Nodal quasiparticle dynamics in the heavy fermion superconductor CeCoIn₅ revealed by precision microwave spectroscopy

Observation of the non-linear Meissner effect

A long-standing theoretical prediction is that in clean, nodal unconventional superconductors the magnetic penetration depth λ, at zero temperature, varies linearly with magnetic field. This non-linear Meissner effect is an equally important manifestation of the nodal state as the well studied linear-in-T dependence of λ, but has never been convincingly experimentally observed. Here we present measurements of the nodal superconductors CeCoIn5 and LaFePO which clearly show this non-linear Meissner effect. We further show how the effect of a small dc magnetic field on λ(T) can be used to distinguish gap nodes from non-nodal deep gap minima. Our measurements of KFe2As2 suggest that this material has such a non-nodal state.

Influence of Magnetite Nanoparticles Shape and Spontaneous Surface Oxidation on the Electron Transport Mechanism

The spontaneous oxidation of a magnetite surface and shape design are major aspects of synthesizing various nanostructures with unique magnetic and electrical properties, catalytic activity, and biocompatibility. In this article, the roles of different organic modifiers on the shape and formation of an oxidized layer composed of maghemite were discussed and described in the context of magnetic and electrical properties. It was confirmed that Fe3O4 nanoparticles synthesized in the presence of triphenylphosphine could be characterized by cuboidal shape, a relatively low average particle size (9.6 ± 2.0 nm), and high saturation magnetization equal to 55.2 emu/g. Furthermore, it has been confirmed that low-frequency conductivity and dielectric properties are related to surface disordering and oxidation. The electric energy storage possibility increased for nanoparticles with a disordered and oxidized surface, whereas the dielectric losses in these particles were strongly related to their size. The cuboidal magnetite nanoparticles synthesized in the presence of triphenylphosphine had an ultrahigh electrical conductivity (1.02 × 10-4 S/cm at 10 Hz) in comparison to the spherical ones. At higher temperatures, the maghemite content altered the behavior of electrons. The electrical conductivity can be described by correlated barrier hopping or overlapping large polaron tunneling. Interestingly, the activation energies of electrons transport by the surface were similar for all the analyzed nanoparticles in low- and high-temperature ranges.

Anomalous normal fluid response in a chiral superconductor UTe2

Chiral superconductors have been proposed as one pathway to realize Majorana normal fluid at its boundary. However, the long-sought 2D and 3D chiral superconductors with edge and surface Majorana normal fluid are yet to be conclusively found. Here, we report evidence for a chiral spin-triplet pairing state of UTe2 with surface normal fluid response. The microwave surface impedance of the UTe2 crystal was measured and converted to complex conductivity, which is sensitive to both normal and superfluid responses. The anomalous residual normal fluid conductivity supports the presence of a significant normal fluid response. The superfluid conductivity follows the temperature behavior predicted for an axial spin-triplet state, which is further narrowed down to a chiral spin-triplet state with evidence of broken time-reversal symmetry. Further analysis excludes trivial origins for the observed normal fluid response. Our findings suggest that UTe2 can be a new platform to study exotic topological excitations in higher dimension.

Conductivity Spectrum of Ultracold Atoms in an Optical Lattice

We measure the conductivity of neutral fermions in a cubic optical lattice. Using in situ fluorescence microscopy, we observe the alternating current resultant from a single-frequency uniform force applied by displacement of a weak harmonic trapping potential. In the linear response regime, a neutral-particle analog of Ohm's law gives the conductivity as the ratio of total current to force. For various lattice depths, temperatures, interaction strengths, and fillings, we measure both real and imaginary conductivity, up to a frequency sufficient to capture the transport dynamics within the lowest band. The spectral width of the real conductivity reveals the current dissipation rate in the lattice, and the integrated spectral weight is related to thermodynamic properties of the system through a sum rule. The global conductivity decreases with increased band-averaged effective mass, which at high temperatures approaches a T-linear regime. Relaxation of current is observed to require a finite lattice depth, which breaks Galilean invariance and enables damping through collisions between fermions.

Dielectric resonator method for determining gap symmetry of superconductors through anisotropic nonlinear Meissner effect

We present a new measurement method which can be used to image the gap nodal structure of superconductors whose pairing symmetry is under debate. This technique utilizes a high quality factor microwave resonance involving the sample of interest. While supporting a circularly symmetric standing wave current pattern, the sample is perturbed by a scanned laser beam, creating a photoresponse that was previously shown to reveal the superconducting gap anisotropy. Simulation and the measurement of the photoresponse of an unpatterned Nb film show less than 8% anisotropy, as expected for a superconductor with a nearly isotropic energy gap along with expected systematic uncertainty. On the other hand, measurement of a YBa₂Cu₃O_7-δ thin film shows a clear 4-fold symmetric image with ∼12.5% anisotropy, indicating the well-known 4-fold symmetric d_x²-y² gap nodal structure in the ab-plane. The deduced gap nodal structure can be further cross-checked by low temperature surface impedance data, which are simultaneously measured. The important advantage of the presented method over the previous spiral resonator method is that it does not require a complicated lithographic patterning process which limits one from testing various kinds of materials due to photoresponse arising from patterning defects. This advantage of the presented technique, and the ability to measure unpatterned samples such as planar thin films and single crystals, enables one to survey the pairing symmetry of a wide variety of unconventional superconductors.

