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Muon spin rotation and relaxation in Pr 1 - x Nd x Os 4 Sb 12 : Superconductivity and magnetism in Pr-rich alloys

The Pr-rich end 0 ≤ x ≤ 0.25 of the alloy series Pr 1-x Nd x ⁢Os 4 ⁢Sb 12 has been studied using muon spin rotation and relaxation. The end compound PrOs 4 ⁢Sb 12 is an unconventional heavy-fermion superconductor, which exhibits a spontaneous magnetic field associated with broken time-reversal symmetry (TRS) in the superconducting phase. Further, no such field is observed in the Nd-doped alloys for x ≥ 0.05, indicating that TRS has been restored. The superfluid density from the vortex-lattice field distribution is insensitive to Nd concentration for x ≲ 0.2, indicating that TRS restoration does not have a strong effect on the superconducting state. No Nd 3+ static magnetism, ordered or disordered, is found down to the lowest temperatures of measurement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Identification of a characteristic doping for charge order phenomena in Bi-2212 cuprates via RIXS

Identifying quantum critical points (QCPs) and their associated fluctuations may hold the key to unraveling the unusual electronic phenomena observed in cuprate superconductors. Recently, signatures of quantum fluctuations associated with charge order (CO) have been inferred from the anomalous enhancement of CO excitations that accompany the reduction of the CO order parameter in the superconducting state. Furthermore, to gain more insight about the interplay between CO and superconductivity, we investigate the doping dependence of this phenomenon throughout the Bi-2212 cuprate phase diagram using resonant inelastic x-ray scattering (RIXS) at the Cu L 3 edge. As doping increases, the CO wavevector decreases, saturating near a commensurate value of 0.25 r.l.u. beyond a characteristic doping p c , where the correlation length becomes shorter than the apparent periodicity (4a 0 ). Such behavior is indicative of the fluctuating nature of the CO; and the proliferation of CO excitations in the superconducting state also appears strongest at p c , consistent with expected behavior at a CO QCP. Intriguingly, p c appears to be near optimal doping, where the superconducting transition temperature T c is maximal.

36 MATERIALS SCIENCE↗

Quantum excitations of static charges in the Ginzburg-Landau model of superconductivity

We point out that in superconductors there may exist localized quantum excitations of the electric and condensate fields surrounding a static charge, which cannot be interpreted as simply the ground state of the screened charge plus some number of massive photons. This is illustrated via a lattice Monte Carlo calculation of the energy spectrum of a pair of separated static charges in an effective Ginzburg-Landau model of superconductivity.

36 MATERIALS SCIENCE↗

Fluctuating Ru trimer precursor to a two-stage electronic transition in RuP

Superconductivity in binary ruthenium pnictides occurs proximal to and upon suppression of a non-magnetic ground state, preceded by a pseudogap phase associated with Fermi surface instability, and its critical temperature, T c , is maximized around the pseudogap quantum critical point. By analogy with isoelectronic iron based counterparts, antiferromagnetic fluctuations became ''usual suspects" as putative mediators of superconducting pairing. Here we report on a high temperature local symmetry breaking in RuP, nonsuperconducting parent of the maximum- T c branch of these novel superconductors, revealed by combined nanostructure-sensitive powder and single crystal X-ray total scattering analyses. Large local distortions of Ru chains associated with orbital-charge trimerization, further assembled into hexamers, exist above the two-stage electronic transition in RuP. In the pseudogap regime the precursors order with distortions retaining their strength, whereas they acquire spin-singlet characteristics which dramatically enhances the distortion as the nonmagnetic ground state establishes. The precursors enable the nonmagnetic ground state and presumed complex oligomerization, and the relevance of pseudogap fluctuations for superconductivity emerges as a distinct prospect. As a transition metal system in which partial d-manifold filling combined with high crystal symmetry promotes electronic instabilities, this represents a further example of local electronic precursors underpinning the macroscopic collective behavior of quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Frustrated magnetic interactions in FeSe

