Mixed Singlet Research Articles

Probing magnetic and triplet correlations in spin-split superconductors with magnetic impurities

A superconductor (SC) in proximity to a ferromagnetic insulator (FMI) is predicted to exhibit mixed singlet and triplet correlations. The magnetic proximity effect of FMI spin splits the energy of Bogoliubov excitations and leads to a spin polarization at the surface for superconducting films that are thinner than the superconducting coherence length. In this work, we study manifestations of these phenomena in the properties of a magnetic impurity coupled via Kondo coupling to this FMI/SC system. Using the numerical renormalization group (NRG) method, we compute the properties of the ground state and low-lying excited states of a model that incorporates the Kondo interaction and a Ruderman-Kittel-Kasuya-Yosida (RKKY)-like interaction with the surface spin polarization. Our main finding is an energy splitting of the lowest even fermion-parity states caused by the proximity to the FMI. As the Kondo coupling increases, the splitting grows and saturates to a universal value equal to twice the exchange field of the FMI. We introduce a two-site model that can be solved analytically and provides a qualitative understanding of this and other NRG results. In addition, using perturbation theory, we demonstrate that the mechanism behind the splitting involves the RKKY field and the triplet correlations of the spin-split superconductor. A scaling analysis combined with NRG shows that the splitting can be written as a single-parameter scaling function of the ratio of the Kondo temperature and the superconducting gap, which is also numerically obtained. Published by the American Physical Society 2024

Enhanced Superconductivity and Upper Critical Field in Ta‐Doped Weyl Semimetal Td‐MoTe2 (Adv. Mater. 19/2023)

Exotic Superconductivity In article number 2207841, Fucong Fei, Zhicheng Zhong, Fengqi Song, Xuefeng Wang, and co-workers report boosted superconductivity with a transition temperature of about 7.5 K in Ta-doped MoTe2 single crystals under ambient pressure. An enhanced upper critical field beyond the Pauli limit is also observed in Ta-doped Weyl semimetal Td-MoTe2, which is likely due to the mixed singlet–triplet superconductivity.

Enhanced Superconductivity and Upper Critical Field in Ta-Doped Weyl Semimetal Td -MoTe2.

2D transition metal dichalcogenides are promising platforms for next-generation electronics and spintronics. The layered Weyl semimetal (W,Mo)Te2 series features structural phase transition, nonsaturated magnetoresistance, superconductivity, and exotic topological physics. However, the superconducting critical temperature of the bulk (W,Mo)Te2 remains ultralow without applying a high pressure. Here, the significantly enhanced superconductivity is observed with a transition temperature as large as about 7.5 K in bulk Mo1- x Tax Te2 single crystals upon Ta doping (0 ≤ x≤ 0.22), which is attributed to an enrichment of density of states at the Fermi level. In addition, an enhanced perpendicular upper critical field of 14.5 T exceeding the Pauli limit is also observed in Td -phase Mo1- x Tax Te2 (x= 0.08), indicating the possible emergence of unconventional mixed singlet-triplet superconductivity owing to the inversion symmetry breaking. This work provides a new pathway for exploring the exotic superconductivity and topological physics in transition metal dichalcogenides.

Temperature Tuning of Coherent Mixing between States Driving Singlet Fission in a Spiro-Fused Terrylenediimide Dimer.

The excited-state dynamics of a spiro-fused terrylene-3,4:11,12-bis(dicarboximide) (TDI) dimer (sTDI2) in toluene and 2-methyltetrahydrofuran (mTHF) were investigated as a function of temperature using femtosecond- and nanosecond-transient absorption spectroscopy, as well as two-dimensional electronic spectroscopy. The spiro conjugation and the corresponding geometry of this compound guarantee a short intermonomer distance along with a partial orbital overlap between the orthogonal TDI π-electron systems, providing electronic coupling between the TDIs. Photoexcitation of sTDI2 in toluene, a low dielectric solvent, at 295 K, results in the ultrafast formation of a state composed of a coherent mixture of singlet 1(S1S0), multiexciton 1(T1T1), and charge-transfer (CT) electronic characters. This mixed species decays to decorrelated triplet states on the nanosecond timescale, completing the process of intramolecular singlet fission (SF) in sTDI2. Upon decreasing the temperature from 295 to 200 K, the contribution of the 1(T1T1) state to the mixed species decreases concurrently with an increase in the CT state character. We attribute this behavior to the variation in the vibrational energy level alignment between the states comprising the mixture due to changes in the temperature and hence the local dielectric environment. In contrast, photoexcitation of sTDI2 in more polar mTHF at 295 K results in the formation of a mixed singlet and CT state before undergoing symmetry-breaking charge separation, owing to the increased stabilization of the CT state in the medium. However, in glassy mTHF at 85 K, photoexcited sTDI2 exhibits discernible multiexciton character, comparable to that observed in toluene at 200 K, which we rationalize by the similarity of the dielectric constants under these two sets of conditions. These observations of mixed states of varying diabatic contributions over the range of experimental conditions show that the temperature and the static dielectric constant can directly control the composition of the electronically mixed excited state of sTDI2 and thus the fate of the SF process.

