Sign-changing Order Parameter Research Articles

Atomic-Scale Andreev Probe of Unconventional Superconductivity.

Recent emergence of low-dimensional unconventional superconductors and their exotic interface properties calls for new approaches to probe the pairing symmetry, a fundamental and frequently elusive property of the superconducting condensate. Here, we introduce the unique capability of tunneling Andreev reflection (TAR) to probe unconventional pairing symmetry, utilizing the sensitivity of this technique to specific Andreev reflections. Specifically, suppression of the lowest-order Andreev reflection due to quantum interference but emergence of the higher-order Andreev processes provides direct evidence of the sign-changing order parameter in the paradigmatic FeSe superconductor. TAR spectroscopy also reveals two superconducting gaps, points to a possibility of a nodal gap structure, and directly confirms that superconductivity is locally suppressed along the nematic twin boundary, with preferential and near-complete suppression of the larger energy gap. Our findings therefore enable new, atomic-scale insight into microscopic, inhomogeneous, and interfacial properties of emerging quantum materials.

Hyperbolic Fringe Signal for Twin Impurity Quasiparticle Interference.

We study the quasiparticle interference (QPI) pattern emanating from a pair of adjacent impurities on the surface of a gapped superconductor (SC). We find that hyperbolic fringes (HFs) in the QPI signal can appear due to the loop contribution of the two-impurity scattering, where the locations of the two impurities are the hyperbolic focus points. For a single pocket Fermiology, a HF pattern signals chiral SC order for nonmagnetic impurities and requires magnetic impurities for a nonchiral SC. For a multipocket scenario, a sign-changing order parameter such as an s_{±} wave likewise yields a HF signature. We discuss twin impurity QPI as a new tool to complement the analysis of superconducting order from local spectroscopy.

Charge correlations suppress unconventional pairing in the Holstein model

In a recent work by Schrodi $\textit{et al}$. [Phys. Rev. B. $\textbf{104}$, L140506 (2021)], the authors find an unconventional superconducting state with a sign-changing order parameter using the Migdal-Eliashberg theory, including the first vertex correction. This unconventional solution arises despite using an isotropic bare electron-phonon coupling in the Hamiltonian. We examine this claim using hybrid quantum Monte Carlo for a single-band Holstein model with a cuprate-like noninteracting band structure and identical parameters to Schrodi $\textit{et al}$.. Our Monte Carlo results for these parameters suggest that unconventional pairing correlations do not exceed their noninteracting values at any carrier concentration we have checked. Instead, strong charge-density-wave correlations persist at the lowest accessible temperatures for dilute and nearly half-filled bands. Lastly, we present arguments for how vertex-corrected Migdal-Eliashberg calculation schemes can lead to uncontrolled results in the presence of Fermi surface nesting.

Unconventional Bulk Superconductivity in YFe_{2}Ge_{2} Single Crystals.

Sharp superconducting transition anomalies observed in a new generation of single crystals establish that bulk superconductivity is intrinsic to high purity YFe_{2}Ge_{2}. Low temperature heat capacity measurements suggest a disorder and field dependent residual Sommerfeld coefficient, consistent with disorder-induced in-gap states as expected for a sign-changing order parameter. The sevenfold reduction in disorder scattering in these new crystals to residual resistivities ≃0.45 μΩ cm was achieved using a new liquid transport growth technique, paving the way for multiprobe experiments investigating the normal and superconducting states of YFe_{2}Ge_{2}.

Nature of the spin resonance mode in CeCoIn5

Spin-fluctuation-mediated unconventional superconductivity can emerge at the border of magnetism, featuring a superconducting order parameter that changes sign in momentum space. Detection of such a sign-change is experimentally challenging, since most probes are not phase-sensitive. The observation of a spin resonance mode (SRM) from inelastic neutron scattering is often seen as strong phase-sensitive evidence for a sign-changing superconducting order parameter, by assuming the SRM is a spin-excitonic bound state. Here we show that for the heavy fermion superconductor CeCoIn5, its SRM defies expectations for a spin-excitonic bound state, and is not a manifestation of sign-changing superconductivity. Instead, the SRM in CeCoIn5 likely arises from a reduction of damping to a magnon-like mode in the superconducting state, due to its proximity to magnetic quantum criticality. Our findings emphasize the need for more stringent tests of whether SRMs are spin-excitonic, when using their presence to evidence sign-changing superconductivity.

Sign changing pairing in single layer FeSe/SrTiO3 revealed by nonmagnetic impurity bound states

The discovery of high-temperature superconductivity in single layer FeSe epitaxially grown on SrTiO3(001) substrates has instigated extensive debate over whether its pairing symmetry is conventional sign-preserving s-wave or unconventional sign-changing. Here, we probe the pairing state for single layer FeSe/SrTiO3 grown by molecular beam epitaxy using scanning tunneling microscopy/spectroscopy. We observe robust in-gap bound states induced by non-magnetic Fe-vacancy defects within the Fe-plane, which exhibit strong spatial electron-hole asymmetry with two-fold symmetry in hole states and four-fold in electron states. The bound states exhibit no energy shift or splitting under an applied magnetic field, consistent with a sign-changing order parameter. This is further confirmed by defect bound state quasiparticle interference that shows a sign-changing behavior with a pair of corresponding peaks at the positive and negative energies near the impurity bound states. Our findings provide unambiguous evidence for a sign-changing pairing symmetry for single layer FeSe/SrTiO3.

