Physical Review X

Iron-based high-temperature superconductors, the discovery of which began only in 2008, have galvanized the research on superconductivity. What microscopic mechanism(s) is responsible for the electron pairing underlying their superconductivity? Some essential clues to the answer to this question lie in the symmetry properties of the quantum-mechanical wave functions of the electron pairs. So far, the clues that are available indicate a complex picture rather than a clear origin and raise puzzles themselves. While the pair wave functions of most iron-based superconductors seem to show the highest symmetry possible–the kind called “nodeless s±-wave symmetry,” five compounds, KFe₂As₂, Ba_1-xK_xFe₂As₂, BaFe₂(As_1-xP_x)₂, LaFePO, and LiFeP stand out in contrast, with their pair wave functions displaying lower symmetry that is referred to as “nodal.” In this paper, we present new experimental data on nodal superconductors that suggests some significant common threads in the diverse clues and puts relevant constraints on theoretical modeling.

The evidence of nodal superconductivity in the above five compounds raises two interesting questions specifically: First, does the presence of P (as in the last three compounds) play any special role in inducing nodal behavior? Second, since BaFe₂(As_1-xP_x)₂ is derived from substitutional isovalent doping of BaFe₂As₂ by P, how does the symmetry evolve as the doping is varied? With these questions in mind, we have substituted Fe with Ru in the Fe₂As₂ layers as an alternative way to isovalent doping of BaFe₂As₂ by substituting As with P, and chosen for our investigation two Ru-doped compounds: the optimally doped Ba(Fe_0.64Ru_0.36)₂As₂, and an underdoped Ba(Fe_0.77Ru_0.23)₂As₂. For comparison, we have also investigated a P-doped BaFe₂(As_0.82P_0.18)₂, which is more underdoped than Ba(Fe_0.77Ru_0.23)₂As₂.

The measurements we have performed are thermal-conductivity measurements at ultra-low temperatures down to 50 mK and for a range of magnetic-field strength. The data demonstrates, for all three compounds, an unambiguous linear dependence of the thermal conductivity on temperature when it approaches absolute zero–a strong evidence for the nodal behavior in the pair wave functions of these compounds. The existence of nodal superconductivity in the optimally doped Ba(Fe_0.64Ru_0.36)₂As₂ suggests a common origin with the nodal superconductivity induced by P doping, rather than a special element-specific role of P. And, clearly, nodal superconductivity persists robustly as the doping is decreased, from that in Ba(Fe_0.64Ru_0.36)₂As₂, to that in the underdoped Ba(Fe_0.77Ru_0.23)₂As₂, and to that in the strongly underdoped BaFe₂(As_0.82P_0.18)₂. This robustness goes against a recent empirical proposal for how a transition from nodeless to nodal superconductivity may be induced by tuning the relative height of the pnictogen layers to the iron layers.

We present the ultra-low-temperature heat-transport study of iron-based superconductors Ba(Fe_1-xRu_x)₂As₂ and BaFe₂(As_1-xP_x)₂. For optimally doped Ba(Fe_0.64Ru_0.36)₂As₂, a large residual κ₀/T at zero field and a √H dependence of κ₀(H)/T are observed, which provide strong evidences for nodes in the superconducting gap. This result demonstrates one more nodal superconductor in iron pnictides. The similarities between isovalent Fe and P dopings strongly suggest that the nodal superconductivity in Ba(Fe_0.64Ru_0.36)₂As₂ may have the same origin as in BaFe₂(As_0.67P_0.33)₂. Furthermore, in underdoped Ba(Fe_0.77Ru_0.23)₂As₂ and strongly underdoped BaFe₂(As_0.82P_0.18)₂, κ₀/T manifests similar nodal behavior, which result shows the robustness of nodal superconductivity in the underdoped regime and puts constraint on theoretical models.

