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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↗

Disorder-dependent slopes of the upper critical field in nodal and nodeless superconductors

In this work we study the slopes of the upper critical field S = ∂H c2 /∂T at the superconducting transition temperature T c in anisotropic superconductors with transport (nonmagnetic) scattering employing the Ginzburg-Landau theory, developed for this case by Pokrovsky and Pokrovsky [Phys. Rev. B 54, 13275 (1996)]. We find unexpected behavior of the slopes for a d -wave superconductor and, in a more general case, of materials with line nodes in the order parameter. Specifically, the presence of line nodes causes S to decrease with increasing nonmagnetic scattering parameter P = ℏ/2πT c0 τ (T c0 is for the clean limit, τ is the scattering time), unlike the nodeless case where the slope increases. In a pure d -wave case, the slope changes from decreasing to increasing when the scattering parameter approaches P ≈ 0.91 P crit , where P crit ≈ 0.28, at which T c → 0, which implies the existence of a “gapless” state in d -wave superconductors with transport scattering in the interval, 0.91 P crit < P < P crit . Furthermore, we consider the mixed (s + d)-wave order parameter with four nodes on a cylindrical Fermi surface when the d part is dominant, or no nodes at all when the s-wave phase dominates. We find that the presence of nodes causes the slope S(P) to decrease initially with increasing P, whereas in the nodeless state, S(P) monotonically increases. Therefore, relatively straightforward measurements of the disorder dependence of the slope of H c2 at T c can help distinguish between nodal and nodeless order parameters, which is particularly useful for quickly assessing newly discovered superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Consistency between reflection momentum-resolved electron energy loss spectroscopy and optical spectroscopy measurements of the long-wavelength density response of Bi 2 Sr 2 CaCu 2 O 8 + x

The density fluctuation spectrum captures many fundamental properties of strange metals. Using momentum-resolved electron energy-loss spectroscopy (M-EELS), we recently showed that the density response of the strange metal Bi 2 Sr 2 CaCu 2 O 8+x (Bi-2212) at large momentum, q, exhibits a constant-in-frequency continuum reminiscent of the marginal Fermi liquid (MFL) hypothesis of the late 1980s. However, reconciling this observation with infrared (IR) optics experiments, which show a well-defined plasmon excitation at q ~ 0, has been challenging. Here we report M-EELS measurements of Bi-2212 using 4× improved momentum resolution, allowing us to reach the optical limit. For momenta q < 0.04 r.l.u., the M-EELS data show a plasmon feature that is quantitatively consistent with IR optics. For q > 0.04 r.l.u., the spectra become incoherent with an MFL-like, constant-in-frequency form. Here we speculate that, at finite frequency, ω, and nonzero q, some attribute of this Planckian metal randomizes the probe electron, causing it to lose information about its own momentum.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Local condensation of charge-4 ⁢e superconductivity at a nematic domain wall

In the fluctuation regime that precedes the onset of pairing in multi-component superconductors, such as nematic and chiral superconductors, the normal state is generally unstable towards the formation of charge-4e order – an exotic quantum state in which electrons form coherent quartets rather than Cooper pairs. However, charge-4e order is often suppressed by other competing composite orders, such as nematics. Importantly, the formation of nematic domains is unavoidable due to the long-range strains generated, leading to one-dimensional regions where the competing nematic order is suppressed. Here, we employ a real-space variational approach to demonstrate that, in such nematic domain walls, charge-4e order is locally condensed via a vestigial-order mechanism. Here, we explore the experimental manifestations of this effect and discuss materials in which it can be potentially observed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnetic phase diagram of a two-orbital model for bilayer nickelates with varying doping