Exotic pairing state in quasicrystalline superconductors under a magnetic field

We theoretically study the effect of a magnetic field on quasicrystalline superconductors, by modelling them as the attractive Hubbard model on the Penrose-tiling structure. We find that at low temperatures and under a high magnetic field there appears an exotic superconducting state with the order parameter changing its sign in real space. We discuss the state in comparison with the Fulde-Ferrell-Larkin-Ovchinnikov state proposed many years ago for periodic systems, clarifying commonalities and differences. It is remarkable that, even in the absence of periodicity, the electronic system finds a way to keep a coherent superconducting state with a spatially sign-changing order parameter compatible with the underlying quasiperiodic structure.

Quasiparticle interference and symmetry of superconducting order parameter in strongly electron-doped iron-based superconductors

Motivated by recent experimental reports of significant spin–orbit coupling (SOC) and a sign-changing order-parameter in the Li1−xFex(OHFe)1−yZnySe superconductor with only electron pockets present, we study the possible Cooper-pairing symmetries and their quasiparticle interference (QPI) signatures. We find that each of the resulting states—s-wave, d-wave and helical p-wave—can have a fully gapped density of states consistent with angle-resolved photoemission spectroscopy experiments and, due to SOC, are a mixture of spin singlet and triplet components leading to intra- and inter-band features in the QPI signal. Analyzing predicted QPI patterns we find that only the spin-triplet dominated even parity A1g (s-wave) and B2g (d-wave) pairing states are consistent with the experimental data. Additionally, we show that these states can indeed be realized in a microscopic model with atomic-like interactions and study their possible signatures in spin-resolved STM experiments.

In-gap bound states induced by a single nonmagnetic impurity in sign-preserving s -wave superconductors with incipient bands

We have investigated the in-gap bound states (IGBS) induced by a single nonmagnetic impurity in multiband superconductors with incipient bands. Contrary to the naive expectation, we found that even if the superconducting (SC) order parameter is a sign-preserving $s$ wave on the Fermi surfaces, the incipient bands may still affect the appearance and locations of the IGBS, although the gap between the incipient bands and the Fermi level is much larger than the SC gap. Therefore in scanning tunneling microscopy experiments, the IGBS induced by a single nonmagnetic impurity are not the definitive evidence for the sign-changing order parameter on the Fermi surfaces. Our findings have special implications for the experimental determination of the pairing symmetry in the FeSe-based superconductors.

Induced unconventional superconductivity on the surface states of Bi2Te3 topological insulator

Topological superconductivity is central to a variety of novel phenomena involving the interplay between topologically ordered phases and broken-symmetry states. The key ingredient is an unconventional order parameter, with an orbital component containing a chiral px + ipy wave term. Here we present phase-sensitive measurements, based on the quantum interference in nanoscale Josephson junctions, realized by using Bi2Te3 topological insulator. We demonstrate that the induced superconductivity is unconventional and consistent with a sign-changing order parameter, such as a chiral px + ipy component. The magnetic field pattern of the junctions shows a dip at zero externally applied magnetic field, which is an incontrovertible signature of the simultaneous existence of 0 and π coupling within the junction, inherent to a non trivial order parameter phase. The nano-textured morphology of the Bi2Te3 flakes, and the dramatic role played by thermal strain are the surprising key factors for the display of an unconventional induced order parameter.

Unconventional superconductivity and interaction induced Fermi surface reconstruction in the two-dimensional Edwards model.

We study the competition between unconventional superconducting pairing and charge density wave (CDW) formation for the two-dimensional Edwards Hamiltonian at half filling, a very general two-dimensional transport model in which fermionic charge carriers couple to a correlated background medium. Using the projective renormalization method we find that a strong renormalization of the original fermionic band causes a new hole-like Fermi surface to emerge near the center of the Brillouin zone, before it eventually gives rise to the formation of a charge density wave. On the new, disconnected parts of the Fermi surface superconductivity is induced with a sign-changing order parameter. We discuss these findings in the light of recent experiments on iron-based oxypnictide superconductors.

Using controlled disorder to distinguishs±ands++gap structure in Fe-based superconductors

We reconsider the effect of disorder on the properties of a superconductor characterized by a sign-changing order parameter appropriate for Fe-based materials. Within a simple two band model, we calculate simultaneously $T_c$, the change in residual resistivity $\Delta \rho_0$, and the zero-energy density of states, and show how these results change for various types of gap structures and assumptions regarding the impurity scattering. The rate of $T_c$ suppression is shown to vary dramatically according to details of the impurity model considered. We search therefore for a practical, experimentally oriented signature of a gap of the $s_\pm$ type, and propose that observation of particular evolution of the penetration depth, nuclear magnetic resonance relaxation rate, or thermal conductivity temperature dependence with disorder would suffice.

