When a second-order magnetic phase transition is tuned to zero temperature by a non-thermal parameter, quantum fluctuations are critically enhanced, often leading to the emergence of unconventional superconductivity. In these `quantum critical superc
onductors it has been widely reported that the normal-state properties above the superconducting transition temperature $T_c$ often exhibit anomalous non-Fermi liquid behaviors and enhanced electron correlations. However, the effect of these strong critical fluctuations on the superconducting condensate below $T_c$ is less well established. Here we report measurements of the magnetic penetration depth in heavy-fermion, iron-pnictide, and organic superconductors located close to antiferromagnetic quantum critical points showing that the superfluid density in these nodal superconductors universally exhibit, unlike the expected $T$-linear dependence, an anomalous 3/2 power-law temperature dependence over a wide temperature range. We propose that this non-integer power-law can be explained if a strong renormalization of effective Fermi velocity due to quantum fluctuations occurs only for momenta $bm{k}$ close to the nodes in the superconducting energy gap $Delta(bm{k})$. We suggest that such `nodal criticality may have an impact on low-energy properties of quantum critical superconductors.
Scanning tunneling spectroscopy is used to study the real-space local density of states (LDOS) of a two-dimensional electron system in magnetic field, in particular within higher Landau levels (LL). By Fourier transforming the LDOS, we find a set of
n radial minima at fixed momenta for the nth LL. The momenta of the minima depend only on the inverse magnetic length. By comparison with analytical theory and numerical simulations, we attribute the minima to the nodes of the quantum cyclotron orbits, which decouple in Fourier representation from the random guiding center motion due to the disorder. This robustness of the nodal structure of LL wave functions should be viewed as a key property of quantum Hall states.
The normal-state charge transport is studied systematically in high-quality single crystals of BaFe$_2$(As$_{1-x}$P$_x$)$_2$ ($0 leq x leq 0.71$). By substituting isovalent P for As, the spin-density-wave (SDW) state is suppressed and the dome-shaped
superconducting phase ($T_c lesssim 31$ K) appears. Near the SDW end point ($xapprox0.3$), we observe striking linear temperature ($T$) dependence of resistivity in a wide $T$-range, and remarkable low-$T$ enhancement of Hall coefficient magnitude from the carrier number estimates. We also find that the magnetoresistance apparently violates the Kohlers rule and is well scaled by the Hall angle $Theta_H$ as $Deltarho_{xx}/rho_{xx} propto tan^2Theta_H$. These non-Fermi liquid transport anomalies cannot be attributed to the simple multiband effects. These results capture universal features of correlated electron systems in the presence of strong antiferromagnetic fluctuations.
We report high-sensitivity microwave measurements of the in-plane penetration depth $lambda_{ab}$ and quasiparticle scattering rate $1/tau$ in several single crystals of hole-doped Fe-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$ ($xapprox 0.55$).
While power-law temperature dependence of $lambda_{ab}$ with the power $sim 2$ is found in crystals with large $1/tau$, we observe exponential temperature dependence of superfluid density consistent with the existence of fully opened two gaps in the cleanest crystal we studied. The difference may be a consequence of different level of disorder inherent in the crystals. We also find a linear relation between the low-temperature scattering rate and the density of quasiparticles, which shows a clear contrast to the case of d-wave cuprate superconductors with nodes in the gap. These results demonstrate intrinsically nodeless order parameters in the Fe-arsenides.
To elucidate the underlying nature of the hidden order (HO) state in heavy-fermion compound URu2Si2, we measure electrical transport properties of ultraclean crystals in a high field/low temperature regime. Unlike previous studies, the present system
with much less impurity scattering resolves a distinct anomaly of the Hall resistivity at H*=22.5 T well below the destruction field of the HO phase ~36 T. In addition, a novel quantum oscillation appears above a magnetic field slightly below H*. These results indicate an abrupt reconstruction of the Fermi surface, which implies a possible phase transition well within the HO phase caused by a band-dependent destruction of the HO parameter. The present results definitely indicate that the HO transition should be described by an itinerant electron picture.
Using scanning tunneling spectroscopy in ultra-high vacuum at low temperature (T = 0.3 K) and high magnetic fields (B < 12 T), we directly probe electronic wave functions across an integer quantum Hall transition. In accordance with theoretical predi
ctions, we observe the evolution from localized drift states in the insulating phases to branched extended drift states at the quantum critical point. The observed microscopic behavior close to the extended state indicates points of localized quantum tunneling, which are considered to be decisive for a quantitative description of the transition.
