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The surprising discovery of superconductivity in layered iron-based materials, with transition temperatures climbing as high as 55 K, has led to thousands of publications on this subject over the past two years. Although there is general consensus on the unconventional nature of the Cooper pairing state of these systems, several central questions remain — including the role of magnetism, the nature of chemical and structural tuning, and the resultant pairing symmetry — and the search for universal properties and principles continues. Here we review the progress of research on iron-based superconducting materials, highlighting the main experimental benchmarks that have been reached so far and the important questions that remain to be conclusively answered. The surprising discovery of high-temperature superconductivity in a material containing a strong magnet—iron—has led to thousands of publications. By placing all the data in context, it becomes clear what we know and where we are headed.

In cuprate high-temperature superconductors, an antiferromagnetic Mott insulating state can be destabilized toward unconventional superconductivity by either hole or electron doping. In hole-doped (p-type) cuprates, a charge ordering (CO) instability competes with superconductivity inside the pseudogap state. We report resonant x-ray scattering measurements that demonstrate the presence of charge ordering in the n-type cuprate Nd2–xCexCuO4 near optimal doping. We find that the CO in Nd2–xCexCuO4 occurs with similar periodicity, and along the same direction, as in p-type cuprates. However, in contrast to the latter, the CO onset in Nd2–xCexCuO4 is higher than the pseudogap temperature, and is in the temperature range where antiferromagnetic fluctuations are first detected. Our discovery opens a parallel path to the study of CO and its relationship to antiferromagnetism and superconductivity.

In the physics of condensed matter, quantum critical phenomena and unconventional superconductivity are two major themes. In electron-doped cuprates, the low critical field (HC2) allows one to study the putative quantum critical point (QCP) at low temperature and to understand its connection to the long-standing problem of the origin of the high-TC superconductivity. Here we present measurements of the low-temperature normal-state thermopower (S) of the electron-doped cuprate superconductor La2−x Ce x CuO₄ (LCCO) from x = 0.11–0.19. We observe quantum critical S/T versus ln(1/T) behavior over an unexpectedly wide doping range x = 0.15–0.17 above the QCP (x = 0.14), with a slope that scales monotonically with the superconducting transition temperature (TC with H = 0). The presence of quantum criticality over a wide doping range provides a window on the criticality. The thermopower behavior also suggests that the critical fluctuations are linked with TC. Above the superconductivity dome, at x = 0.19, a conventional Fermi-liquid S ∝ T behavior is found for T ≤ 40 K.

The occurrence of electrons and holes in n-type copper oxides has been achieved by chemical doping, pressure, and/or deoxygenation. However, the observed electronic properties are blurred by the concomitant effects such as change of lattice structure, disorder, etc. Here, we report on successful tuning the electronic band structure of n-type Pr 2 − x Ce x CuO 4 (x = 0.15) ultrathin films, via the electric double layer transistor technique. Abnormal transport properties, such as multiple sign reversals of Hall resistivity in normal and mixed states, have been revealed within an electrostatic field in range of −2 V to + 2 V, as well as varying the temperature and magnetic field. In the mixed state, the intrinsic anomalous Hall conductivity invokes the contribution of both electron and hole-bands as well as the energy dependent density of states near the Fermi level. The two-band model can also describe the normal state transport properties well, whereas the carrier concentrations of electrons and holes are always enhanced or depressed simultaneously in electric fields. This is in contrast to the scenario of Fermi surface reconstruction by antiferromagnetism, where an anti-correlation is commonly expected.

In the high-temperature cuprate superconductors, the pervasiveness of anomalous electronic transport properties suggests that violation of conventional Fermi liquid behavior is closely tied to superconductivity. In other classes of unconventional superconductors, atypical transport is well correlated with proximity to a quantum critical point, but the relative importance of quantum criticality in the cuprates remains uncertain. Here, we identify quantum critical scaling in the electron-doped cuprate material La2-xCexCuO4 with a line of quantum critical points that surrounds the superconducting phase as a function of magnetic field and charge doping. This zero-temperature phase boundary, which delineates a metallic Fermi liquid regime from an extended non-Fermi liquid ground state, closely follows the upper critical field of the overdoped superconducting phase and gives rise to an expanse of distinct non-Fermi liquid behavior at finite temperatures. Together with signatures of two distinct flavors of quantum fluctuations, these facts suggest that quantum criticality plays a significant role in shaping the anomalous properties of the cuprate phase diagram.

