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Anomalous thermodynamic properties of quantum critical superconductors

Recent high-precision measurements employing different experimental techniques have unveiled an anomalous peak in the doping dependence of the London penetration depth which is accompanied by anomalies in the heat capacity in iron-pnictide superconductors at the optimal composition associated with the hidden antiferromagnetic quantum critical point. Here, we argue that finite temperature effects can be a cause of observed features. Specifically we show that quantum critical magnetic fluctuations under superconducting dome can give rise to a nodal-like temperature dependence of both specific heat and magnetic penetration depth in a fully gapped superconductor. In the presence of line nodes in the superconducting gap fluctuations can lead to the significant renormalization of the relative slope of T-linear penetration depth which is steepest at the quantum critical point. The results we obtain are general and can be applied beyond the model we use.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Prediction of s ± -Wave Superconductivity Enhanced by Electronic Doping in Trilayer Nickelates La 4 Ni 3 O 10 under Pressure

Motivated by the recently reported signatures of superconductivity in trilayer La 4 ⁢Ni 3 ⁢O 10 under pressure, here we comprehensively study this system using ab initio and random-phase approximation techniques. Without electronic interactions, the Ni d 3z 2 –r 2 orbitals show a bonding-antibonding and nonbonding splitting behavior via the O p z orbitals inducing a “trimer” lattice in La 4⁢ Ni 3 ⁢O 10 , analogous to the dimers of La 3 ⁢Ni 2 ⁢O 7 . The Fermi surface consists of three electron sheets with mixed e g orbitals, and a hole and an electron pocket made up of the d 3⁢z 2 –r 2 orbital, suggesting a Ni two-orbital minimum model. In addition, we find that superconducting pairing is induced in the s ± -wave channel due to partial nesting between the M = (π,π) centered pockets and portions of the Fermi surface centered at the Γ = (0,0) point. With changing electronic density n, the s ± instability remains leading and its pairing strength shows a domelike behavior with a maximum around n = 4.2 ( ~6.7% electron doping). The superconducting instability disappears at the same electronic density as that in the new 1313 stacking La 3 ⁢Ni 2 ⁢O 7 , correlated with the vanishing of the hole pocket that arises from the trilayer sublattice, suggesting that the high-T c superconductivity of La 3⁢ Ni 2 ⁢O 7 does not originate from a trilayer and monolayer structure. Furthermore, we confirm the experimentally proposed spin state in La 4 ⁢Ni 3 ⁢O 10 with an in-plane (π, π) order and antiferromagnetic coupling between the top and bottom Ni layers, and spin zero in the middle layer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates La 3 ⁢Ni 2 ⁢O 7

Motivated by the recently proposed alternating single-layer trilayer stacking structure for the nickelate La 3 ⁢Ni 2 ⁢O 7 , we comprehensively study this system using ab initio and random-phase approximation techniques. Here, our analysis unveils similarities between this novel La 3⁢ Ni 2 ⁢O 7 structure and other Ruddlesden-Popper nickelate superconductors, such as a similar charge-transfer gap value and orbital-selective behavior of the eg orbitals. Pressure primarily increases the bandwidths of the Ni e g bands, suggesting an enhancement of the itinerant properties of those e g states. By changing the cell volume ratio V/V 0 from 0.9 to 1.10, we found that the bilayer structure in La 3 ⁢Ni 2 ⁢O 7 always has lower energy than the single-layer trilayer stacking La 3 ⁢Ni 2 ⁢O 7 . In addition, we observe a “self-doping” effect (compared to the average 1.5 electrons per eg orbital per site of the entire structure) from the trilayer to the single-layer sublattices and this effect will be enhanced by overall electron doping. Moreover, we find a leading d x 2 -y 2 -wave pairing state that is restricted to the single layer. Because the effective coupling between the single layers is very weak, due to the nonsuperconducting trilayer in-between, this suggests that the superconducting transition temperature T c in this structure should be much lower than in the bilayer structure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tuning the Intrinsic Anisotropy with Disorder in the Ca K Fe 4 As 4 Superconductor