The structurally simplest high-temperature superconductor FeSe exhibits an intriguing superconducting nematic paramagnetic phase with unusual spin excitation spectra that are different from typical spin waves; thus, determining its effective magnetic exchange interactions is challenging. In this work, we report neutron scattering measurements of spin fluctuations of FeSe in the tetragonal paramagnetic phase. We show that the equal-time magnetic structure factor, S(Q), can be effectively modeled using the self-consistent Gaussian approximation calculation with highly frustrated nearest-neighbor (J 1 ) and next-nearest-neighbor (J 2 ) exchange couplings, and very weak further neighbor exchange interaction. Our results elucidate the frustrated magnetism in FeSe, which provides a natural explanation for the highly tunable superconductivity and nematicity in FeSe and related materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Exploring the Dirac nature of RbBi 2

Characteristics of topological semimetals such as a nonsaturating magnetoresistance (MR), a field-induced metal to semiconducting crossover and a robust resistivity plateau are observed under a magnetic field in type-I RbBi 2 bulk superconductor with $\mathrm{T}$ c = 4.15 K. The MR exhibits a notable 3500% increase at 2 K and 9 T and the resistivity follows a power law temperature dependence, while the MR ∝ $\mathrm{H}$ 1.26 , indicating weak carrier compensation. Further, first principles calculations provided insights into the dynamical stability of the cubic structure at 0 K. Both hole and electron pockets are observed at the Fermi surface. The electron-phonon interaction constant indicates weak coupling strength (<1) that leads to a maximum predicted $\mathrm{T}$ c of 2.852 K. Just below the Fermi level, E F , the electronic band structure consists of linear band crossings at the $\mathrm{X}$ points in the Brillouin zone (BZ) corresponding to massless, symmetry-protected Dirac fermions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Loop-current charge density wave driven by long-range Coulomb repulsion on the kagomé lattice

Recent experiments on vanadium-based nonmagnetic kagomé metals A⁢V 3 ⁢Sb 5 ⁢(A=K,Rb,Cs) revealed evidence for possible spontaneous time-reversal symmetry (TRS) breaking in the charge density wave (CDW) ordered state. The long-sought-after quantum order of loop currents has been suggested as a candidate for the TRS breaking state. However, a microscopic model for the emergence of the loop-current CDW due to electronic correlations is still lacking. Here, in this work, we calculate the susceptibility of the real and imaginary bond orders on the kagomé lattice near van Hove filling, and reveal the importance of next-nearest-neighbor Coulomb repulsion V 2 in triggering the instability toward imaginary bond ordered CDW. The concrete effective single-orbital t–V 1 –V 2 model on the kagomé lattice is then studied, where t and V 1 are the hopping and Coulomb repulsion on the nearest-neighbor bonds. We obtain the mean-field ground states, analyze their properties, and determine the phase diagram in the plane spanned by V 1 and V 2 at van Hove filling. The region dominated by V 1 is occupied by a 2⁢a 0 ×2⁢a 0 real CDW insulator with the inverse of Star-of-David (ISD) bond configuration. Increasing V 2 indeed drives a first-order transition from ISD to stabilized loop-current insulators that exhibit four possible current patterns of different topological properties, leading to orbital Chern insulators. We then extend these results away from van Hove filling and show that electron doping helps the stabilization of loop currents, and gives rise to doped orbital Chern insulators with emergent Chern Fermi pockets carrying large Berry curvature and orbital magnetic moment. Our findings provide a concrete model realization of the loop-current Chern metal at the mean-field level for the TRS breaking normal state of the kagomé superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nodeless superconductivity in the noncentrosymmetric compound ThIrSi