Atomic Line Defects and Topological Superconductivity in Unconventional Superconductors

Topological superconductors (TSCs) are correlated quantum states with simultaneous off-diagonal long-range order and nontrivial topological invariants. They produce gapless or zero energy boundary excitations, including Majorana zero modes and chiral Majorana edge states with topologically protected phase coherence essential for fault-tolerant quantum computing. Candidate TSCs are very rare in nature. Here, we propose a novel route toward emergent quasi-one-dimensional (1D) TSCs in naturally embedded quantum structures such as atomic line defects in unconventional spin-singlet $s$-wave and $d$-wave superconductors. We show that inversion symmetry breaking and charge transfer due to the missing atoms lead to the occupation of incipient impurity bands and mixed parity spin singlet and triplet Cooper pairing of neighboring electrons traversing the line defect. Nontrivial topological invariants arise and occupy a large part of the parameter space, including the time reversal symmetry breaking Zeeman coupling due to applied magnetic field or defect-induced magnetism, creating TSCs in different topological classes with robust Majorana zero modes at both ends of the line defect. Beyond providing a novel mechanism for the recent discovery of zero-energy bound states at both ends of an atomic line defect in monolayer Fe(Te,Se) superconductors, the findings pave the way for new material realizations of the simplest and most robust 1D TSCs using embedded quantum structures in unconventional superconductors with large pairing energy gaps and high transition temperatures.

Influence of Vibronic Coupling on Ultrafast Singlet Fission in a Linear Terrylenediimide Dimer.

Singlet fission (SF) is a photophysical process capable of boosting the efficiency of solar cells. Recent experimental investigations into the mechanism of SF provide evidence for coherent mixing between the singlet, triplet, and charge transfer basis states. Up until now, this interpretation has largely focused on electronic interactions; however, nuclear motions resulting in vibronic coupling have been suggested to support rapid and efficient SF in organic chromophore assemblies. Further information about the complex interactions between vibronic excited states is needed to understand the potential role of this coupling in SF. Here, we report mixed singlet and correlated triplet pair states giving rise to sub-50 fs SF in a terrylene-3,4:11,12-bis(dicarboximide) (TDI) dimer in which the two TDI molecules are covalently linked by a direct N-N connection at one of their imide positions, leading to a linear dimer with perpendicular TDI π systems. We observe the transfer of low-frequency coherent wavepackets between the initial predominantly singlet states to the product triplet-dominated states. This implies a non-negligible dependence of SF on nonadiabatic coupling in this dimer. We interpret our experimental results in the framework of a modified Holstein Hamiltonian, which predicts that vibronic interactions between low-frequency singlet modes and high-frequency correlated triplet pair motions lead to mixing of the pure basis states. These results highlight how nonadiabatic mixing can shape the complex potential energy landscape underlying ultrafast SF.

Multireference Ground and Excited State Electronic Structures of Free- versus Iron Porphyrin-Carbenes.

Iron porphyrin carbenes (IPCs) are important reaction intermediates in engineered carbene transferase enzymes and homogeneous catalysis. However, discrepancies between theory and experiment complicate the understanding of IPC electronic structure. In the literature, this has been framed as whether the ground state is an open- vs closed-shell singlet (OSS vs CSS). Here we investigate the structurally dependent ground and excited spin-state energetics of a free carbene and its IPC analogs with variable trans axial ligands. In particular, for IPCs, multireference ab initio wave function methods are more consistent with experiment and predict a mixed singlet ground state that is dominated by the CSS (Fe(II) ← {:C(X)Y}0) configuration (i.e., electrophilic carbene) but that also has a small, non-negligible contribution from an Fe(III)-{C(X)Y}-• configuration (hole in d(xz), i.e., radical carbene). In the multireference approach, the "OSS-like" excited states are metal-to-ligand charge transfer (MLCT) in nature and are energetically well above the CSS-dominated ground state. The first, lowest energy of these "OSS-like" excited states is predicted to be heavily weighted toward the Fe(III)-{C(X)Y}-• (hole in d(yz)) configuration. As expected from exchange considerations, this state falls energetically above a triplet of the same configuration. Furthermore, potential energy surfaces (PESs) along the IPC Fe-C(carbene) bond elongation exhibit increasingly strong mixings between CSS/OSS characters, with the Fe(III)-{C(X)Y}-• configuration (hole in d(xz)) growing in weight in the ground state during bond elongation. The relative degree of electrophilic/radical carbene character along this structurally relevant PES can potentially play a role in reactivity and selectivity patterns in catalysis. Future studies on IPC reaction coordinates should evaluate contributions from ground and excited state multireference character.