In this paper, we report on the anisotropy of the London penetration depth of CaKFe 4 As 4 , discussing how it relates to its electronic structure and how it modifies under introduction of disorder, both chemically induced (by Ni substitution) and irradiation induced (by 3.5-MeV protons). Indeed, CaKFe 4 As 4 is particularly suitable for the study of fundamental superconducting properties due to its stoichiometric composition, exhibiting clean-limit behavior in the pristine samples and having a fairly high critical temperature, T c ≈35 K. The London penetration depth λ L is measured with a microwave-coplanar-resonator technique that allows us to deconvolve the anisotropic contributions λ L,ab and λ L,c and obtain the anisotropy parameter γλ=λ L,c /λ L,ab . The γλ(T) found for the undoped pristine sample is in good agreement with previous literature and is here compared to ab initio density-functional-theory and Eliashberg calculations. The dependence of γλ(T) on both chemical and irradiation-induced disorder is discussed to highlight which method is more suitable to decrease the direction dependence of the electromagnetic properties while maintaining a high critical temperature. Lastly, the relevance of an intrinsic anisotropy such as γλ on application-related anisotropic parameters (critical current, pinning) is discussed in light of the recent employment of CaKFe 4 As 4 in the production of wires.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nematic superconductivity in LiFeAs

The role of nematic order for the mechanism of high-temperature superconductivity is highly debated. In most iron-based superconductors (IBSs) the tetragonal symmetry is broken already in the normal state, resulting in orthorhombic lattice distortions, static stripe magnetic order, or both. Superconductivity then emerges, at least at weak doping, already from the state with broken C 4 rotational symmetry. One of the few stoichiometric IBSs, lithium iron arsenide superconducts below 18 K and does not display either structural or magnetic transition in the normal state. Here we demonstrate, using angle-resolved photoemission spectroscopy, that even the superconducting state in LiFeAs is also a nematic one. We observe spontaneous breaking of the rotational symmetry in the gap amplitude on all Fermi surfaces, as well as unidirectional distortion of the Fermi pockets. Remarkably, these deformations are hardly visible above superconducting T c . Our results demonstrate the realization of the phenomenon of superconductivity-induced nematicity in IBSs, emphasizing the intimate relation between them. Furthermore, we suggest a theoretical explanation based on the emergence of a secondary instability inside the superconducting state, which leads to the nematic order and s–d mixing in the gap function.

36 MATERIALS SCIENCE↗

Intrinsic and doping-enhanced superconductivity in monolayer 1 H − TaS 2 : Critical role of charge ordering and spin-orbit coupling

The interplay of superconductivity with charge density wave (CDW) in metallic transition-metal dichalcogenides has been widely debated, and viable strategies manipulating these quantum states in the two-dimensional (2D) limit remain unclear. Using the ab initio anisotropic Migdal-Eliashberg theory, we successfully explain the superconductivity observed in monolayer 1H-TaS 2 by simultaneously determining its precise CDW structure and treating the marked modification of electron-phonon interaction and critical temperature T c by spin-orbit coupling effects. With this paradigm, we further show that electron doping weakens the CDW order leading to increased T c up to 11 K, along with a single-gap to two-gap superconductivity transition due to the suppression of the CDW gap. By contrast, a low hole doping barely affects the CDW but still yields a significantly enhanced superconducting order, implying their good coexistence. Combined with the synergistic behavior of CDW and superconductivity, which cooperate upon TaS 2 thickness reduction causing an unusual rise of T c , our results unravel diversified interactions between the two collective orders in ultrathin TaS 2 , being competition, coexistence or cooperation depending on external stimuli, which provide key clues for controlling correlated states in devices based on 2D CDW superconductors.

