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DOE OSTI2024

Practically universal representation of the Helfand-Werthamer upper critical field for any transport scattering rate

Here, the simplified scaling of the orbital upper critical field, H c2 ⁡(T), for an isotropic s-wave superconductor is introduced. To facilitate the analysis of the experimental data, we suggest a simple but accurate approximation of the Helfand-Werthamer upper critical field in the entire temperature range valid for any transport scattering rate: H c⁢2 ⁡/⁢H c⁢⁢2 ⁡(0) ≈ (1 -t 2 )/(1 + 0.42t 1.47 ).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Superconductivity in single crystals of ZrP 1.27 Se 0.73

Results are reported for single crystals of the PbFCl-type layered compound ZrP 1.27 Se 0.73 that were produced using the iodine vapor transport method. Electrical transport, magnetization, and heat capacity measurements reveal disordered metallic behavior and the occurrence of bulk superconductivity, with a transition temperature (T c ) of 7.1 K and an anisotropic orbitally limited upper critical field. 31 P nuclear magnetic resonance measurements provide additional microscopic information, where the line shape, Knight shift, and spin-lattice relaxation data are consistent with the superconductivity originating from the corrugated Zr-P(2c)/Se plane. This suggests that the superconductivity first forms in the corrugated plane and the bulk superconductivity eventually occurs via coupling between the square planar layers. These data also show that either there are multiple superconducting gaps or there is a single gap that does not fully open across the entire Fermi surface. Finally, these results clarify the superconducting state in this material and will enable further measurements that require single-crystal specimens.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Interorbital nematicity and the origin of a single electron Fermi pocket in FeSe

The electronic structure of the enigmatic iron-based superconductor FeSe has puzzled researchers since spectroscopic probes failed to observe the expected electron pocket at the Y point in the 1-Fe Brillouin zone. It has been speculated that this pocket, essential for an understanding of the superconducting state, is either absent or incoherent. In this study, we perform a theoretical study of the preferred nematic order originating from nearest-neighbor Coulomb interactions in an electronic model relevant for FeSe. We find that at low temperatures the dominating nematic components are of interorbital d x z – d x y and d y z – d x y character, with spontaneously broken amplitudes for these two components. This interorbital nematic order naturally leads to distinct hybridization gaps at the X and Y points of the 1-Fe Brillouin zone, and may thereby produce highly anisotropic Fermi surfaces with only a single electron pocket at one of these momentum-space locations. The associated superconducting gap structure obtained with the generated low-energy electronic band structure from spin-fluctuation mediated pairing agrees well with that measured experimentally. Finally, from a comparison of the computed spin susceptibility to available neutron scattering data, we discuss the necessity of additional self-energy effects, and explore the role of orbital-dependent quasiparticle weights as a minimal means to include them.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Specific heat and gap structure of a nematic superconductor: Application to FeSe

We report the results of our in-depth analysis of spectroscopic and thermodynamic properties of a multiorbital metal, like FeSe, which first develops a nematic order and then undergoes a transition into a superconducting state, which coexists with nematicity. We analyze the angular dependence of the gap function and specific heat C v (T) of such a nematic superconductor. We specifically address three issues: (i) the angular dependence of the gap in light of the competition between the nematicity-induced s - d mixture and the orbital transmutation of low-energy excitations in the nematic state, (ii) the effect of nematicity on the magnitude of the jump of the specific heat C v (T) at T c and the temperature dependence of C v (T) below T c , and (iii) a potential transition at T c1 < T c from an s + d state to an s + e iη d state that breaks time-reversal symmetry. We consider two scenarios for a nematic order: scenario A, in which this order develops between d xz and d yz orbitals on hole and electron pockets, and scenario B, in which there is an additional component of the nematic order for d xy fermions on the two electron pockets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

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↗
DOE OSTI2023

Cascade of vestigial orders in two-component superconductors: Nematic, ferromagnetic, s -wave charge- 4 e , and d -wave charge- 4 e states