Universal pair-breaking in transition-metal-substituted iron-pnictide superconductors

The experimental transport scattering rate was determined for a wide range of optimally doped transition-metal-substituted FeAs-based compounds with the ThCr${}_{2}$Si${}_{2}$ (122) crystal structure. The maximum transition temperature ${T}_{c}$ for several Ba-, Sr-, and Ca-based 122 systems follows a universal rate of suppression with increasing scattering rate indicative of a common pair-breaking mechanism. Extraction of standard pair-breaking parameters puts a limit of $\ensuremath{\sim}$26 K on the maximum ${T}_{c}$ for all transition-metal-substituted 122 systems, in agreement with experimental observations, and sets a critical scattering rate of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ s${}^{\ensuremath{-}1}$ for the suppression of the superconducting phase. The observed critical scattering rate is much weaker than that expected for a sign-changing order parameter with strong interband scattering, providing important constraints on the nature of the superconducting gap in the 122 family of iron-based superconductors.

Weak Spin Fluctuation with Finite Wave Vector and Superconducting Gap Symmetry in KxFe2-ySe2:77Se Nuclear Magnetic Resonance

We report $^{77}$Se-nuclear magnetic resonance (NMR) results down to sufficiently low temperatures under magnetic fields parallel to both the $ab$-plane and the c-axis in a paramagnetic/superconducting (PM/SC) phase of K$_x$Fe$_{2-y}$Se$_2$. The observation of anisotropy in the orbital part of the Knight shift results in the anisotropy of its spin part increasing on approaching the transition temperature. The anisotropy of the Korringa relation suggests the presence of the weak spin fluctuations with a finite wave vector $\bm{q}$, which induce the magnetic fluctuations along the ab-plane at the Se site. Such fluctuations do not correspond to the stripe $(\pi,0)$ correlation of the Fe moment observed in many Fe-based superconductors, and are not contradictory to weak $(\pi,\pi)$ correlations. The nuclear spin-lattice relaxation rate $1/T_1$ shows a field-independent $T_1T \sim const.$ behavior at low temperatures for $H \parallel ab$, which is attributed to the nonzero density of states at the Fermi level and can be explained by the sign-changing order parameter even for nodeless gaps. The temperature dependence of $1/T_1$ is reproduced well by nodeless models with two isotropic gaps or a single anisotropic gap. The obtained gap magnitude in the isotropic two-gap model is comparable to those obtained in the angle-resolved photoemission spectroscopy experiments.

One-Sign Order Parameter in Iron Based Superconductor

The onset of superconductivity at the transition temperature is marked by the onset of order, which is characterized by an energy gap. Most models of the iron-based superconductors find a sign-changing (s±) order parameter [1–6], with the physical implication that pairing is driven by spin fluctuations. Recent work, however, has indicated that LiFeAs has a simple isotropic order parameter [7–9] and spin fluctuations are not necessary [7,10], contrary to the models [1–6]. The strength of the spin fluctuations has been controversial [11,12], meaning that the mechanism of superconductivity cannot as yet be determined. We report the momentum dependence of the superconducting energy gap, where we find an anisotropy that rules out coupling through spin fluctuations and the sign change. The results instead suggest that orbital fluctuations assisted by phonons [13,14] are the best explanation for superconductivity.

Magnetic Resonant Mode in the Low-Energy Spin-Excitation Spectrum of SuperconductingRb2Fe4Se5Single Crystals

We have studied the low-energy spin-excitation spectrum of the single-crystalline Rb(2)Fe(4)Se(5) superconductor (T(c)=32 K) by means of inelastic neutron scattering. In the superconducting state, we observe a magnetic resonant mode centered at an energy of ℏω(res)=14 meV and at the (0.5 0.25 0.5) wave vector (unfolded Fe-sublattice notation), which differs from the ones characterizing magnetic resonant modes in other iron-based superconductors. Our finding suggests that the 245-iron selenides are unconventional superconductors with a sign-changing order parameter, in which bulk superconductivity coexists with the √5×√5 magnetic superstructure. The estimated ratios of ℏω(res)/k(B)T(c)≈5.1±0.4 and ℏω(res)/2Δ≈0.7±0.1, where Δ is the superconducting gap, indicate moderate pairing strength in this compound, similar to that in optimally doped 1111 and 122 pnictides.

Effect of Mn impurities on the superconductivity inNaxCoO2∙yH2O

To shed light on the symmetry of the superconducting order parameter in ${\mathrm{Na}}_{x}\mathrm{Co}{\mathrm{O}}_{2}∙y{\mathrm{H}}_{2}\mathrm{O}$, the Mn doping effects are studied. X-ray absorption spectroscopy verifies that the doped Mn impurities occupy the Co sites and are with a valance close to $+4$. Impurity scattering by Mn is in the unitary limit that, however, does not lead to strong ${T}_{c}$ suppression. This absence of the strong impurity effects on ${T}_{c}$ is inconsistent with the simple picture of a sign-changing order parameter. Coexistence of the $s$-wave superconducting order parameter and the nodal one is proposed to reconcile all the existing experiments and has been implied by the specific heat experiments.