The proximity effect at the interface between a topological insulator and a superconductor is predicted to give rise to chiral topological superconductivity and Majorana fermion excitations. In most topological insulators studied to date, however, the conducting bulk states have overwhelmed the transport properties and precluded the investigation of the interplay of the topological surface state and Cooper pairs. Here, we demonstrate the superconducting proximity effect in the surface state of SmB6 thin films which display bulk insulation at low temperatures. The Fermi velocity in the surface state deduced from the proximity effect is found to be as large as 105m/s , in good agreement with the value obtained from a separate transport measurement. We show that high transparency between the topological insulator and a superconductor is crucial for the proximity effect. The finding here opens the door to investigation of exotic quantum phenomena using all-thin-film multilayers with high-transparency interfaces.

In 1928, Dirac proposed a wave equation to describe relativistic electrons 1 . Shortly afterwards, Klein solved a simple potential step problem for the Dirac equation and encountered an apparent paradox: the potential barrier becomes transparent when its height is larger than the electron energy. For massless particles, backscattering is completely forbidden in Klein tunnelling, leading to perfect transmission through any potential barrier 2 , 3 . The recent advent of condensed-matter systems with Dirac-like excitations, such as graphene and topological insulators, has opened up the possibility of observing Klein tunnelling experimentally 4 – 6 . In the surface states of topological insulators, fermions are bound by spin–momentum locking and are thus immune from backscattering, which is prohibited by time-reversal symmetry. Here we report the observation of perfect Andreev reflection in point-contact spectroscopy—a clear signature of Klein tunnelling and a manifestation of the underlying ‘relativistic’ physics of a proximity-induced superconducting state in a topological Kondo insulator. Our findings shed light on a previously overlooked aspect of topological superconductivity and can serve as the basis for a unique family of spintronic and superconducting devices, the interface transport phenomena of which are completely governed by their helical topological states. Perfect transmission of electrons through a finite potential barrier between a normal metal and a topological superconducting state is demonstrated, as evidenced by an exact doubling of conductance in point contact measurements.

As an exemplary Kondo insulator, SmB6 has been studied for several decades. However, direct evidence for the development of the Kondo coherent state and for the evolution of the electronic structure in the material has not been obtained due to the compound’s rather complicated electronic and thermal transport behavior. Recently, these open questions have attracted increasing attention as the emergence of a time-reversal-invariant topological surface state in the Kondo insulator has been suggested. Here, we use point-contact spectroscopy to reveal the temperature dependence of the electronic states in SmB6 . We demonstrate that SmB6 is a model Kondo insulator: Below 100 K, the conductance spectra reflect the Kondo hybridization of Sm ions, but, below about 30K , signatures of inter-ion correlation effects clearly emerge. Moreover, we find evidence that the low-temperature insulating state of this exemplary Kondo-lattice compound harbors conduction states on the surface, in support of predictions of nontrivial topology in Kondo insulators.

The electron-doped material Nd$_{2-x}$Ce$_x$CuO$_4$ becomes superconducting with a Ce$^{4+}$ composition around 0.16, but only after removal of a minuscule amount of extraneous oxygen. This enigmatic behavior was addressed here. A small fraction of copper in the CuO$_2$ planes of Nd$_{2-x}$Ce$_x$CuO$_4$ was substituted by cobalt-57, which serves as a microprobe of the chemical environment. Deoxygenation brought about little change in the Mossbauer spectra both above and below the optimal superconducting concentration; however, for x = 0.16 a change was observed. In the latter, a major fraction of the magnetically split, five-coordinate species showed itself as a paramagnetically relaxed doublet upon deoxygenation. The abundance of the paramagnetically relaxed species corresponds closely to the diamagnetic volume fraction and thus provides a microscopic signature of the superconducting phase.

This paper is dedicated to the memory of Professor K. Alex M\"uller. I present a few remarks about my interactions with Alex over the years. Then I present a very brief summary of recent transport studies of the strange metal normal-state in the high-temperature copper oxide superconductors, a subject of great interest to Alex.