The superconductor ThIrSi, with Tc=6.5K, is expected to show unusual features in view of its noncentrosymmetric structure and the presence of heavy elements featuring a sizable spin-orbit coupling. Here, we report a comprehensive study of its electronic properties by means of magnetization, muon-spin rotation and relaxation (μ⁢SR) and nuclear magnetic resonance (NMR) measurements. Both the superfluid density ρ sc ⁡(T) (determined via transverse-field μ⁢SR) and the spin-lattice relaxation rate T–1 1⁡(T) (determined via NMR) suggest a nodeless superconductivity. Furthermore, the absence of spontaneous magnetic fields below T c , as evinced from zero-field μ⁢SR measurements, indicates a preserved time-reversal symmetry in the superconducting state of ThIrSi. Finally, temperature-dependent upper critical fields as well as field-dependent superconducting muon-spin relaxations suggest the presence of multiple superconducting gaps in ThIrSi.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Structure of Charge Density Waves in La1.875Ba0.125CuO4

Although charge-density wave (CDW) correlations exist in several families of cuprate superconductors, they exhibit substantial variation in CDW wavevector and correlation length, indicating a key role for CDW-lattice interactions. We investigated this interaction in La1.875Ba0.125CuO4 using single crystal x-ray diffraction to collect a large number of CDW peak intensities, and determined the Cu and La/Ba atomic distortions induced by the formation of CDW order. Within the CuO2 planes, the distortions involve a periodic modulation of the Cu-Cu spacing along the direction of the ordering wave vector. The charge ordering within the copper-oxygen layer induces an out-of-plane breathing modulation of the surrounding lanthanum layers, which leads to a related distortion on the adjacent copper-oxygen layer. Our result implies that the CDW-related structural distortions do not remain confined to a single layer but rather propagate an appreciable distance through the crystal. This leads to overlapping structural modulations, in which CuO2 planes exhibit distortions arising from the orthogonal CDWs in adjacent layers as well as distortions from the CDW within the layer itself. We attribute this striking effect to the weak c-axis charge screening in cuprates and suggest this effect could help couple the CDW between adjacent planes in the crystal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Following the Higgs mode across the BCS-BEC crossover in two dimensions

Although substantial effort has been dedicated to analyzing the Higgs (amplitude) mode in superconducting systems, there are relatively few studies of the Higgs peak's dispersion and width, quantities which are observable in spectroscopic measurements. These properties can be obtained from the location of the pole of the amplitude (Higgs) susceptibility in the lower half plane of complex frequency. We analyze the behavior of the Higgs mode in a two-dimensional neutral fermionic superfluid at T = 0 throughout the crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) behavior. Here, this occurs when the dressed chemical potential μ changes sign from positive to negative. For μ > 0, we find a pole in the Higgs susceptibility in the lower half plane of frequency and demonstrate that it leads to a well-defined peak in spectroscopic probes. For μ < 0, the pole still exists but is “hidden,” not giving rise to a peak in spectroscopic probes. Extending this analysis to a charged superconductor, we find that the Higgs mode is unaffected by the long-range Coulomb interaction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Characterization of two electronic subsystems in cuprates through optical conductivity

Understanding the physical properties of unconventional superconductors as well as of other correlated materials presents a formidable challenge. Their unusual evolution with doping, frequency, and temperature has frequently led to non-Fermi-liquid (non-FL) interpretations. Optical conductivity is a major challenge in this context. Here, the optical spectra of two archetypal cuprates, underdoped HgBa 2 CuO 4+δ and optimally doped Bi 2 Sr 2 CaCu 2 O 8+δ , are interpreted based on the standard Fermi-liquid (FL) paradigm. At both dopings, perfect frequency-temperature FL scaling is found to be modified by the presence of a second, gapped electronic subsystem. Further, this non-FL component emerges as a well-defined mid-infrared spectral feature after the FL contribution, determined independently by transport, is subtracted. Temperature, frequency, and doping evolution of the MIR feature identify a gapped rather than dissipative response. In contrast, the dissipative response is found to be relevant for pnictides and ruthenates. Such an unbiased FL/non-FL separation is extended across the cuprate phase diagram, capturing all the key features of the normal state and providing a natural explanation why the superfluid density is attenuated on the overdoped side. Thus, we obtain a unified interpretation of optical responses and transport measurements in all analyzed physical regimes and all analyzed compounds.