Logarithmic Upturn in Low-Temperature Electronic Transport as a Signature of d-Wave Order in Cuprate Superconductors

In cuprate superconductors, high magnetic fields have been used extensively to suppress superconductivity and expose the underlying normal state. Early measurements revealed insulatinglike behavior in underdoped material versus temperature T, in which resistivity increases on cooling with a puzzling log(1/T) form. We instead use microwave measurements of flux-flow resistivity in YBa_{2}Cu_{3}O_{6+y} and Tl_{2}Ba_{2}CuO_{6+δ} to study charge transport deep inside the superconducting phase, in the low-temperature and low-field regime. Here, the transition from metallic low-temperature resistivity (dρ/dT>0) to a log(1/T) upturn persists throughout the superconducting doping range, including a regime at high carrier dopings in which the field-revealed normal-state resistivity is Fermi-liquid-like. The log(1/T) form is thus likely a signature of d-wave superconducting order, and the field-revealed normal state's log(1/T) resistivity may indicate the free-flux-flow regime of a phase-disordered d-wave superconductor.

Theory of scanning tunneling spectroscopy: from Kondo impurities to heavy fermion materials

Kondo systems ranging from the single Kondo impurity to heavy fermion materials present us with a plethora of unconventional properties whose theoretical understanding is still one of the major open problems in condensed matter physics. Over the last few years, groundbreaking scanning tunneling spectroscopy (STS) experiments have provided unprecedented new insight into the electronic structure of Kondo systems. Interpreting the results of these experiments-the differential conductance and the quasi-particle interference spectrum-however, has been complicated by the fact that electrons tunneling from the STS tip into the system can tunnel either into the heavy magnetic moment or the light conduction band states. In this article, we briefly review the theoretical progress made in understanding how quantum interference between these two tunneling paths affects the experimental STS results. We show how this theoretical insight has allowed us to interpret the results of STS experiments on a series of heavy fermion materials providing detailed knowledge of their complex electronic structure. It is this knowledge that is a conditio sine qua non for developing a deeper understanding of the fascinating properties exhibited by heavy fermion materials, ranging from unconventional superconductivity to non-Fermi-liquid behavior in the vicinity of quantum critical points.

Nodal to nodeless superconducting energy-gap structure change concomitant with fermi-surface reconstruction in the heavy-fermion compound CeCoIn(5)

The London penetration depth λ(T) was measured in single crystals of Ce_{1-x}R_{x}CoIn_{5}, R=La, Nd, and Yb down to T_{min}≈50  mK (T_{c}/T_{min}∼50) using a tunnel-diode resonator. In the cleanest samples Δλ(T) is best described by the power law Δλ(T)∝T^{n}, with n∼1, consistent with the existence of line nodes in the superconducting gap. Substitutions of Ce with La, Nd, and Yb lead to similar monotonic suppressions of T_{c}; however, the effects on Δλ(T) differ. While La and Nd substitution leads to an increase in the exponent n and saturation at n∼2, as expected for a dirty nodal superconductor, Yb substitution leads to n>3, suggesting a change from nodal to nodeless superconductivity. This superconducting gap structure change happens in the same doping range where changes of the Fermi-surface topology were reported, implying that the nodal structure and Fermi-surface topology are closely linked.

Magnetic field modulated microwave spectroscopy across phase transitions and the search for new superconductors

This article introduces magnetic field modulated microwave spectroscopy (MFMMS) as a unique and high-sensitivity technique for use in the search for new superconductors. MFMMS measures reflected microwave power as a function of temperature. The modulation induced by the external ac magnetic field enables the use of phase locked detection with the consequent sensitivity enhancement. The MFMMS signal across several prototypical structural, magnetic, and electronic transitions is investigated. A literature review on microwave absorption across superconducting transitions is included. We show that MFMMS can be used to detect superconducting transitions selectively with very high sensitivity.

Direct evidence for a magnetic f-electron-mediated pairing mechanism of heavy-fermion superconductivity in CeCoIn5

To identify the microscopic mechanism of heavy-fermion Cooper pairing is an unresolved challenge in quantum matter studies; it may also relate closely to finding the pairing mechanism of high-temperature superconductivity. Magnetically mediated Cooper pairing has long been the conjectured basis of heavy-fermion superconductivity but no direct verification of this hypothesis was achievable. Here, we use a novel approach based on precision measurements of the heavy-fermion band structure using quasiparticle interference imaging to reveal quantitatively the momentum space (k-space) structure of the f-electron magnetic interactions of CeCoIn5. Then, by solving the superconducting gap equations on the two heavy-fermion bands Ek(α,β) with these magnetic interactions as mediators of the Cooper pairing, we derive a series of quantitative predictions about the superconductive state. The agreement found between these diverse predictions and the measured characteristics of superconducting CeCoIn5 then provides direct evidence that the heavy-fermion Cooper pairing is indeed mediated by f-electron magnetism.

Surface-resistance measurements using superconducting stripline resonators

We present a method to measure the absolute surface resistance of conductive samples at a set of GHz frequencies with superconducting lead stripline resonators at temperatures 1-6 K. The stripline structure can easily be applied for bulk samples and allows direct calculation of the surface resistance without the requirement of additional calibration measurements or sample reference points. We further describe a correction method to reduce experimental background on high-Q resonance modes by exploiting TEM-properties of the external cabling. We then show applications of this method to the reference materials gold, tantalum, and tin, which include the anomalous skin effect and conventional superconductivity. Furthermore, we extract the complex optical conductivity for an all-lead stripline resonator to find a coherence peak and the superconducting gap of lead.