Superconductivity and Kondo effect, both discovered at the beginning of the 20th century, are two of the most celebrated phenomena in condensed matter physics. Both demonstrate that at cryogenic temperatures the resistivity of certain materials that behave as normal metals at higher temperatures can undergo spectacular changes. Superconductivity drives a zero-resistance state below a critical temperature T_c, and the Kondo effect shows up as an unusual logarithmic increase of the resistivity below the so-called Kondo temperature T_K. Remarkably, these two phenomena have their origins in electronic many-body correlations and are both characterized by a singlet ground state, albeit of different origin. Superconductivity arises from the formation of spin-singlet Cooper pairs of conduction electrons, whereas the Kondo effect comes rather from a composite spin-singlet state formed by a magnetic impurity and surrounding mobile electrons. Interestingly, when the different microscopic mechanisms for both phenomena are present, a complicated synergy arises. Using a quantum-dot device, which plays the role of a fully tunable magnetic impurity and which a number of superconducting leads are in contact with, we are able to draw a comprehensive picture of the interplay of superconductivity and Kondo effect that has so far not been available experimentally.

The setup that we use relies on a superconducting quantum-interference device (SQUID) in which the Josephson junctions are defined by a double quantum dot realized from a single carbon nanotube. Various gate electrodes allow us to control at the single-electron level the number of charges on the quantum dots and to record the corresponding supercurrent flowing in the device from the SQUID modulations. When the number of charges on a quantum dot is odd and in the normal conducting state of the device, the dot behaves as a spin-1/2 magnetic impurity whose interaction with the mobile electrons gives rise to a Kondo singlet state. Turning superconductivity on, we have found the following: First, fingerprints of this Kondo state, in the form of a positive supercurrent, are clearly visible when the Kondo effect competes strongly with superconductivity (in other words, when the Kondo temperature is large compared to the superconducting gap). Second, as the relative strength of the Kondo effect is weakened, an abrupt (first-order) reversal in the direction of the supercurrent occurs, marking the beginning of the regime where the Kondo mechanism becomes ineffective. Exploiting the tunability of our device, we are then able to establish experimentally, in connection with theoretical predictions, a generic phase diagram for the competition between the Kondo scale and the superconducting gap.

Looking ahead, we see a rather promising future. By combining the kind of high-quality device fabrication and fine-tuned supercurrent measurements that have been achieved here with simultaneous local-transport spectroscopy of the Andreev electronic states of the quantum dots, a new level of understanding of superconducting nanostructures with strong electronic correlations should become possible.

We study a carbon-nanotube quantum dot embedded in a superconducting-quantum-interference-device loop in order to investigate the competition of strong electron correlations with a proximity effect. Depending on whether local pairing or local magnetism prevails, a superconducting quantum dot will exhibit a positive or a negative supercurrent, referred to as a 0 or π Josephson junction, respectively. In the regime of a strong Coulomb blockade, the 0-to-π transition is typically controlled by a change in the discrete charge state of the dot, from even to odd. In contrast, at a larger tunneling amplitude, the Kondo effect develops for an odd-charge (magnetic) dot in the normal state, and quenches magnetism. In this situation, we find that a first-order 0-to-π quantum phase transition can be triggered at a fixed valence when superconductivity is brought in, due to the competition of the superconducting gap and the Kondo temperature. The superconducting-quantum-interference-device geometry together with the tunability of our device allows the exploration of the associated phase diagram predicted by recent theories. We also report on the observation of anharmonic behavior of the current-phase relation in the transition regime, which we associate with the two accessible superconducting states. Our results finally demonstrate that the spin-singlet nature of the Kondo state helps to enhance the stability of the 0 phase far from the mixed-valence regime in odd-charge superconducting quantum dots.