Motivated by the recently discovered high-T c bilayer nickelate superconductor La 3⁢ Ni 2 ⁢O 7 , we comprehensively research a bilayer 2×2×2 cluster for different electronic densities n by using the Lanczos method. We also employ the random-phase approximation to quantify the first magnetic instability with increasing Hubbard coupling strength, also varying n. Based on the spin structure factor S(q), we have obtained a rich magnetic phase diagram in the plane defined by n and U/W, at fixed Hund coupling, where U is the Hubbard strength and W the bandwidth. We have observed numerous states, such as A-AFM, Stripes, G-AFM, and C-AFM. At half-filling, n=2 (two electrons per Ni site, corresponding to N=16 electrons), the canonical superexchange interaction leads to a robust G-AFM state (π,π,π) with antiferromagnetic couplings both in-plane and between layers. By increasing or decreasing electronic densities, ferromagnetic tendencies emerge from the “half-empty” and “half-full” mechanisms, leading to many other interesting magnetic tendencies. In addition, the spin-spin correlations become weaker both in the hole or electron doping regions compared with half-filling. At n=1.5 (or N=12), density corresponding to La 3 ⁢Ni 2 ⁢O 7 , we obtained the “Stripe 2” ground state (antiferromagnetic coupling in one in-plane direction, ferromagnetic coupling in the other, and antiferromagnetic coupling along the z axis) in the 2×2×2 cluster. In addition, we obtained a much stronger AFM coupling along the z axis than the magnetic coupling in the xy plane. The random-phase approximation calculations with varying n give very similar results as Lanczos, even though both techniques are based on quite different procedures. Additionally, a state with q/π=(0.6,0.6,1) close to the E-phase wavevector is found in our RPA calculations by slightly reducing the filling to n=1.25, possibly responsible for the E-phase SDW recently observed in experiments. In conclusion, our predictions can be tested by chemically doping La 3 ⁢Ni 2 ⁢O 7 .

36 MATERIALS SCIENCE↗

Interplay of the Spin Density Wave and a Possible Fulde-Ferrell-Larkin-Ovchinnikov State in CeCoIn 5 in Rotating Magnetic Field

The d-wave superconductor CeCoIn 5 has been proposed as a strong candidate for supporting the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state near the low-temperature boundary of its upper critical field. Neutron diffraction, however, finds spin-density-wave (SDW) order in this part of the phase diagram for field in the a-b plane, and evidence for the SDW disappears as the applied field is rotated toward the tetragonal c axis. It is important to understand the interplay between the SDW and a possible FFLO state in CeCoIn 5 , as the mere existence of an SDW does not necessarily exclude an FFLO state. In this work, based on a model constructed on the basis of available experiments, we show that an FFLO state competes with an SDW phase. The SDW state in CeCoIn 5 is stabilized when the field is directed close to the a-b plane. When the field is rotated toward the c axis, the FFLO state emerges, and the SDW phase disappears. In the FFLO state, the nodal planes with extra quasiparticles (where the superconducting order parameter is zero) are perpendicular to the field, and in the SDW phase, the quasiparticle density of states is reduced. We test this model prediction by measuring heat transported by normal quasiparticles in the superconducting state. As a function of field, we observe a reduction of thermal conductivity for field close to the a-b plane and an enhancement of thermal conductivity when field is close to the c axis, consistent with theoretical expectations. Our modeling and experiments, therefore, indicate the existence of the FFLO state when field is parallel to the c axis.

36 MATERIALS SCIENCE↗

Attractive Effect of a Strong Electronic Repulsion: The Physics of Vertex Divergences

While the breakdown of the perturbation expansion for the many-electron problem has several formal consequences, here we unveil its physical effect: flipping the sign of the effective electronic interaction in specific scattering channels. By decomposing local and uniform susceptibilities of the Hubbard model via their spectral representations, we prove how entering the nonperturbative regime causes an enhancement of the charge response, ultimately responsible for the phase-separation instabilities close to the Mott metal-insulator transition. Furthermore, our analysis opens a new route for understanding phase transitions in the nonperturbative regime and clarifies why attractive effects emerging from a strong repulsion can induce phase separations but not s-wave pairing or charge-density wave instabilities.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

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↗

Pseudospin Paramagnons and the Superconducting Dome in Magic Angle Twisted Bilayer Graphene

We present a theory of superconductivity in twisted bilayer graphene in which attraction is generated between electrons on the same honeycomb sublattice when the system is close to a sublattice polarization instability. The resulting Cooper pairs are spin-polarized valley singlets. Because the sublattice polarizability is mainly contributed by interband fluctuations, superconductivity occurs over a wide range of filling fraction. It is suppressed by (i) applying a sublattice polarizing field (generated by an aligned BN substrate) or (ii) changing moiré band filling to favor valley polarization. The enhanced intrasublattice attraction close to sublattice polarization instability is analogous to enhanced like-spin attraction in liquid 3 He near the melting curve and the enhanced valley-singlet repulsion close to valley-polarization instabilities is analogous to enhanced spin-singlet repulsion in metals that are close to a ferromagnetic instability. Here, we comment on the relationship between our pseudospin paramagnon model and the rich phenomenology of superconductivity in twisted bilayer and multilayer graphene.