Mass-like band-gap creation in superconducting topological insulator due to mixed singlet and triplet states

We investigate proximity-induced mixed spin-singlet and spin-triplet superconducting state on the surface states of a topological insulator. Such hybrid structure features fundamentally distinct electron–hole excitations and resulting effective superconducting subgap. Studying the particle-hole and time-reversal symmetry properties of the mixed state Dirac–Bogoliubov–de Gennes effective Hamiltonian gives rise to manifesting possible topological phase exchange of surface states, since the mixed-spin channels leads to appearance of a band gap on the surface states. This can be verified by evaluating topological invariant winding number for chiral eigenstates, via the introducing a chiral symmetry operator. We interestingly find the role of mixed-spin superconducting state as creating a mass-like gap in topological insulator by means of appearing new mixed-spin channels and . The interplay between superconducting spin-singlet and triplet correlations actually results in gaped surface states, where the size of gap can be controlled by tuning the relative s- and p -waves pairing potentials. We show that the system is in different topology classes by means of using chiral or no-chiral spin-triplet symmetry. In addition, the resulting effective superconductor subgap manipulated at the Fermi surface presents a complicated dependency on mixed-spin channels. Furthermore, we investigate the resulting subgap tunneling conductance in N/S, and also Josephson current in S/I/S junctions to unveil the influence of effective symmetry of mixed superconducting gap. The results can pave the way to realize the effective superconducting gap in noncentrosymmetric superconductors with mixed-spin state.

Parity-mixing superconducting phase in the Rashba-Hubbard model and its topological properties from dynamical mean-field theory

We investigate parity-mixing superconductivity in the two-dimensional Hubbard model with Rashba spin-orbit coupling, using Cellular Dynamical Mean-Field Theory (CDMFT). A superconducting state with mixed singlet $d$-wave and triplet $p$-wave character is found in a wide range of doping. The singlet component decreases with the amplitude of the Rashba spin-orbit coupling, whereas the triplet component increases, but both disappear at about 20\% doping. The effect of a Zeeman field is also investigated; it tends to suppress both types of superconductivity, but induces nontrivial topological properties: the computed bulk Chern number is nonzero in the mixed superconductivity phase, at least in the underdoped region. A strong suppression of the excitation gap occurs slightly after optimal doping; this might be the sign of a topological transition within the superconducting dome.

Spin-selective coupling to Majorana zero modes in mixed singlet and triplet superconducting nanowires

We theoretically investigate the transport properties of a quasi one dimensional ferromagnet-superconductor junction where the superconductor consists of mixed singlet and triplet pairings. We show that the relative orientation of the stoner field ($\bf{\tilde{h}}$) in the ferromagnetic lead and the $\bf{d}$ vector of the superconductor acts like a on-off switch for the zero bias conductance of the device. In the regime, where triplet pairing amplitude dominates over the singlet counterpart (topological phase), a pair of Majorana zero modes appear at each end of the superconducting part of the nanowire. When $\bf{\tilde{h}}$ is parallel or anti-parallel to the $\bf{d}$ vector, transport gets completely blocked due to blockage in pairing while, when $\bf{\tilde{h}}$ and $\bf{d}$ are perpendicular to each other, the zero energy two terminal differential conductance spectra exhibits sharp transition from $4e^2/h$ to $2e^2/h$ as the magnetization strength in the lead becomes larger than the chemical potential indicating the spin selective coupling of pair of Majorana zero modes to the lead.