Stimulated Brillouin scattering (SBS) in an optical medium is a nonlinear process through which intense laser light interacts with a material to produce coherent phonons through photon-phonon coupling. Since its discovery in 1964, stimulated Brillouin scattering in bulk macroscopic) media and (micron-scaled) optical fibers has been extensively studied and exploited for manipulating both phonons and photons. Realizations of coherent phonon generation, slow light, and a host of new light sources are just a few examples of its importance. Through stimulated Brillouin scattering, the photon-phonon coupling is generally mediated by electrostriction—a nonlinear contraction of the material under the influence of the light—and depends very little on the geometry or size of the material. In this theoretical paper, we open up a new direction in the study of stimulated Brillouin scattering by demonstrating that a new, powerful, and geometry-dependent form of stimulated Brillouin scattering emerges in the absence of intrinsic material electrostriction as light is confined to nanoscales.

The systems we have investigated are nanoscale waveguides. The new form of stimulated Brillouin scattering has its origin in the enormous radiation pressure generated by light confined to the nanoscale and in a boundary-induced nonlinearity. We show that the radiation pressure and the boundary-induced nonlinearity can already generate powerful SBS nonlinearity on their own. When coherently combined with electrostriction, they are seen to produce giant SBS effects that are several orders of magnitude stronger than what has been seen to date in any other waveguide system. Such enhanced couplings could enable efficient stimulated Brillouin scattering in silicon waveguides for the first time.

More generally, we have developed a new theoretical formulation of stimulated Brillouin scattering that accurately incorporates the effects of boundary-induced nonlinearities and radiation pressure, both of which are shown to have tremendous impact on photon-phonon coupling at subwavelength scales. Our application of this formalism already reveals a rich landscape of new stimulated Brillouin processes within nanoscale systems. More applications of this formalism in the rapidly developing field of optomechanics are certainly to be expected.

Stimulated Brillouin scattering (SBS) is traditionally viewed as a process whose strength is dictated by intrinsic material nonlinearities with little dependence on waveguide geometry. We show that this paradigm breaks down at the nanoscale, as tremendous radiation pressures produce new forms of SBS nonlinearities. A coherent combination of radiation pressure and electrostrictive forces is seen to enhance both forward and backward SBS processes by orders of magnitude, creating new geometric degrees of freedom through which photon-phonon coupling becomes highly tailorable. At nanoscales, the backward-SBS gain is seen to be 10⁴ times greater than in conventional silica fibers with 100 times greater values than predicted by conventional SBS treatments. Furthermore, radically enhanced forward-SBS processes are 10⁵ times larger than any known waveguide system. In addition, when nanoscale silicon waveguides are cooled to low temperatures, a further 10–100 times increase in SBS gain is seen as phonon losses are reduced. As a result, a 100-μm segment of the waveguide has equivalent nonlinearity to a kilometer of fiber. Couplings of this magnitude would enable efficient chip-scale stimulated Brillouin scattering in silicon waveguides for the first time. More generally, we develop a new full-vectorial theoretical formulation of stimulated Brillouin scattering that accurately incorporates the effects of boundary-induced nonlinearities and radiation pressure, both of which are seen to have tremendous impact on photon-phonon coupling at subwavelength scales. This formalism, which treats both intermode and intramode coupling within periodic and translationally invariant waveguide systems, reveals a rich landscape of new stimulated Brillouin processes when applied to nanoscale systems.

Imagine in a type-II superconductor a tiny tornado of circulating electric current of a radius of tens of nanometers surrounding a normal-state core (where magnetic field lines go through): You have a picture of a vortex. Such a vortex tends to repel another; it can move or become pinned by microscopic defects in the superconductor. When millions of them are generated by a strong magnetic field, vortices can—through an act of balancing the pinning effect and the intervortex repulsion—self-organize into a critical state, from which avalanche events involving the motion of many vortices can occur at the slightest magnetic or thermal trigger. Much has been learned about the critical state of the vortex matter and the dynamics of the associated avalanches, much remains to be explored and made sense of. In this experimental paper, we reveal new types of vortex dynamics through spatially resolved, real-time observations enabled by a state-of-the-art magneto-optical imaging technique.

