Volovik effect in the ±s-wave state for the iron-based superconductors

In-Plane Magnetic Penetration Depth in Sr_{2}RuO_{4}: Muon-Spin Rotation and Relaxation Study

We report on measurements of the in-plane magnetic penetration depth (λ_{ab}) in single crystals of Sr_{2}RuO_{4} down to ≃0.015  K by means of muon-spin rotation-relaxation. The linear temperature dependence of λ_{ab}^{-2} for T≲0.7  K suggests the presence of nodes in the superconducting gap. This statement is further substantiated by observation of the Volovik effect, i.e., the reduction of λ_{ab}^{-2} as a function of the applied magnetic field. The experimental zero-field and zero-temperature value of λ_{ab}=124(3)  nm agrees with λ_{ab}≃130  nm, calculated based on results of electronic structure measurements reported in A. Tamai et al. [High-resolution photoemission on Sr_{2}RuO_{4} reveals correlation-enhanced effective spin-orbit coupling and dominantly local self-energies, Phys. Rev. X 9, 021048 (2019)PRXHAE2160-330810.1103/PhysRevX.9.021048]. Our analysis reveals that a simple nodal superconducting energy gap, described by the lowest possible harmonic of a gap function, does not capture the dependence of λ_{ab}^{-2} on T, so the higher angular harmonics of the energy gap function need to be introduced.

Discovery of segmented Fermi surface induced by Cooper pair momentum

[Figure: see text].

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}.

Multiple gaps revealed by low temperature specific heat in the 1111-type CaFe0.88Co0.12AsF single crystals

Low-temperature specific heat (SH) is measured on the 1111-type CaFe_0.88 Co_0.12AsF single crystals under different magnetic fields. A clear SH jump with the height [Formula: see text] mJ mol^-1 K^-2 is observed at the superconducting transition temperature T _c . The electronic SH coefficient [Formula: see text] increases linearly with the field below 5 T and a kink is observed around 5 T, indicating a multi-gap feature in the present system. Such a sign is also reflected in the T _c   -  B data. A detailed analysis shows that this behavior can be interpreted in terms of a two-gap scenario with the ratio [Formula: see text]-4.5.

Superconducting properties of thes±-wave state: Fe-based superconductors

Although the pairing mechanism of Fe-based superconductors (FeSCs) has not yet been settled with consensus with regard to the pairing symmetry and the superconducting (SC) gap function, the vast majority of experiments support the existence of spin-singlet sign-changings-wave SC gaps on multi-bands (s±-wave state). This multi-bands±-wave state is a very unique gap stateper seand displays numerous unexpected novel SC properties, such as a strong reduction of the coherence peak, non-trivial impurity effects, nodal-gap-like nuclear magnetic resonance signals, various Volovik effects in the specific heat (SH) and thermal conductivity, and anomalous scaling behaviors with a SH jump and condensation energy versusTc, etc. In particular, many of these non-trivial SC properties can easily be mistaken as evidence for a nodal-gap state such as ad-wave gap. In this review, we provide detailed explanations of the theoretical principles for the various non-trivial SC properties of thes±-wave pairing state, and then critically compare the theoretical predictions with experiments on FeSCs. This will provide a pedagogical overview of to what extent we can coherently understand the wide range of different experiments on FeSCs within thes±-wave gap model.

Superconductivity and disorder effect in TlNi2Se(2-x)S(x) compounds

After our first discovery of multi-band superconductivity (SC) in the TlNi2Se2 crystal, we successfully grew a series of TlNi2Se(2-x)S(x) (0.0 ≤ x ≤ 2.0) single crystals. Measurements of resistivity, specific heat, and susceptibility were carried out on these crystals. Superconductivity with T(C) = 2.3 K was first observed in the TlNi2S2 crystal, which also appears to involve heavy electrons with an effective mass m* = 13-25 m(b), as inferred from the normal state electronic specific heat and the upper critical field, H(C2)(T). It was found that bulk SC and heavy-electron behavior is preserved in all the studied TlNi2Se(2-x)S(x) samples. In the mixed state, a novel change of the field dependence of the residual specific heat coefficient, γ(N)(H), occurs in TlNi2Se(2-x)S(x) with increasing S content. We also found that the T(C) value changes with the disorder degree induced by the partial substitution of S for Se, characterized by the residual resistivity ratio (RRR). Thus, the TlNi2Se(2-x)S(x) system provides a platform to study the effect of disorder on the multi-band SC.

Specific heat versus field for LiFe(1-x)Cu(x)As

LiFeAs is one of the new class of iron superconductors with a bulk [Formula: see text] in the 15-17 K range. We report on the specific heat characterization of single crystal material prepared by self-flux growth techniques with significantly improved properties, including a much decreased residual gamma, γ(r) (≡C/T as T → 0), in the superconducting state. Thus, in contrast to previous explanations of a finite γ(r) in LiFeAs being due to intrinsic states in the superconducting gap, the present work shows that such a finite residual γ in LiFeAs is instead a function of sample quality. Further, since LiFeAs has been characterized as nodeless with multiple superconducting gaps, we report here on its specific heat properties in zero and applied magnetic fields, to compare to similar results on nodal iron superconductors. For comparison, we also investigate LiFe(0.98)Cu(0.02)As, which has the reduced T(c) of ≈9 K and an H(c2) of 15 T. Interestingly, although presumably both LiFeAs and LiFe(0.98)Cu(0.02)As are nodeless, they clearly show a non-linear dependence of the electronic density of states (is proportional to specific heat γ) at the Fermi energy in the mixed state with the applied field, similar to the Volovik effect for nodal superconductors. However, rather than indicating nodal behavior, the satisfactory comparison with a recent theory for γ(H) for a superconductor with two isotropic gaps in the presence of impurities argues for nodeless behavior. Thus, in terms of specific heat in a magnetic field, LiFeAs can serve as the prototypical multiband, nodeless iron superconductor.