Electronically ordered states that break multiple symmetries can melt in multiple stages, similarly to liquid crystals. In a partially melted phase, known as vestigial phase, a bilinear made out of combinations of the multiple components of the primary order parameter condenses. Multicomponent superconductors are thus natural candidates for vestigial order since they break both the U⁡(1)-gauge and also time-reversal or lattice symmetries. Here, we use group theory to classify all possible real-valued and complex-valued bilinears of a generic two-component superconductor on a tetragonal or hexagonal lattice. While the more widely investigated real-valued bilinears correspond to vestigial nematic or ferromagnetic order, the little explored complex-valued bilinears correspond to a vestigial charge-4e condensate, which itself can have an underlying s-wave, d x 2 –y 2 -wave, or d xy -wave symmetry. To properly describe the fluctuating regime of the superconducting Ginzburg-Landau action and thus access these competing vestigial phases, we employ both a large-N and a variational method. We show that while vestigial order can be understood as a weak-coupling effect in the large-N approach, it is akin to a moderate-coupling effect in the variational method. Despite these distinctions, both methods yield similar results in wide regions of the parameter space spanned by the quartic Landau coefficients. Specifically, we find that the nematic and ferromagnetic phases are the leading vestigial instabilities, whereas the various types of charge-4⁢e order are attractive albeit subleading vestigial channels. The only exception is for the hexagonal case, in which the nematic and s-wave charge-4e vestigial states are degenerate. Finally, we discuss the limitations of our approach, as well as the implications of our results for the realization of exotic charge-4⁢e states in material candidates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Using Disorder to Identify Bogoliubov Fermi-Surface States

We argue that a superconducting state with a Fermi surface of Bogoliubov quasiparticles, a Bogoliubov Fermi surface (BG-FS), can be identified by the dependence of physical quantities on disorder. In particular, we show that a linear dependence of the residual density of states at weak disorder distinguishes a BG-FS state from other nodal superconducting states. We further demonstrate the stability of supercurrent against impurities and a characteristic Drude-like behavior of the optical conductivity. Our results can be directly applied to electron irradiation experiments on candidate materials of BG-FSs, including Sr 2 RuO 4 , FeSe 1-x S x , and UBe 13 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Microscopic origin of ultranodal superconducting states in spin- 1 2 systems

Several unconventional superconductors show indications of zero-energy excitations in the superconducting state consistent with the existence of a so-called Bogoliubov-Fermi surface (BFS). In particular, FeSe isovalently substituted with S seems to acquire a nonzero density of states at zero energy at low temperatures as the system goes into the tetragonal phase, consistent with a previously proposed phenomenological theory assuming an anisotropic spin singlet pairing gap coexisting with a nonunitary interband triplet component. Here we search for a microscopic model that can support the coexistence of singlet pairing with other orders, including interband nonunitary triplet pairing with magnetization, and discuss several candidates that indeed stabilize ground states with BFS. We show that with proper choice of the coupling strength of the various orders in our model, spontaneous breaking of C 4 rotational symmetry is realized at low temperatures. This feature resembles the findings of recent angle-resolved photoemission experiments in Fe(Se,S) in the tetragonal phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Leggett modes in a Dirac semimetal

Abstract Experiments have shown that several materials, including MgB 2 , iron-based superconductors and monolayer NbSe 2 , are multiband superconductors. Superconducting pairing in multiple bands can give rise to phenomena not available in a single band, including Leggett modes. A Leggett mode is the collective periodic oscillation of the relative phase between the phases of the superconducting condensates formed in the different bands. The experimental observation of Leggett modes is challenging because multiband superconductors are rare and because these modes describe charge fluctuations between bands and therefore are hard to probe directly. Also, the excitation energy of a Leggett mode is often larger than the superconducting gaps, and therefore they are strongly overdamped via relaxation processes into the quasiparticle continuum. Here, we show that Leggett modes and their frequency can be detected in a.c. driven superconducting quantum interference devices. We then use the results to analyse the measurements of such a quantum device, one based on a Dirac semimetal Cd 3 As 2 , in which superconductivity is induced by proximity to superconducting Al. These results show the theoretically predicted signatures of Leggett modes, and therefore we conclude that a Leggett mode is present in the two-band superconducting state of Cd 3 As 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Block orbital-selective Mott insulators: A spin excitation analysis

