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DOE OSTI2021

Magnetic flux noise in superconducting qubits and the gap states continuum

In the present study we investigate the selected local aspects of the metal-induced gap states (MIGSs) at the disordered metal–insulator interface, that were previously proposed to produce magnetic moments responsible for the magnetic flux noise in some of the superconducting qubit modalities. Our analysis attempts to supplement the available studies and provide new theoretical contribution toward their validation. In particular, we explicitly discuss the behavior of the MIGSs in the momentum space as a function of the onsite energy deviation, that mimics random potential disorder at the interface in the local approximation. It is found, that when the difference between the characteristic electronic potentials in the insulator increases, the corresponding MIGSs become more localized. This effect is associated with the increasing degree of the potential disorder that was earlier observed to produce highly localized MIGSs in the superconducting qubits. At the same time, the presented findings show that the disorder-induced localization of the MIGSs can be related directly to the decay characteristics of these states as well as to the bulk electronic properties of the insulator. As a result, our study reinforces plausibility of the previous corresponding investigations on the origin of the flux noise, but also allows to draw future directions toward their better verification.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Thermodynamic signatures of an antiferromagnetic quantum critical point inside a superconducting dome

Recent experiments in unconventional superconductors, and in particular iron-based materials, have reported evidence of an antiferromagnetic quantum critical point (AFM-QCP) emerging inside the superconducting dome of the phase diagram. Fluctuations associated with such an AFM-QCP are expected to promote unusual temperature dependencies of thermodynamic quantities. Here, we compute the T dependence of the specific heat C(T) deep inside a fully gapped s +– superconducting state as the AFM-QCP is approached. We find that at the AFM-QCP, the specific heat C(T) vanishes quadratically with temperature, as opposed to the typical exponential suppression seen in fully gapped BCS superconductors. This robust result is due to a nonanalytic contribution to the free energy arising from the general form of the bosonic (AFM) propagator in the SC state. Away from the AFM-QCP, as temperature is lowered, C(T) shows a crossover from a T2 behavior to an exponential behavior, with the crossover temperature scale set by the value of the superconducting gap and the distance to the QCP. As a result, we argue that these features in the specific heat can be used to unambiguously determine the existence of AFM-QCPs inside the superconducting domes of iron-based and other fully gapped unconventional superconductors.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Single-gap isotropic s- wave superconductivity in single crystals AuSn 4

In this article, London, λ L (T), and Campbell, λ C (T), penetration depths were measured in single crystals of a topological superconductor candidate AuSn 4 . At low temperatures, λ L (T) is exponentially attenuated and, if fitted with the power law, λ(T) ~ T n , gives exponents n > 4, indistinguishable from the isotropic single s- wave gap Bardeen-Cooper-Schrieffer (BCS) asymptotic. The superfluid density fits perfectly in the entire temperature range to the BCS theory. The superconducting transition temperature, T c = 2.40 ± 0.05 K, does not change after 2.5 MeV electron irradiation, indicating the validity of the Anderson theorem for isotropic s- wave superconductors. Campbell penetration depth before and after electron irradiation shows no hysteresis between the zero-field cooling (ZFC) and field cooling (FC) protocols, consistent with the parabolic pinning potential. Interestingly, the critical current density estimated from the original Campbell theory decreases after irradiation, implying that a more sophisticated theory involving collective effects is needed to describe vortex pinning in this system. In general, our thermodynamic measurements strongly suggest that the bulk response of the AuSn 4 crystals is fully consistent with the isotropic s- wave weak-coupling BCS superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Hybridization of Bogoliubov Quasiparticles between Adjacent CuO 2 Layers in the Triple-Layer Cuprate Bi 2 Sr 2 Ca 2 Cu 3 O 10 + δ Studied by Angle-Resolved Photoemission Spectroscopy