36 MATERIALS SCIENCE↗

Superconductivity in multiorbital systems with repulsive interactions: Hund's pairing versus spin-fluctuation pairing

Hund's pairing refers to Cooper pairing generated by onsite interactions that become attractive due to large Hund's exchange J. This is possible in multiorbital systems even when all local bare interactions are repulsive, since attractions in specific channels are given by certain linear combinations of interaction parameters. On the other hand, pairing processes such as the exchange of spin fluctuations are also present. We compare mean-field Hund's pairing and spin-fluctuation-mediated pairing using electronic bands appropriate for different classes of multiorbital systems over a wide range of interaction parameters. We find that, for systems without clear nesting features, the superconducting state generated by the Hund's mechanism agrees well with that from the full fluctuation exchange vertex when Hund's exchange and spin-orbit coupling are sufficiently large. On the other hand, for systems characterized by a peaked finite-momentum particle-hole susceptibility, spin-fluctuation pairing generally dominates over Hund's pairing. From this perspective Hund's pairing states appear unlikely to be realized in systems like Sr 2 RuO 4 and generic iron-based superconductors.

36 MATERIALS SCIENCE↗

Spin-triplet superconductivity from excitonic effect in doped insulators

Despite being of fundamental importance and potential interest for topological quantum computing, spin-triplet superconductors remain rare in solid state materials after decades of research. In this work, we present a three-particle mechanism for spin-triplet superconductivity in multiband systems, where an effective attraction between doped electrons is produced from the Coulomb repulsion via a virtual interband transition involving a third electron [V. Crépel, L. Fu, Sci. Adv. 7, eabh2233 (2021)]. Our theory is analytically controlled by an interband hybridization parameter and explicitly demonstrated in doped band insulators with the example of an extended Hubbard model. Our theory of exciton-mediated pairing reveals how, as a matter of principle, a two-particle bound state can arise from the strong electron repulsion upon doping, opening a viable path to Bose–Einstein condensate (BEC)–Bardeen–Cooper–Schrieffer (BCS) physics in solid state systems. In light of this theory, we propose that recently discovered dilute superconductors such as ZrNCl, WTe 2 , and moiré materials can be spin-triplet and compare the expected consequences of our theory with experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Anisotropic, multiband, and strong-coupling superconductivity of the Pb 0.64 ⁢Bi 0.36 alloy

This paper presents theoretical and experimental studies on the superconductivity of Pb ⁢0.64 ⁢Bi 0.36 alloy, which is a prototype of strongly coupled superconductors and exhibits one of the strongest coupling under ambient pressure among the materials studied so far. The critical temperature, the specific heat in the superconducting state, and the magnetic critical fields are experimentally determined. Deviations from the single-gap s-wave BCS-like behavior are observed. The electronic structure, phonons, and electron-phonon interactions are analyzed in relation to the metallic Pb, explaining why the Pb-Bi alloy exhibits such a large value of the electron-phonon coupling parameter λ ≃ 2. Superconductivity is studied using the isotropic Eliashberg formalism as well as the anisotropic density functional theory for superconductors. Here, we find that while Pb is a two-gap superconductor with well-defined separate superconducting gaps, in the Pb-Bi alloy an overlapped three-gap-like structure is formed with a strong anisotropy. Furthermore, the chemical disorder, inherent to this alloy, leads to strong electron scattering, which is found to reduce the critical temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Multiorbital singlet pairing and d + d superconductivity

Recent experiments in multiband Fe-based and heavy-fermion superconductors have challenged the long-held dichotomy between simple s - and d -wave spin-singlet pairing states. Here, we advance several time-reversal-invariant irreducible pairings that go beyond the standard singlet functions through a matrix structure in the band/orbital space, and elucidate their naturalness in multiband systems. We consider the s τ 3 multiorbital superconducting state for Fe-chalcogenide superconductors. This state, corresponding to a d + d intra- and inter-band pairing, is shown to contrast with the more familiar d + i d state in a way analogous to how the B- triplet pairing phase of 3 He superfluid differs from its A- phase counterpart. In addition, we construct an analog of the s τ 3 pairing for the heavy-fermion superconductor CeCu 2 Si 2 , using degrees-of-freedom that incorporate spin-orbit coupling. Our results lead to the proposition that d -wave superconductors in correlated multiband systems will generically have a fully-gapped Fermi surface when they are examined at sufficiently low energies.