We present a comprehensive study of the spin excitations—as measured by the dynamical spin structure factor S(q,ω)—of the so-called block-magnetic state of low-dimensional orbital-selective Mott insulators. We realize this state via both a multi-orbital Hubbard model and a generalized Kondo-Heisenberg Hamiltonian. Due to various competing energy scales present in the models, the system develops periodic ferromagnetic islands of various shapes and sizes, which are antiferromagnetically coupled. The 2×2 particular case was already found experimentally in the ladder material BaFe2Se3 that becomes superconducting under pressure. Here we discuss the electronic density as well as Hubbard and Hund coupling dependence of S(q,ω) using density matrix renormalization group method. Several interesting features were identified: (1) An acoustic (dispersive spin-wave) mode develops. (2) The spin-wave bandwidth establishes a new energy scale that is strongly dependent on the size of the magnetic island and becomes abnormally small for large clusters. (3) Optical (dispersionless spin excitation) modes are present for all block states studied here. In addition, a variety of phenomenological spin Hamiltonians have been investigated but none matches entirely our results that were obtained primarily at intermediate Hubbard U strengths. Our comprehensive analysis provides theoretical guidance and motivation to crystal growers to search for appropriate candidate materials to realize the block states, and to neutron scattering experimentalists to confirm the exotic dynamical magnetic properties unveiled here, with a rich mixture of acoustic and optical features.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Critical magnetic fields and electron pairing in magic-angle twisted bilayer graphene

The velocities of the quasiparticles that form Cooper pairs in a superconductor are revealed by the upper critical magnetic field. Here we use this property to assess superconductivity in magic-angle twisted bilayer graphene (MATBG), which has been observed over a range of moiré band-filling, twist angle, and screening environment conditions. An average Fermi velocity can be defined as $v$$^{*}_{F}$ ≡ k B T c ℓ c /ℏ, where T c and ℓ c are the critical temperature and magnetic length, respectively. An advantage of this definition is that $v$$^{*}_{F}$ can be directly extracted from the existing experimental data. Mean-field theory calculations of upper critical fields in model superconductors are consistent with the expectation that Fermi velocities defined in this way are nearly independent of the strength of pairing interaction. Moreover, for fixed strength pairing interaction, minima in $v$$^{*}_{F}$ as a function of band filling are coincident with maxima in T c , as expected from the McMillan formula. Since no association between T c maxima and $v$$^{*}_{F}$ minima is present in MATBG experimental data, we argue that the pairing interaction in MATBG is strongly filling-factor dependent. Furthermore, any theory of MATBG superconductivity must explain this dependence, which is apparently primarily responsible for the observed superconducting domes.

2-dimensional systems↗
DOE OSTI2023

Band structure, superconductivity, and polytypism in AuSn 4

The orthorhombic compound AuSn 4 is compositionally similar to the Dirac node arc semimetal PtSn 4 . AuSn 4 is, contrary to PtSn 4 , superconducting with a critical temperature of T c = 2.35 K. Recent measurements present indications for quasi-two-dimensional superconducting behavior in AuSn 4 . Here we present measurements of the superconducting density of states and the band structure of AuSn 4 through scanning tunneling microscopy and angular resolved photoemission spectroscopy (ARPES). The superconducting gap values in different portions of the Fermi surface are spread around Δ 0 = 0.4 meV, which is close to but somewhat larger than Δ = 1.76k B T c expected from BCS theory. We observe superconducting features in the tunneling conductance at the surface up to temperatures about 20% larger than bulk T c . The band structure calculated with density functional theory follows well the results of ARPES. The crystal structure presents two possible stackings of Sn layers, giving two nearly degenerate polytypes. This makes AuSn 4 a rather unique case with a three-dimensional electronic band structure but properties ressembling those of low-dimensional layered compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Preferred Spin Excitations in the Bilayer Iron-Based Superconductor $CaK(Fe_{0.96}Ni_{0.04})_4As_4$ with Spin-Vortex Crystal Order

Spin-orbit coupling (SOC) is a key to understand the magnetically driven superconductivity in iron-based superconductors, where both local and itinerant electrons are present and the orbital angular momentum is not completely quenched. Here, we report a neutron scattering study on the bilayer compound CaK(Fe 0.96 Ni 0.04 ) 4 As 4 with superconductivity coexisting with a noncollinear spin-vortex crystal magnetic order that preserves the tetragonal symmetry of the Fe-Fe plane. In the superconducting state, two spin resonance modes with odd and even L symmetries due to the bilayer coupling are found similar to the undoped compound CaKFe 4 As 4 but at lower energies. Polarization analysis reveals that the odd mode is c-axis polarized, and the low-energy spin anisotropy can persist to the paramagnetic phase at high temperature, which closely resembles other systems with in-plane collinear and c-axis biaxial magnetic orders. Overall, these results provide the missing piece of the puzzle on the SOC effect in iron-pnictide superconductors, and also establish a common picture of c-axis preferred magnetic excitations below T c regardless of the details of magnetic pattern or lattice symmetry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Unconventional gate-induced superconductivity in transition-metal dichalcogenides