Hybridization of Bogoliubov quasiparticles (BQPs) between the CuO 2 layers in the triple-layer cuprate high-temperature superconductor Bi 2 Sr 2 Cu 2 Cu 3 O 10+δ is studied by angle-resolved photoemission spectroscopy (ARPES). In the superconducting state, an anticrossing gap opens between the outer- and inner-BQP bands, which we attribute primarily to interlayer single-particle hopping with possible contributions from interlayer Cooper pairing. We find that the d-wave superconducting gap of both BQP bands smoothly develops with momentum without an abrupt jump in contrast to a previous ARPES study. Hybridization between the BQPs also gradually increases in going from the off nodal to the antinodal region, which is explained by the momentum dependence of the interlayer single-particle hopping. As possible mechanisms for the enhancement of the superconducting transition temperature, the hybridization between the BQPs as well as the combination of phonon modes of the triple CuO 2 layers and spin fluctuations represented by a four-well model are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Electronic nature of chiral charge order in the kagome superconductor CsV 3 Sb 5

Kagome superconductors with T C up to 7 K have been discovered for over 40 y. Recently, unconventional chiral charge order has been reported in kagome superconductor KV 3 Sb 5 , with an ordering temperature of one order of magnitude higher than the T C . However, the chirality of the charge order has not been reported in the cousin kagome superconductor CsV 3 Sb 5 , and the electronic nature of the chirality remains elusive. In this paper, we report the observation of electronic chiral charge order in CsV 3 Sb 5 via scanning tunneling microscopy (STM). We observe a 2 × 2 charge modulation and a 1 × 4 superlattice in both topographic data and tunneling spectroscopy. 2 × 2 charge modulation is highly anticipated as a charge order by fundamental kagome lattice models at van Hove filling, and is shown to exhibit intrinsic chirality. We find that the 1 × 4 superlattices form various small domain walls, and can be a surface effect as supported by our first-principles calculations. Crucially, we find that the amplitude of the energy gap opened by the charge order exhibits real-space modulations, and features 2 × 2 wave vectors with chirality, highlighting the electronic nature of the chiral charge order. STM study at 0.4 K reveals a superconducting energy gap with a gap size 2Δ = 0.85 meV, which estimates a moderate superconductivity coupling strength with 2Δ/k B T C = 3.9. Furthermore, when further applying a c-axis magnetic field, vortex core bound states are observed within this gap, indicative of clean-limit superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Supermodulation-driven evolution of the nodal structure of bismuth-based cuprate superconductors

Recent work has shown novel properties of twisted cuprates. In this paper, I point out that related phenomena occur intrinsically in bismuth-based cuprate superconductors due to the presence of the BiO supermodulation. As the ratio of the supermodulation potential to the superconducting energy gap increases, two critical points are found where semi-Dirac nodes form (that is, they have quadratic dispersion in one direction and linear dispersion in the orthogonal direction). The first critical point should be realized in Bi2212, the second in Bi2201. Implications of these findings are discussed.

Cuprates↗

DOE OSTI2022

Theory of superconductivity in doped quantum paraelectrics

Abstract Recent experiments on Nb-doped SrTiO 3 have shown that the superconducting energy gap to the transition temperature ratio maintains the Bardeen–Cooper–Schrieffer (BCS) value throughout its superconducting dome. Motivated by these and related studies, we show that the Cooper pairing mediated by a single soft transverse-optical phonon is the most natural mechanism for such a superconducting dome given experimental constraints, and present the microscopic theory for this pairing mechanism. Furthermore, we show that this mechanism is consistent with the T 2 resistivity in the normal state. Lastly, we discuss what physical insights SrTiO 3 provides for superconductivity in other quantum paraelectrics such as KTaO 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Stripe order enhanced superconductivity in the Hubbard model

Unidirectional (“stripe”) charge density wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high-temperature superconductors, where it generally competes with superconductivity. Nonetheless, on theoretical grounds it has been conjectured that stripe order (or other forms of “optimal” inhomogeneity) may play an essential positive role in the mechanism of high-temperature superconductivity. Here, we report density matrix renormalization group studies of the Hubbard model on long four- and six-leg cylinders, where the hopping matrix elements transverse to the long direction are periodically modulated—mimicking the effect of putative period 2 stripe order. We find that even modest amplitude modulations can enhance the long-distance superconducting correlations by many orders of magnitude and drive the system into a phase with a substantial spin gap and superconducting quasi–long-range order with a Luttinger exponent, K sc ~ 1.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Imaging the energy gap modulations of the cuprate pair-density-wave state