36 MATERIALS SCIENCE↗

Surface Cooper-Pair Spin Waves in Triplet Superconductors

Here, we study the electrodynamics of spin triplet superconductors including dipolar interactions, which give rise to an interplay between the collective spin dynamics of the condensate and orbital Meissner screening currents. Within this theory, we identify a class of spin waves that originate from the coupled dynamics of the spin-symmetry breaking triplet order parameter and the electromagnetic field. In particular, we study magnetostatic spin wave modes that are localized to the sample surface. We show that these surface modes can be excited and detected using experimental techniques such as microwave spin wave resonance spectroscopy or nitrogen-vacancy magnetometry, and propose that the detection of these modes offers a means for the identification of spin triplet superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Pair Density Wave Order from Electron Repulsion

A pair density wave (PDW) is a superconductor whose order parameter is a periodic function of space, without an accompanying spatially uniform component. Since PDWs are not the outcome of a weak-coupling instability of a Fermi liquid, a generic pairing mechanism for PDW order has remained elusive. Here, we describe and solve models having robust PDW phases. To access the intermediate coupling limit, we invoke large-$N$ limits of Fermi liquids with repulsive BCS interactions that admit saddle point solutions. We show that the requirements for long-range PDW order are that the repulsive BCS couplings must be nonmonotonic in space and that their strength must exceed a threshold value. We obtain a phase diagram with both finite temperature transitions to PDW order and a $T = 0$ quantum critical point, where non-Fermi liquid behavior occurs.

2-dimensional systems↗

Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators

The topological superconducting state is a highly sought-after quantum state hosting topological order and Majorana excitations. Here, in this Letter, we explore the mechanism to realize the topological superconductivity (TSC) in the doped Mott insulators with time-reversal symmetry (TRS). Through large-scale density matrix renormalization group study of an extended triangular-lattice t–J model on the six- and eight-leg cylinders, we identify a d + id-wave chiral TSC with spontaneous TRS breaking, which is characterized by a Chern number C=2 and quasi-long-range superconducting order. We map out the quantum phase diagram with by tuning the next-nearest-neighbor (NNN) electron hopping and spin interaction. In the weaker NNN-coupling regime, we identify a pseudogaplike phase with a charge stripe order coexisting with fluctuating superconductivity, which can be tuned into d -wave superconductivity by increasing the doping level and system width. The TSC emerges in the intermediate-coupling regime, which has a transition to a d-wave superconducting phase with larger NNN couplings. The emergence of the TSC is driven by geometrical frustrations and hole dynamics which suppress spin correlation and charge order, leading to a topological quantum phase transition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evolution of the Magnetic Excitations in Electron-Doped La 2 - x Ce x CuO 4

Here we investigated the high energy spin excitations in electron-doped La 2-x Ce x CuO 4 , a cuprate superconductor, by resonant inelastic x-ray scattering (RIXS) measurements. Efforts were paid to disentangle the paramagnon signal from non-spin-flip spectral weight mixing in the RIXS spectrum at Q ∥ =(0.6π,0) and (0.9π,0) along the (1 0) direction. Our results show that, for doping level x from 0.07 to 0.185, the variation of the paramagnon excitation energy is marginal. We discuss the implication of our results in connection with the evolution of the electron correlation strength in this system.