The superconductors we investigate are thin (200-nm-thick) YBa₂Cu₃O_x films grown to have a designed multiterraced surface structure. The magneto-optical images we obtain tell a vivid story. Bundles of vortices move along the terrace steps in the form of numerous, intermittent avalanches that grow like needles, some starting at the two film edges perpendicular to the steps and some from the deep interior of the film. Analyzing images of more than 10 000 avalanche events taken at different magnetic fields, we find that the avalanche-like motion of the vortices is essentially one-dimensional, intermittent, and self-similar and that it doesn’t require a threshold field.

What is the mechanism behind this observation? Our suggestion is the following: Linear defects, that exist and run in the direction parallel to the terrace steps, form narrow channels of confinement for the vortices. Traffic jams, or clogging, then occur along the channels in a random fashion as more and more vortices are generated in the channels and pinned by the strong pinning sites. Whenever one of the blocked parts of the channels breaks open due to excessive pressure from the incoming vortices, an avalanche occurs. This mechanism differs from that underlying the thermo-magnetic dendritic avalanches seen in many superconducting films.

This work has relevance for applications of superconducting films, where understanding the stability of vortex matter and achieving it is of crucial importance. Our results also raise fundamental questions about how the approach to the macroscopic critical state, either smooth or intermittent, is related to the physics of individual vortices in superconductors.

Intermittent filamentary dynamics of the vortex matter in superconductors is found in films of YBa₂Cu₃O_7-δ deposited on tilted substrates. Deposition of this material on such substrates creates parallel channels of easy flux penetration when a magnetic field is applied perpendicular to the film. As the applied field is gradually increased, magneto-optical imaging reveals that flux penetrates via numerous quasi-one-dimensional jumps. The distribution of flux avalanche sizes follows a power law, and data collapse is obtained by finite-size scaling, with the depth of the flux front used as crossover length. The intermittent behavior shows no threshold value in the applied field, in contrast to conventional flux jumping. The results strongly suggest that the quasi-one-dimensional flux jumps are of a different nature than the thermomagnetic dendritic (branching) avalanches that are commonly found in superconducting films.

It was Richard Feynman who first proposed, in 1982, the far-reaching concept of a “quantum computer”—a device more powerful than digital computers that makes direct use of quantum mechanics to perform computational operations. The first proposals for the physical implementation of quantum computation appeared in the ’90s. Among those, the idea of using electron spins trapped in electrostatic semiconductor quantum dots as the building blocks of a quantum computer (the so-called spin qubits), put forward by Daniel Loss and David DiVincenzo in 1997, emerged as the most propitious one. The first decade of the new century saw a steady improvement in the decoherence time for spin qubits (the time over which the information carried by the spin qubits is lost) by 7 orders of magnitude, with the present state-of-the-art decoherence time being as large as 270  μs!

Nevertheless, the implementation of the original Loss-DiVincenzo proposal posed a considerable technical challenge. It used quantum tunneling between qubits to enable their communication with each other, and thus required that the qubits be placed very close to each other. This requirement not only leaves little space for the placement of the vast amount of gates and wirings needed to define the electrostatic quantum dots, but also makes it challenging to control the local magnetic field needed for single-qubit operations. For these reasons, no system with more than a couple of spin qubits has been successfully implemented thus far. In the present work, we leap over this long-standing problem with an entirely different strategy of using metallic floating gates to couple together qubits that are separated over a long range.

This new strategy bestows the required space for gates and wirings and also dispenses with the demand for local manipulation of the magnetic field. We have analyzed it in great detail and shown, both analytically and numerically, that distant spins in an array of quantum dots can indeed be coupled, and coupled selectively. We have also shown how to implement in our design the CNOT operation, which can be used to entangle qubits, providing the set of operations required for universal quantum computation. That entanglement between the distant qubits, a purely quantum effect, can be achieved by classical objects—the metallic floating gates—is rather amazi