The low temperature specific heat of the superconductor MgCNi$_3$ and a non-superconductor MgC$_{0.85}$Ni$_3$ is investigated in detail. An additional contribution is observed from the data of MgCNi$_3$ but absent in MgC$_{0.85}$Ni$_3$, which is demonstrated to be insensitive to the applied magnetic field even up to 12 Tesla. A detailed discussion on its origin is then presented. By subtracting this additional contribution, the zero field specific heat of MgCNi$_3$ can be well described by the BCS theory with the gap ratio ($Delta/k_BT_c$) determined by the previous tunneling measurements. The conventional s-wave pairing state is further proved by the magnetic field dependence of the specific heat at low temperatures and the behavior of the upper critical field.
We have measured magnetization at high pressure in the uranium ferromagnetic superconductor UGe$_2$ and analyzed the magnetic data using Takahashis spin fluctuation theory. There is a peak in the pressure dependence of the width of the spin fluctuation spectrum in the energy space $T_0$ at $P_x$, the phase boundary of FM1 and FM2 where the superconducting transition temperature $T_{sc}$ is highest. This suggests a clear correlation between the superconductivity and pressure-enhanced magnetic fluctuations developed at $P_x$. The pressure effect on $T_{Curie}/T_0$, where $T_{Curie}$ is the Curie temperature, suggests that the less itinerant ferromagnetic state FM2 is changed to a more itinerant one FM1 across $P_x$. Peculiar features in relations between $T_0$ and $T_{sc}$ in uranium ferromagnetic superconductors UGe$_2$, URhGe and UCoGe are discussed in comparison with those in high-$T_c$ cuprate and heavy fermion superconductors.
The newly discovered iron pnictide superconductors apparently present an unusual case of interband-channel pairing superconductivity. Here we show that, in the limit where the pairing occurs within the interband channel, several surprising effects occur quite naturally and generally: different density-of-states on the two bands lead to several unusual properties, including a gap ratio which behaves inversely to the ratio of density-of-states; the weak-coupling limit of the Eliashberg and the BCS theory, commonly taken as equivalent, in fact predict qualitatively different dependence of the $Delta_{1}/Delta_{2}$ and $Delta/T_{c}$ ratios on coupling constants. We show analytically that these effects follow directly from the interband character of superconductivity. Our results show that in the interband-only pairing model the maximal gap ratio is $sqrt{N_{2}/N_{1}}$ as strong-coupling effects act only to reduce this ratio. This suggests that if the large experimentally reported gap ratios (up to a factor 2) are correct, the pairing mechanism must include more intraband interaction than is usually assumed.
Elucidating the microscopic origin of nematic order in iron-based superconducting materials is important because the interactions that drive nematic order may also mediate the Cooper pairing. Nematic order breaks fourfold rotational symmetry in the iron plane, which is believed to be driven by either orbital or spin degrees of freedom. However, as the nematic phase often develops at a temperature just above or coincides with a stripe magnetic phase transition, experimentally determining the dominant driving force of nematic order is difficult. Here, we use neutron scattering to study structurally the simplest iron-based superconductor FeSe, which displays a nematic (orthorhombic) phase transition at $T_s=90$ K, but does not order antiferromagnetically. Our data reveal substantial stripe spin fluctuations, which are coupled with orthorhombicity and are enhanced abruptly on cooling to below $T_s$. Moreover, a sharp spin resonance develops in the superconducting state, whose energy (~4 meV) is consistent with an electron boson coupling mode revealed by scanning tunneling spectroscopy, thereby suggesting a spin fluctuation-mediated sign-changing pairing symmetry. By normalizing the dynamic susceptibility into absolute units, we show that the magnetic spectral weight in FeSe is comparable to that of the iron arsenides. Our findings support recent theoretical proposals that both nematicity and superconductivity are driven by spin fluctuations.
The charge density wave in the high-temperature superconductor YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) is now known to have two different ordering tendencies differentiated by their $c$-axis correlations. These correspond to ferro- (F-CDW) and antiferro- (AF-CDW) couplings between CDW in neighbouring CuO$_2$ bilayers. This discovery has prompted a number of fundamental questions. For example, how does superconductivity adjust to two competing orders and are either of these orders responsible for the electronic reconstruction? Here we use high-energy x-ray diffraction to study YBa$_2$Cu$_3$O$_{6.67}$ as a function of magnetic field and temperature. We show that regions of the sample with F-CDW correlations suppress superconductivity more strongly than those with AF-CDW correlations. This implies that an inhomogeneous superconducting state exists, in which some regions show a weak or fragile form of superconductivity. By comparison of F-CDW and AF-CDW correlation lengths, it is furthermore concluded that F-CDW ordering is sufficiently long-range to modify the electronic structure. Our study thus suggests that F-CDW correlations have an important impact on superconducting and normal state properties of underdoped YBCO.
In this paper we report the impact of uniaxial strain $varepsilon$ applied along the crystalline $a$ axis on the newly discovered kagome superconductor CsV$_3$Sb$_5$. At ambient conditions, CsV$_3$Sb$_5$ shows a charge-density wave (CDW) transition at $T_{rm CDW}=94.5$ K and superconducts below $T_C = 3.34$ K. In our study, when the uniaxial strain $varepsilon$ is varied from $-0.90%$ to $0.90%$, $T_C$ monotonically increases by $sim 33%$ from 3.0 K to 4.0 K, giving rise to the empirical relation $T_C (varepsilon)=3.4+0.56varepsilon+0.12varepsilon^2$. On the other hand, for $varepsilon$ changing from $-0.76%$ to $1.26%$, $T_{rm CDW}$ decreases monotonically by $sim 10%$ from 97.5 K to 87.5 K with $T_{rm CDW}(varepsilon)=94.5-4.72varepsilon-0.60varepsilon^2$. The opposite response of $T_C$ and $T_{rm CDW}$ to the uniaxial strain suggests strong competition between these two orders. Comparison with hydrostatic pressure measurements indicate that it is the change in the $c$-axis that is responsible for these behaviors of the CDW and superconducting transitions, and that the explicit breaking of the sixfold rotational symmetry by strain has a negligible effect. Combined with our first-principles calculations and phenomenological analysis, we conclude that the enhancement in $T_C$ with decreasing $c$ is caused primarily by the suppression of $T_{rm CDW}$, rather than strain-induced modifications in the bare superconducting parameters. We propose that the sensitivity of $T_{rm CDW}$ with respect to the changes in the $c$-axis arises from the impact of the latter on the trilinear coupling between the $M_1^+$ and $L_2^-$ phonon modes associated with the CDW. Overall, our work reveals that the $c$-axis lattice parameter, which can be controlled by both pressure and uniaxial strain, is a powerful tuning knob for the phase diagram of CsV$_3$Sb$_5$.