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 of the alternating monolayer-trilayer phase of La 3 Ni 2 O 7

Recent studies of La 3 Ni 2 O 7 have identified a bilayer (2222) structure and an unexpected alternating monolayer-trilayer (1313) structure, both of which feature signatures of superconductivity near 80 K under high pressures. Using angle-resolved photoemission spectroscopy, we measure the electronic structure of 1313 samples. In contrast to the previously studied 2222 structure, we find that the 1313 structure hosts a flat band with a markedly different binding energy, as well as an additional electron pocket and band splittings. By comparison to local-density approximation calculations, we find renormalizations of the Ni-d z 2 and Ni-d x 2 -y 2 derived bands to be about 5 to 7 and about 4 respectively, suggesting strong correlation effects. These results reveal important differences in the electronic structure brought about by the distinct structural motifs with the same stoichiometry. Such differences may be relevant to the putative high temperature superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nodeless kagome superconductivity in LaRu 3 Si 2

We report muon spin rotation (μSR) experiments together with first-principles calculations on microscopic properties of superconductivity in the kagome superconductor LaRu 3 Si 2 with T c ≃ 7K. Below Tc, μSR reveals type-II superconductivity with a single s-wave gap, which is robust against hydrostatic pressure up to 2 GPa. We find that the calculated normal state band structure features a kagome flat band, and Dirac as well as van Hove points formed by the Ru-dz 2 orbitals near the Fermi level. We also find that electron-phonon coupling alone can only reproduce a small fraction of T c from calculations, which suggests other factors in enhancing T c such as the correlation effect from the kagome flat band, the van Hove point on the kagome lattice, and the high density of states from narrow kagome bands. Our experiments and calculations taken together point to nodeless moderate coupling kagome superconductivity in LaRu 3 Si 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tuning charge density wave order and superconductivity in the kagome metals KV 3 Sb 5 – x Sn x and RbV 3 Sb 5 – x Sn x

The family of AV 3 Sb 5 (A = K, Rb, Cs) kagome metals exhibits charge density wave (CDW) order, proposed to be chiral, followed by a lower temperature superconducting state. Recent studies have proposed the importance of band structure saddle points proximal to the Fermi energy in governing these two transitions. Here we show the effects of hole doping achieved via chemical substitution of Sn for Sb on the CDW and superconducting states in both KV 3 Sb 5 and RbV 3 Sb 5 and generate a phase diagram. Furthermore, hole doping lifts the Γ pocket and van Hove singularities toward E F causing the superconducting T C in both systems to increase to about 4.5 K, while rapidly suppressing the CDW state.

36 MATERIALS SCIENCE↗

Metastable phase of UTe 2 formed under high pressure above 5 GPa

Uranium ditelluride (UTe 2 ) has attracted recent interest due to its unique superconducting properties, which include the potential for a topological odd-parity superconducting state. Recently, ac-calorimetry measurements under pressure indicate a change in the ground state of UTe 2 from superconducting to antiferromagnetic at 1.4 GPa. In this work, we investigate the effect of pressure on the crystal structure of UTe 2 up to 25 GPa at room temperature using x-ray diffraction. We find that UTe 2 , which at ambient conditions has an orthorhombic (Immm) structure, transforms to a body-centered tetragonal (I4/mmm) structure at 5 GPa in a quasihydrostatic neon (Ne) pressure-transmitting medium. In the absence of a pressure-transmitting medium, this transformation occurs between 5 and 8 GPa. The data were fit with a third-order Birch-Murnaghan equation of state resulting in values of B 0 = 46.0 ± 0.6 GPa , B' = 9.3 ± 0.5 (no pressure medium), and B 0 = 42.5 ± 2.0 GPa , B' = 9.3 (fixed) (neon pressure medium) for the Immm phase. For the I4/mmm phase, B 0 = 78.9 ± 0.5 GPa GPa and B' = 4.2 ± 0.1 (no pressure-transmitting medium), and B 0 = 70.0 ± 1.1 GPa and B' = 4.1 ± 0.2 (neon pressure medium). The high-pressure tetragonal phase is retained after decompression to ambient pressure, with approximately 30% remaining after 2 days. We argue that the observed phase transition into a higher-symmetry structure at P ~ 5 GPa (orthorhombic to tetragonal) is accompanied by an increase in the shortest distance between uranium atoms from 3.6 Å (orthorhombic) to 3.9 Å (tetragonal), which suggests localization of the 5ƒ electrons, albeit with a 10.7% decrease in volume.

36 MATERIALS SCIENCE↗