriguing state of type-II superconductors in which intense quantum fluctuations of the superconducting (SC) order parameter destroy the Abrikosov lattice even at very low temperatures. Such a state has only rarely been observed, however, and remains poorly understood. One of the key questions is the precise origin of such intense quantum fluctuations and the role of nearby non-SC phases or quantum critical points in amplifying these effects. Here we report a high-field magnetotransport study of FeSe_1-xS_x and FeSe_1-xTe_x which show a broad QVL regime both within and beyond their respective electron nematic phases. A clear correlation is found between the extent of the QVL and the strength of the superconductivity. This comparative study enables us to identify the essential elements that promote the QVL regime in unconventional superconductors and to demonstrate that the QVL regime itself is most extended wherever superconductivity is weakest.

Two superconducting states with broken time-reversal symmetry in FeSe1-xSx

Iron-chalcogenide superconductors FeSe1-xSx possess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (μSR) measurements in FeSe1-xSx superconductors for 0 ≤ x ≤ 0.22 covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperature Tc for all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-field μSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x > 0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe1-xSx, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

Using Disorder to Identify Bogoliubov Fermi-Surface States

We argue that a superconducting state with a Fermi surface of Bogoliubov quasiparticles, a Bogoliubov Fermi surface (BG-FS), can be identified by the dependence of physical quantities on disorder. In particular, we show that a linear dependence of the residual density of states at weak disorder distinguishes a BG-FS state from other nodal superconducting states. We further demonstrate the stability of supercurrent against impurities and a characteristic Drude-like behavior of the optical conductivity. Our results can be directly applied to electron irradiation experiments on candidate materials of BG-FSs, including Sr_{2}RuO_{4}, FeSe_{1-x}S_{x}, and UBe_{13}.

Possible Superconductivity with a Bogoliubov Fermi Surface in a Lightly Doped Kagome U(1) Spin Liquid

Whether the doped t-J model on the Kagome lattice supports exotic superconductivity has not been decisively answered. In this Letter, we propose a new class of variational states for this model and perform a large-scale variational Monte Carlo simulation on it. The proposed variational states are parameterized by the SU(2)-gauge rotation angles, as the SU(2)-gauge structure hidden in the Gutzwiller-projected mean-field Ansatz for the undoped model is broken upon doping. These variational doped states smoothly connect to the previously studied U(1) π-flux or 0-flux states, and energy minimization among them yields a chiral noncentrosymmetric nematic superconducting state with 2×2-enlarged unit cell. Moreover, this pair density wave state possesses a finite Fermi surface for the Bogoliubov quasiparticles. We further study experimentally relevant properties of this intriguing pairing state.

Odd-Parity Spin-Triplet Superconductivity in Centrosymmetric Antiferromagnetic Metals

We propose a route to achieve odd-parity spin-triplet (OPST) superconductivity in metallic collinear antiferromagnets with inversion symmetry. Owing to the existence of hidden antiunitary symmetry, which we call the effective time-reversal symmetry (eTRS), the Fermi surfaces of ordinary antiferromagnetic metals are generally spin degenerate, and spin-singlet pairing is favored. However, by introducing a local inversion symmetry breaking perturbation that also breaks the eTRS, we can lift the degeneracy to obtain spin-polarized Fermi surfaces. In the weak-coupling limit, the spin-polarized Fermi surfaces constrain the electrons to form spin-triplet Cooper pairs with odd parity. Interestingly, all the odd-parity superconducting ground states we obtained host nontrivial band topologies manifested as chiral topological superconductors, second-order topological superconductors, and nodal superconductors. We propose that double perovskite oxides with collinear antiferromagnetic or ferrimagnetic ordering, such as SrLaVMoO_{6}, are promising candidate systems where our theoretical ideas can be applied to.

High-pressure phase diagrams of FeSe1-xTex: correlation between suppressed nematicity and enhanced superconductivity

The interplay among magnetism, electronic nematicity, and superconductivity is the key issue in strongly correlated materials including iron-based, cuprate, and heavy-fermion superconductors. Magnetic fluctuations have been widely discussed as a pairing mechanism of unconventional superconductivity, but recent theory predicts that quantum fluctuations of nematic order may also promote high-temperature superconductivity. This has been studied in FeSe_1−xS_x superconductors exhibiting nonmagnetic nematic and pressure-induced antiferromagnetic orders, but its abrupt suppression of superconductivity at the nematic end point leaves the nematic-fluctuation driven superconductivity unconfirmed. Here we report on systematic studies of high-pressure phase diagrams up to 8 GPa in high-quality single crystals of FeSe_1−xTe_x. When Te composition x(Te) becomes larger than 0.1, the high-pressure magnetic order disappears, whereas the pressure-induced superconducting dome near the nematic end point is continuously found up to x(Te) ≈ 0.5. In contrast to FeSe_1−xS_x, enhanced superconductivity in FeSe_1−xTe_x does not correlate with magnetism but with the suppression of nematicity, highlighting the paramount role of nonmagnetic nematic fluctuations for high-temperature superconductivity in this system.

Despite studies in FeSe_1−xS_x, it is yet unconfirmed whether nematic fluctuation can induce superconductivity. Here, the authors study single crystals of FeSe_1−xTe_x showing enhanced superconductivity upon suppression of nematicity.

Bogoliubov-Fermi Surfaces in Noncentrosymmetric Multicomponent Superconductors

We show that when the time reversal symmetry is broken in a multicomponent superconducting condensate without inversion symmetry the resulting Bogoliubov quasiparticles generically exhibit mini-Bogoliubov-Fermi (BF) surfaces, for small superconducting order parameter. The absence of inversion symmetry makes the BF surfaces stable with respect to weak perturbations. With sufficient increase of the order parameter, however, the Bogoliubov-Fermi surface may disappear through a Lifshitz transition, and the spectrum this way become fully gapped. Our demonstration is based on the computation of the effective Hamiltonian for the bands near the normal Fermi surface by the integration over high-energy states. Exceptions to the rule, and experimental consequences are briefly discussed.

On the Remarkable Superconductivity of FeSe and Its Close Cousins

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe1−xSex, intercalated FeSe materials, and monolayer FeSe and FeTe1−xSex on SrTiO3. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.