36 MATERIALS SCIENCE↗

Absence of mixed valency for Pr in pristine and hole-doped PrNiO 2

Infinite-layer nickelates (𝑅⁢NiO 2 ) exhibit some distinct differences as compared to cuprate superconductors, leading to a debate concerning the role of rare-earth ions (𝑅=La,Pr,Nd) in the low-energy many-body physics. Although rare-earth 4⁢𝑓 orbitals are typically treated as inert “core” electrons in studies, this approximation has been questioned. An active participation of 4⁢𝑓 states is most likely for PrNiO 2 based on an analogy to cuprates where Pr cuprates differ significantly from other cuprates. Here, we adopt density functional plus dynamical mean-field theory to investigate the role of Pr 4⁢𝑓 orbitals and more generally the correlated electronic structure of PrNiO 2 and its hole-doped variant. We find that the Pr 4⁢𝑓 states are insulating and show no evidence for either a Kondo resonance or Zhang-Rice singlet formation as they do not have any hybridization channels near the Fermi energy. The biggest effects of hole doping are to shift the Pr 5⁢𝑑 and 4⁢𝑓 states further away from the Fermi energy whereas enhancing the Ni 3⁢𝑑−O 2⁢𝑝 hybridization, thus, reducing correlation effects as the O 2⁢𝑝 states get closer to the Fermi energy. We again find no evidence for either Kondo or Zhang-Rice physics for the 4⁢𝑓 states upon hole doping. Finally, we conclude by commenting on implications for other reduced valence nickelates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Machine learning the spectral function of a hole in a quantum antiferromagnet

Understanding charge motion in a background of interacting quantum spins is a fundamental problem in quantum many-body physics. The most extensively studied model for this problem is the so-called t-t'-t''-J model, where the determination of the parameter t' in the context of cuprate superconductors is challenging. Here we present a theoretical study of the spectral functions of a mobile hole in the t-t'-t''-J model using two machine-learning techniques: K-nearest neighbor regression (KNN) and a feed-forward neural network (FFNN). We employ the self-consistent Born approximation to generate a dataset of about 1.3 x 10 5 spectral functions. Here we show that, for the forward problem, both methods allow for the accurate and efficient prediction of spectral functions, allowing, e.g., rapid searches through parameter space. Furthermore, we find that for the inverse problem (inferring Hamiltonian parameters from spectra), the FFNN can, but the KNN cannot, accurately predict the model parameters using merely the density of states. Our results suggest that it may be possible to use deep-learning methods to predict materials parameters from experimentally measured spectral functions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spin-singlet topological superconductivity in the attractive Rashba-Hubbard model

Fully gapped, spin-singlet superconductors with antisymmetric spin-orbit coupling in a Zeeman magnetic field provide a promising route to realize superconducting states with non-Abelian topological order and therefore fault-tolerant quantum computation. Here we use a quantum Monte Carlo dynamical cluster approximation to study the superconducting properties of a doped two-dimensional attractive Hubbard model with Rashba spin-orbit coupling in a Zeeman magnetic field. We generally find that the Rashba coupling has a beneficial effect towards s-wave superconductivity. In the presence of a finite Zeeman field, when superconductivity is suppressed by Pauli pair breaking, the Rashba coupling counteracts the spin imbalance created by the Zeeman field by mixing the spins, and thus restores superconductivity at finite temperatures. Further, we show that this favorable effect of the spin-orbit coupling is traced to a spin-flip driven enhancement of the amplitude for the propagation of a pair of electrons in time-reversed states. Moreover, by inspecting the Fermi surface of the interacting model, we show that for sufficiently large Rashba coupling and Zeeman field, the superconducting state is expected to be topologically nontrivial.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Vortex dynamics induced by scanning SQUID susceptometry