Materials Science↗

Slope of the upper critical field at T c in two-band superconductors with nonmagnetic disorder: s + + superconductivity in Ba 1 − x K x Fe 2 As 2

A recent theory of the disorder-dependent slope of the upper critical field at the superconducting transition temperature T c , defined as S ≡ |dH c2 /dT| T→T c , is extended to multiband superconductors aimed at iron-based superconductors, considering two constant gaps of different magnitudes and, potentially, different signs. Here, we show that the slope S decreases with increasing nonmagnetic scattering rate P in the s ± pairing state and increases in the s ++ superconductor for a reasonable range of parameters. The experiment shows that in a typical iron-based superconductor, Ba 1–x K x Fe 2 As 2 (BaK122), the nonmagnetic disorder induced by electron irradiation leads to an increasing S(P) across the superconducting “dome,” at different x. This implies that Ba 1–x K x Fe 2 As 2 is likely an s ++ superconductor with two effective gaps of different magnitudes, at least at moderate doping levels, x< 0.6. This work reopens a decade-long discussion about the nature of the superconducting order parameter in iron pnictides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Thermodynamic properties of nodal superconductors close to a magnetic quantum critical point

In this work we study thermodynamic manifestations of the quantum criticality in multiband unconventional superconductors. As a guiding example we consider the scenario of magnetic quantum critical point in the model that captures superconductivity coexistence with the spin-density wave. We show that in situations when the superconducting order parameter has incidental nodes at isolated points, quantum magnetic fluctuations lead to the renormalization of the relative 𝑇-linear slope of the London penetration depth. This leads to the nonmonotonic dependence of the penetration depth as a function of doping and the concomitant peak structure across the quantum critical point. In addition, we determine contribution of magnetic fluctuations to the specific heat at the onset of the coexistence phase. Furthermore, our theoretical analysis is corroborated by making a comparison of our results with the recent experimental data from the low-temperature thermodynamic measurements at optimal composition in BaFe 2 (As 1-x P x ) 2 .

36 MATERIALS SCIENCE↗

Spatially inhomogeneous magnetic superconductors

Here we consider a problem of superconductivity coexistence with the spin-density-wave order in disordered multiband metals. It is assumed that random variations of the disorder potential on short length scales render the interactions between electrons to become spatially correlated. As a consequence, both superconducting and magnetic order parameters become spatially inhomogeneous and are described by the universal phenomenological quantities, whereas all the microscopic details are encoded in the correlation function of the coupling strength fluctuations. We consider a minimal model with two nested two-dimensional Fermi surfaces and disorder potentials which include both intra- and interband scattering. The model is analyzed using the quasiclassical approach to show that short-scale pairing-potential disorder leads to a broadening of the coexistence region.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Doping evolution of the Mott–Hubbard landscape in infinite-layer nickelates

The recent observation of superconductivity in N d 0.8 S r 0.2 N i O 2 has raised fundamental questions about the hierarchy of the underlying electronic structure. Calculations suggest that this system falls in the Mott–Hubbard regime, rather than the charge-transfer configuration of other nickel oxides and the superconducting cuprates. Here, we use state-of-the-art, locally resolved electron energy-loss spectroscopy to directly probe the Mott–Hubbard character of N d 1 − x S r x N i O 2 . Upon doping, we observe emergent hybridization reminiscent of the Zhang–Rice singlet via the oxygen-projected states, modification of the Nd 5d states, and the systematic evolution of Ni 3d hybridization and filling. These experimental data provide direct evidence for the multiband electronic structure of the superconducting infinite-layer nickelates, particularly via the effects of hole doping on not only the oxygen but also nickel and rare-earth bands.