The defining characteristic of Cooper pairs with finite center-of-mass momentum is a spatially modulating superconducting energy gap Δ(r). Recently, this concept has been generalized to the pair density wave (PDW) state predicted to exist in cuprates. Although the signature of a cuprate PDW has been detected in Cooperpair tunneling, the distinctive signature in single-electron tunneling of a periodic Δ(r) modulation has never been observed. Here, using a new approach, we discover strong Δ(r) modulations in Bi 2 Sr 2 CaCu 2 O 8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/a0)(1/8, 0) and Q ≈ (2π/a0)(0, 1/8). Simultaneous imaging of the localdensity- of-states N(r, E) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we discover them to be concentrated in areas where the PDW spatial phase changes by !, as predicted by the theory of half-vortices in a PDW state. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in the canonical cuprate Bi 2 Sr 2 CaCu 2 O 8+δ .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Point-node gap structure of the spin-triplet superconductor UTe 2

In this work, low-temperature electrical and thermal transport, magnetic penetration depth, and heat capacity measurements were performed on single crystals of the actinide superconductor UTe 2 to determine the structure of the superconducting energy gap. Heat transport measurements performed with currents directed along both crystallographic a and b axes reveal a vanishingly small residual fermionic component of the thermal conductivity. The magnetic field dependence of the residual term follows a rapid, quasilinear increase consistent with the presence of nodal quasiparticles, rising toward the a -axis upper critical field where the Wiedemann-Franz law is recovered. Together with a quadratic temperature dependence of the magnetic penetration depth up to T / T c = 0.3 , these measurements provide evidence for an unconventional spin-triplet superconducting order parameter with point nodes. Millikelvin specific heat measurements performed on the same crystals used for thermal transport reveal an upturn below 300 mK that is well described by a divergent quantum-critical contribution to the density of states (DOS). Modeling this contribution with a T - 1 / 3 power law allows restoration of the full entropy balance in the superconducting state and a resultant cubic power law for the electronic DOS below T c , consistent with the point-node gap structure determined by thermal conductivity and penetration depth measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Antiferromagnetism-driven two-dimensional topological nodal-point superconductivity

Magnet/superconductor hybrids (MSHs) hold the promise to host emergent topological superconducting phases. Both one-dimensional (1D) and two-dimensional (2D) magnetic systems in proximity to -wave superconductors have shown evidence of gapped topological superconductivity with zero-energy end states and chiral edge modes. Recently, it was proposed that the bulk transition-metal dichalcogenide 4Hb-TaS 2 is a gapless topological nodal-point superconductor (TNPSC). However, there has been no experimental realization of a TNPSC in a MSH system yet. Here we present the discovery of TNPSC in antiferromagnetic (AFM) monolayers on top of an s-wave superconductor. Our calculations show that the topological phase is driven by the AFM order, resulting in the emergence of a gapless time-reversal invariant topological superconducting state. Using low-temperature scanning tunneling microscopy we observe a low-energy edge mode, which separates the topological phase from the trivial one, at the boundaries of antiferromagnetic islands. As predicted by the calculations, we find that the relative spectral weight of the edge mode depends on the edge’s atomic configuration. Our results establish the combination of antiferromagnetism and superconductivity as a novel route to design 2D topological quantum phases.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2023

Electromagnetic Properties of Aluminum-based Bilayers for Kinetic Inductance Detectors

The complex conductivity of a superconducting thin film is related to the quasiparticle density, which depends on the physical temperature and can also be modified by external pair breaking with photons and phonons. This relationship forms the underlying operating principle of Kinetic Inductance Detectors (KIDs), where the detection threshold is governed by the superconducting energy gap. We investigate the electromagnetic properties of thin-film aluminum that is proximitized with either a normal metal layer of copper or a superconducting layer with a lower T-C, such as iridium, in order to extend the operating range of KIDs. Using the Usadel equations along with the Nam expressions for complex conductivity, we calculate the density of states and the complex conductivity of the resulting bilayers to understand the dependence of the pair breaking threshold, surface impedance, and intrinsic quality factor of superconducting bilayers on the relative film thicknesses. The calculations and analyses provide theoretical insights in designing aluminum-based bilayer kinetic inductance detectors for detection of microwave photons and athermal phonons at the frequencies well below the pair breaking threshold of a pure aluminum film.

