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Register a new userAnomalous scaling of the specific-heat jump $Delta C$ vs. $T_c$ in the Fe-based superconductors: the $pm$S-wave pairing state model
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The strong power law behavior of the specific heat jump $Delta C$ vs. $T_c$ ($Delta C/T_c sim T_c ^{alpha}, alphaapprox 2$), first observed by Budko, Ni, and Canfield (BNC)[1], has been confirmed with several families of the Fe-based superconducting compounds with a series of doping. We show here that this anomalous non-BCS behavior is an intrinsic property of the multiband superconducting state paired by a dominant interband interaction ($V_{inter} > V_{intra}$) reflecting the relation $frac{Delta_h}{Delta_e} sim sqrt{frac{N_e}{N_h}}$ near $T_c$, as in the $pm$S-wave pairing state. Then this $Delta C$ vs. $T_c$ relation can continuously change from the perfect BNC scaling to a considerable deviation at lower $T_c$ region with a moderate variation of the impurity scattering rate.
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Although the pairing mechanism of the Fe-based superconductors (FeSCs) has not yet been settled with a consensus, as to the pairing symmetry and the superconducting (SC) gap function, the abundant majority of experiments are supporting for the spin-singlet sign-changing s-wave SC gaps on multibands ($s^{pm}$-wave state). This multiband $s^{pm}$-wave state is a very unique gap state {it per se} and 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 (NMR) signals, various Volovik effects in the specific heat (SH) and thermal conductivity, and anomalous scaling behaviors with the SH jump and the condensation energy vs. $T_c$, etc. In particular, many of these non-trivial SC properties can be easily mistaken as evidence for a nodal gap state such as a d-wave gap. In this review, we provide detailed explanations of theoretical principles for the various non-trivial SC properties of the $s^{pm}$-wave pairing state, and then critically compare the theoretical predictions with the experiments of the FeSCs. This will provide a pedagogical overview of how much we can coherently understand the wide range of different experiments of the FeSCs within the $s^{pm}$-wave gap model.
We report specific heat capacity measurements on a LiFeAs single crystal at temperatures down to 400 mK and magnetic fields up to 9 Tesla. A small specific heat jump at Tc and finite residual density of states at T=0 K in the superconducting (SC) state indicate that there are strong unitary scatterers that lead to states within the SC gap. A sub-linear magnetic field dependence of the Sommerfeld coefficient gamma(H) at T=0 K is equally well fitted by both a nodal d-wave gap as well as a sign changing multiband pm s-wave gap. When impurity effects are taken into account, however, the linear temperature dependence of the electronic specific heat C_{el}/T at low temperatures argues against a nodal d-wave superconducting gap. We conclude that the SC state of LiFeAs is most compatible with the multiband pm s-wave SC state with the gap values Delta_{small}=0.46 Delta_{large}.
The low temperature specific heat C(B,T) of an YBa2Cu3O7.00 single crystal is measured from 1.2 to 10 K in magnetic fields up to 14 T. The anisotropic component Caniso(T,B)=C(T,B//c)-C(T,B//ab) is a pure vortex quantity obtained directly from experiment. It follows a scaling relation predicted recently for line nodes characteristic of d-wave vortices. Our experimental field and temperature range corresponds to a crossover region where the limit Caniso(T,B)is proportional to T*sqrt(B) does not strictly apply. The variation of the entropy caused by the magnetic field at low T is thermodynamically compatible with measurements near Tc.
Recently it was discovered that the jump in the specific heat at the superconducting transition in pnictide superconductors is proportional to the superconducting transition temperature to the third power, with the superconducting transition temperature varying from 2 to 25 Kelvin including underdoped and overdoped cases. Relying on standard scaling notions for the thermodynamics of strongly interacting quantum critical states, it is pointed out that this behavior is consistent with a normal state that is a quantum critical metal undergoing a pairing instability.
We present a systematic study of the electronic specific heat jump ($Delta C_{rm el}$) at the superconducting transition temperature $T_c$ of K$_{1-x}$Na$_x$Fe$_2$As$_2$. Both $T_c$ and $Delta C_{rm el}$ monotonously decrease with increasing $x$. The specific heat jump scales approximately with a power-law, $Delta C_{rm el} propto T_c^{beta}$, with $beta approx 2$ determined by the impurity scattering rate, in contrast to most iron-pnictide superconductors, where the remarkable Budko-Ni-Canfield (BNC) scaling $Delta C_{rm el} propto T^3$ has been found. Both the $T$ dependence of $C_{rm el}(T)$ in the superconducting state and the nearly quadratic scaling of $Delta C_{rm el}$ at $T_c$ are well described by the Eliashberg-theory for a two-band $d$-wave superconductor with weak pair-breaking due to nonmagnetic impurities. The disorder induced by the Na substitution significantly suppresses the small gaps leading to gapless states in the slightly disordered superconductor, which results in a large observed residual Sommerfeld coefficient in the superconducting state for $x > 0$.
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