36 MATERIALS SCIENCE↗

Bogoliubov Fermi surfaces in spin-$\frac{1}{2}$ systems: Model Hamiltonians and experimental consequences

Bogoliubov Fermi surfaces (BFSs) are topologically protected regions of zero energy excitations in a superconductor whose dimension equals that of the underlying normal state Fermi surface. Examples of Hamiltonians exhibiting this “ultranodal” phase are known to preserve charge-conjugation ($\textit{C}$) and parity ($\textit{P}$) but break time-reversal ($\textit{T}$). In this work, we provide examples of model Hamiltonians that do not necessarily preserve this symmetry pattern but have well-defined sign-changing Pfaffians yielding BFSs. While their topological character has not been recognized previously, some of the models we present have been extensively studied in prior literature. Here, we further examine thermodynamic and electronic properties arising from the ultranodal state. In particular, we study the effect of a weak Zeeman field close to the topological transition and propose distinguishing features of BFSs using residual specific heat and tunneling conductance. Our calculation of the superfluid density in a toy multiband model indicates a window of interband pairing strength where BFSs are stable with a positive superfluid density. We also present additional signatures of BFSs in spin-polarized spectral weight and total magnetization measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Single-crystal growth and superconductivity in RbNi 2 Se 2

Herein we report the synthesis and characterization of RbNi 2 Se 2 , an analog of the iron chalcogenide superconductor Rb x Fe 2 Se 2 , via transport, angle-resolved photoemission spectroscopy, and density functional theory calculations. A superconducting transition at T c =1.20 K is identified. In the normal state, RbNi 2 Se 2 shows paramagnetic and Fermi-liquid behaviors. A large Sommerfeld coefficient yields an effective electron mass of m* ≈ 6m e . In the superconducting state, zero-field electronic specific-heat data C es can be described by a two-gap BCS model, indicating that RbNi 2 Se 2 is a possible multigap superconductor. Our density functional theory calculations and angle-resolved photoemission spectroscopy measurements demonstrate that RbNi 2 Se 2 exhibits relatively weak correlations and multiband characteristics, consistent with the multigap superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Measuring the Debye energy in superconductors via two-electron photoemission spectroscopy

In this work, we demonstrate theoretically that double angle resolved photoemission spectroscopy (2eARPES) can directly probe the existence of Cooper pairs away from the Fermi surface, and can thus provide insight into the characteristic energy scale around the Fermi surface, the Debye energy, in which electrons are bound into Cooper pairs. To this end, we compute the photoelectron counting rate 𝑃 (2) in two different types of unconventional superconductors, a 𝑑 𝑥 2 −𝑦 2 -wave superconductor, and a topological superconductor with a broken time-reversal symmetry. We show that 𝑃 (2) provides insight into the relative strength of intra- and interband pairing in multiband systems, as well as into the spin polarization of the bands.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effective one-band models for the one-dimensional cuprate Ba 2-x Sr x CuO 3+δ

In this work, we consider a multiband Hubbard model H m for Cu and O orbitals in Ba 2-x Sr x CuO 3+δ similar to the three-band model for two-dimensional cuprates. The hopping parameters are obtained from maximally localized Wannier functions derived from ab initio calculations. Using the cell perturbation method, we derive both a generalized t–J model H tJ and a one-band Hubbard model H H to describe the low-energy physics of the system. H tJ has the advantage of having a smaller relevant Hilbert space, facilitating numerical calculations, while additional terms should be included in H H to accurately describe the multiband physics of H m . Using H tJ and the density matrix renormalization group method, we calculate the wave-vector-resolved photoemission and discuss the relevant features in comparison with recent experiments. In agreement with previous calculations, we find that the addition of an attractive nearest-neighbor interaction of the order of the nearest-neighbor hopping shifts the weight from the 3k F to the holon-folding branch. Kinetic effects also contribute to this process.

1-dimensional systems↗