complex conductivity↗

DOE OSTI2022

Quantum Computing with Majorana Kramers Pairs

Here, we propose a universal gate set acting on a qubit formed by the degenerate ground states of a Coulomb-blockaded time-reversal invariant topological superconductor island with spatially separated Majorana Kramers pairs: the “Majorana Kramers qubit.” All gate operations are implemented by coupling the Majorana Kramers pairs to conventional superconducting leads. Interestingly, in such an all-superconducting device, the energy gap of the leads provides another layer of protection from quasiparticle poisoning independent of the island charging energy. Moreover, the absence of strong magnetic fields—which typically reduce the superconducting gap size of the island—suggests a unique robustness of our qubit to quasiparticle poisoning due to thermal excitations. Consequently, the Majorana Kramers qubit should benefit from prolonged coherence times and may provide an alternative route to a Majorana-based quantum computer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Enhanced superconductivity and electron correlations in intercalated ZrTe 3

We report charge density waves (CDWs) with superconductivity, competing Fermi surface instabilities, and collective orders have captured much interest in two-dimensional van der Waals (vdW) materials. Understanding the CDW suppression mechanism, its connection to the emerging superconducting state, and electronic correlations provides opportunities for engineering the electronic properties of vdW heterostructures and thin-film devices. Using a combination of the thermal transport, x-ray photoemission spectroscopy, Raman measurements, and first-principles calculations, we observe an increase in electronic correlations of the conducting states as the CDW is suppressed in ZrT e3 with 5% Cu and Ni intercalation in the vdW gap. As superconductivity emerges, intercalation brings not only decoupling of quasi-one-dimensional conduction electrons with phonons as a consequence of intercalation-induced lattice expansion but also a drastic increase in Zr 2+ at the expense of Zr 4+ metal atoms. These observations not only demonstrate the potential of atomic intercalates in the vdW gap for ground-state tuning but also illustrate the crucial role of the Zr metal valence in the formation of collective electronic orders.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Pressure-Induced Superconductivity in the Wide-Band-Gap Semiconductor Cu 2 Br 2 Se 6 with a Robust Framework

We report pressure-induced superconductivity in a ternary and nonmagnetic Cu-containing semiconductor, Cu 2 Br 2 Se 6 , with a wide band gap of 1.89 eV, in which the Cu and Br atoms generate infinite 2, helical chains along the c-axis and are linked by the cyclohexane-like Se 6 rings to form a three-dimensional framework. We find that this framework is remarkably robust under compression, and the ambient-pressure phase survives at least to our experimental limit of 32.1 GPa. Concurrent semiconductor-to-metal transition and superconductivity are observed above 21.0 GPa. The superconducting temperature monotonically increases from 4.0 to 6.7 K at 40.0 GPa. Furthermore, first-principles calculations show that the emergence of superconductivity is associated with the formation of weak multicentered bonds that involve the increase in coordination of the Cu atoms and a subset of the Se atoms. The observation of superconductivity in this type of nonmagnetic transition-metal-based material will inspire the exploration of related new superconductors under pressure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Spectroscopic evidence for the direct involvement of local moments in the pairing process of the heavy-fermion superconductor CeCoIn 5