Superconductivity in few-layer semiconducting transition-metal dichalcogenides (TMDs) can be induced by field-effect doping through ionic-liquid gating. While several experimental observations have been collected over the years, a fully consistent theoretical picture is still missing. Here we develop a realistic framework that combines the predictive power of first-principles simulations with the versatility and insight of Bardeen-Cooper-Schrieffer gap equations to rationalize such experiments. The multivalley nature of semiconducting TMDs is taken into account, together with the doping- and momentum-dependent electron-phonon and Coulomb interactions. Consistently with experiments, we find that superconductivity occurs when the electron density is large enough that the 𝑄 valleys get occupied, as a result of a large enhancement of electron-phonon interactions. Despite being phonon driven, the superconducting state is predicted to be sensitive to Coulomb interactions, which can lead to the appearance of a relative sign difference between valleys and thus to a 𝑠 +− character. We discuss qualitatively how such scenario may account for many of the observed physical phenomena for which no microscopic explanation has been found so far, including in particular the presence of a large subgap density of states, and the sample-dependent dome-shaped dependence of 𝑇 𝑐 on accumulated electron density. Our results provide a comprehensive analysis of gate-induced superconductivity in semiconducting TMDs, and introduce an approach that will likely be valuable for other multivalley electronic systems, in which superconductivity occurs at relatively low electron density.

2-dimensional systems↗
DOE OSTI2023

Incoherent electronic band states in Mn-substituted BaFe 2 As 2

Chemical substitution is commonly used to explore new ground states in materials, yet the role of disorder is often overlooked. In Mn-substituted BaFe 2 ⁢As 2 (MnBFA), superconductivity (SC) is absent, despite being observed for nominal hole-doped phases. Instead, a glassy magnetic phase emerges, associated with the S = 5/2 Mn local spins. In this work, we present a comprehensive investigation of the electronic structure of MnBFA using angle-resolved photoemission spectroscopy (ARPES). We find that Mn causes a small and orbital-specific reduction of the electron pockets, only partially disrupting nesting conditions. Based upon the analysis of the spectral properties, we observe, for all bands, an increase in the electronic scattering rate as a function of Mn content. This is interpreted as increasing band incoherence, which we propose as the primary contributor to the suppression of the magnetic order in MnBFA. Further, this finding connects the MnBFA electronic band structure properties to the glassy magnetic behavior observed in these materials and suggests that SC is absent because of the collective magnetic impurity behavior that scatters the Fe-derived excitations. Additionally, our analysis shows that the binding energy (E B ) dependence of the imaginary part of the self-energy [Im⁡Σ⁡(E B )] is best described by a fractional scaling (Im⁡Σ⁡(E B )∝$\sqrt-E_{B}$). These results indicate that Mn tunes MnBFA into an electronic disordered phase between the correlated Hund's metal in BaFe 2 ⁢As 2 and the Hund's insulator in BaMn 2 ⁢As 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Superfluid Weight Bounds from Symmetry and Quantum Geometry in Flat Bands

Flat-band superconductivity has theoretically demonstrated the importance of band topology to correlated phases. In two dimensions, the superfluid weight, which determines the critical temperature through the Berezinksii-Kosterlitz-Thouless criteria, is bounded by the Fubini-Study metric at zero temperature. We show this bound is nonzero within flat bands whose Wannier centers are obstructed from the atoms—even when they have identically zero Berry curvature. Next, we derive general lower bounds for the superfluid weight in terms of momentum space irreps in all 2D space groups, extending the reach of topological quantum chemistry to superconducting states. We find that the bounds can be naturally expressed using the formalism of real space invariants (RSIs) that highlight the separation between electronic and atomic degrees of freedom. Finally, using exact Monte Carlo simulations on a model with perfectly flat bands and strictly local obstructed Wannier functions, we find that an attractive Hubbard interaction results in superconductivity as predicted by the RSI bound beyond mean field. Hence, obstructed bands are distinguished from trivial bands in the presence of interactions by the nonzero lower bound imposed on their superfluid weight.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