In this work, we measured the local magnetic response of a niobium thin film by applying a millitesla-scale AC magnetic field using a micron-scale field coil and detecting the response with a micron-scale pickup loop in a scanning superconducting quantum interference device (SQUID) susceptometry measurement. Near the film's critical temperature, we observed a steplike nonlinear and dissipative magnetic response due to the dynamics of a small number of vortex-antivortex pairs induced in the film by the local applied AC field. We modeled the dynamics of the measurement using a combined two-dimensional London-Maxwell and time-dependent Ginzburg-Landau approach, allowing us to construct a detailed real-space picture of the vortex motion causing the observed dissipative response. This work pushes scanning SQUID susceptometry of two-dimensional superconductors beyond the regime of linear response and lays the foundation for microscopic studies of vortex dynamics and pinning in superconducting devices and more exotic materials systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Phonon softening and slowing-down of charge density wave fluctuations in BaNi 2 As 2

BaNi 2 As 2 is a nonmagnetic analog of the iron pnictide superconductors, and exhibits an incommensurate charge density wave (IC-CDW) and a sizable elastoresistance. Here, in this Letter, phonons in BaNi 2 As 2 associated with the IC-CDW and uniform in-plane lattice distortions are investigated using high-resolution inelastic x-ray scattering. The in-plane transverse acoustic phonons reveal no softening at temperatures where the elastoresistance increases strongly, indicating the latter to be electronically driven. Systematic phonon measurements suggest the IC-CDW occurs in two stages upon cooling: Underdamped phonons first soften to zero energy well above the IC-CDW ordering temperature, then the resulting quasielastic IC-CDW fluctuations gradually slow down and coalesce into the static IC-CDW order. A possible origin for our observations is the IC-CDW in BaNi 2 As 2 being uniaxial, which provides an additional Ising degree of freedom favorable for disordered IC-CDW modulations, and accounts for the elastoresistance through a weak coupling to the lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Decay rates of almost strong modes in Floquet spin chains beyond Fermi's Golden Rule

The stability and dynamics of almost strong zero and π modes in weakly nonintegrable Floquet spin chains are investigated. Such modes can also be viewed as localized Majorana modes at the edge of a topological superconductor. Perturbation theory in the strength of integrability breaking interaction J z is employed to estimate the decay rates of these modes, and compared to decay rates obtained from exact diagonalization. Here, the structure of the perturbation theory and thus the lifetime of the modes is governed by the conservation of quasienergy modulo 2π/T, where T is the period of the Floquet system. If there are 4n – 1 bulk excitations whose quasienergies add up to zero (or π/T for a π mode), one obtains a decay channel of the Majorana mode with a decay rate proportional to $J$$^{2n}_{z}$. Thus the lifetime is sensitively controlled by the width of the single-particle Floquet bands. For regimes where the decay rates are quadratic in J z , an analytic expression for the decay rate in terms of an infinite temperature autocorrelation function of the integrable model is derived, and shown to agree well with exact diagonalization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Universal and nonuniversal features of Bardeen-Cooper-Schrieffer theory with finite-range interactions

Here, we study analytic solutions to the Bardeen-Cooper-Schrieffer (BCS) gap equation for isotropic superconductors with finite-range interaction potentials over the full range of temperatures from absolute zero to the superconducting critical temperature 0 ≤ T ≤ T c . Using these solutions Δ (ε,T), we provide a proof of the universality of the temperature dependence of the BCS gap ratio at the Fermi level Δ (ε = 0,T)/T c . Moreover, by examining the behavior of this ratio as a function of energy ε, we find that nonuniversal features emerge away from the Fermi level, and these features take the form of a temperature-independent multiplicative factor F(ε), which is equal to Δ (ε,T)/Δ(ε = 0,T) up to exponentially small corrections, i.e., the error terms vanish like e -1/λ in the weak-coupling limit λ → 0. We discuss the model-dependent features of both F(ε) and T c , and we illustrate their behavior focusing on several concrete examples of physically relevant finite-range potentials. Comparing these cases for fixed coupling constants, we highlight the importance of the functional form of the interaction potential in determining the size of the critical temperature and provide guidelines for choosing potentials which lead to higher values of T c . We also propose experimental signatures which could be used to probe the energy dependence of the gap and potentially shed light on the underlying mechanisms giving rise to superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