The microscopic mechanism for electron pairing in heavy-fermion superconductors remains a major challenge in quantum materials. Some form of magnetic mediation is widely accepted with spin fluctuations as a prime candidate. A novel mechanism, “composite pairing” based on the cooperative two-channel Kondo effect directly involving the f -electron moments, has also been proposed for some heavy-fermion compounds including CeCoIn 5 . The origin of the spin-resonance peak observed in neutron-scattering measurements on CeCoIn 5 is still controversial and the corresponding hump-dip structure in the tunneling conductance is missing. This is in contrast to the cuprate and Fe-based high-temperature superconductors, where both characteristic signatures are observed, indicating spin fluctuations are likely involved in the pairing process. In this study, we report results from planar tunneling spectroscopy along three major crystallographic orientations of CeCoIn 5 over wide ranges of temperature and magnetic field. The pairing gap opens at T p ~ 5 K , well above the bulk T c = 2.3 K , and its directional dependence is consistent with d x 2 – y 2 symmetry. With increasing magnetic field, this pairing gap is suppressed as expected but, intriguingly, a gaplike structure emerges smoothly, increasing linearly up to the highest field applied. This field-induced gaplike feature is only observed below T p . The concomitant appearance of the pairing gap and the field-induced gaplike feature, along with its linear increase with field, indicates that the f -electron local moments are directly involved in the pairing process in CeCoIn 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Optical and photoemission investigation of structural and magnetic transitions in the iron-based superconductor Sr 0.67 Na 0.33 Fe 2 As 2

We report the temperature-dependent optical conductivity and angle-resolved photoemission spectroscopy (ARPES) studies of the multiband iron-based superconductor Sr 0.67 Na 0.33 Fe 2 As 2 . Measurements were made in the high-temperature tetragonal paramagnetic phase, below the structural and magnetic transitions at $T_N$ $≃$ 125 K in the orthorhombic spin-density-wave (SDW)-like phase and $T_r$ $≃$42 K in the reentrant tetragonal double-Q magnetic phase where both charge and SDWorder exist, and below the superconducting transition at $T_c$ $≃$ 10 K. The free-carrier component in the optical conductivity is described by two Drude contributions: one strong and broad and the other weak and narrow. The broad Drude component decreases dramatically below TN and Tr , with much of its strength being transferred to a bound excitation in the midinfrared, while the narrow Drude component shows no anomalies at either of the transitions, actually increasing in strength at low temperature while narrowing dramatically. The behavior of an infrared-active mode suggests zone folding below Tr. Below Tc the dramatic decrease in the low-frequency optical conductivity signals the formation of a superconducting energy gap. ARPES reveals holelike bands at the center of the Brillouin zone (BZ), with both electron- and holelike bands at the corners. Below $T_N$, the hole pockets at the center of the BZ decrease in size, consistent with the behavior of the broad Drude component; however, below $T_r$ the electronlike bands shift and split, giving rise to a low-energy excitation in the optical conductivity at $≃$20 meV. The $C_2$ and $C_4$ magnetic states, with resulting spin-density-wave and charge-SDW order, respectively, lead to a significant reconstruction of the Fermi surface that has profound implications for the transport originating from the electron and hole pockets but appears to have relatively little impact on the superconductivity in this material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Nanoscale heterogeneity induced by nonmagnetic Zn dopants in the quantum critical metal CeCoIn 5 : 115 In NQR/NMR and 59 Co NMR study

We report antiferromagnetism in a prototypical quantum critical metal CeCoIn 5 is known to be induced by slight substitutions of nonmagnetic Zn atoms for In. In nominally 7% Zn-substituted CeCoIn 5 , an antiferromagnetic (AFM) state coexists with heavy fermion superconductivity. Heterogeneity of the electronic states is investigated in Zn-doped CeCoIn 5 by means of nuclear quadrupole and magnetic resonances (NQR and NMR). Site-dependent NQR relaxation rates 1/T 1 indicate that the AFM state is locally nucleated around Zn substituents in the matrix of a heavy fermion state, and percolates through the bulk at the AFM transition temperature T N . At lower temperatures, an anisotropic superconducting (SC) gap below the SC transition temperature Tc, and the SC state permeates through the AFM regions via a SC proximity effect. Applying an external magnetic field induces a spin-flop transition near 5T, reducing the volume of the AFM regions. Consequently, a short-ranged inhomogeneous AFM state survives and coexists with a paramagnetic Fermi liquid state at high fields.

36 MATERIALS SCIENCE↗