Thermal transport in topological-insulator-based superconducting hybrid structures with mixed singlet and triplet pairing states

In the framework of the Bogoliubov–de Gennes equation, we investigate the thermal transport properties in topological-insulator-based superconducting hybrid structures with mixed spin-singlet and spin-triplet pairing states, and emphasize the different manifestations of the spin-singlet and spin-triplet pairing states in the thermal transport signatures. It is revealed that the temperature-dependent differential thermal conductance strongly depends on the components of the pairing state, and the negative differential thermal conductance only occurs in the spin-singlet pairing state dominated regime. It is also found that the thermal conductance is profoundly sensitive to the components of the pairing state. In the spin-singlet pairing state controlled regime, the thermal conductance obviously oscillates with the phase difference and junction length. With increasing the proportion of the spin-triplet pairing state, the oscillating characteristic of the thermal conductance fades out distinctly. These results suggest an alternative route for distinguishing the components of pairing states in topological-insulator-based superconducting hybrid structures.

Partial in Situ Reduction of Copper(II) Resulting in One-Pot Formation of 2D Neutral and 3D Cationic Copper(I) Iodide–Pyrazine Coordination Polymers: Structure and Emissive Properties

On the way to copper(I) iodide coordination polymers with specific luminescent properties, the in situ reduction of Cu(II) in the presence of KI and bidentate N-heteroatomic ligand, either pyrazine (pyz) or 4,4'-bipyridine (bpy), resulted in one two-dimensional and two three-dimensional new coordination networks. Starting from Cu(NO3)2·3H2O in the presence of pyz, successive precipitation of known yellow [(CuII)2(pyz)]n, new orange [CuII(pyz)]n, and new dark blue {[CuI(pyz)2]·I5}n polymeric solids was observed. Starting from the same salt in the presence of bpy resulted in the successive precipitation of known yellow [(CuII)2(bpy)]n and new brown {[CuII(NO3)(bpy)2]·I3·(dmf·H2O)}n coordination polymers. By using either Cu(CH3COO)2·H2O or Cu(BF4)2 as starting materials, both known forms, yellow [(CuII)2(bpy)]n and orange [CuII(bpy)]n, precipitated successively. The new solids were characterized by IR spectroscopy and X-ray analysis. [CuII(pyz)]n represents the missing member in the row of two-dimensional coordination networks with general formula [CuIX(pyz)]n (X = Cl, Br, I). Its steady state and time-resolved characterization together with DFT and TDDFT calculations revealed that the emission at room temperature is mainly delayed fluorescence originating from mixed singlet metal-to-ligand charge transfer and halide-to-ligand charge transfer states, while that at 77 K is phosphorescence, associated with the small singlet-triplet energy differences (ΔE = 70 meV).

Transport and noise properties of a normal metal–superconductor–normal metal junction with mixed singlet and chiral triplet pairings

We study transport and zero frequency shot noise properties of a normal metal–superconductor–normal metal (NSN) junction, with the superconductor having mixed singlet and chiral triplet pairings. We show that in the subgapped regime when the chiral triplet pairing amplitude dominates over that of the singlet, a resonance phenomena emerges out at zero energy where all the quantum mechanical scattering probabilities acquire a value of 0.25. At the resonance, crossed Andreev reflection mediating through such junction, acquires a zero energy peak. This reflects as a zero energy peak in the conductance as well depending on the doping concentration. We also investigate shot noise for this system and show that shot noise cross-correlation is negative in the subgapped regime when the triplet pairing dominates over the singlet one. The latter is in sharp contrast to the positive shot noise obtained when the singlet pairing is the dominating one.

Mixed parity pairing in a dipolar gas

We show that fermionic dipoles in a two-layer geometry form Cooper pairs with both singlet and triplet components when they are tilted with respect to the normal of the planes. The mixed parity pairing arises because the interaction between dipoles in the two different layers is not inversion symmetric. We use an efficient eigenvalue approach to calculate the zero-temperature phase diagram of the system as a function of the dipole orientation and the layer distance. The phase diagram contains purely triplet as well as mixed singlet and triplet superfluid phases. We show in detail how the pair wave function for dipoles residing in different layers smoothly changes from singlet to triplet symmetry as the orientation of the dipoles is changed. Our results indicate that dipolar quantum gases can be used to unambiguously observe mixed parity pairing.

Near-UV photodissociation dynamics of CH₂I₂.

The near-UV photodissociation dynamics of CH2I2 has been investigated using a combination of velocity-map (slice) ion imaging and ab initio calculations characterizing the excited states. Ground state I((2)P3/2) and spin-orbit excited I*((2)P1/2) atoms were probed using 2 + 1 resonance-enhanced multiphoton ionization (REMPI) or with single-photon VUV ionization. Two-color ion images were recorded at pump wavelengths of 355 nm, 266 nm and 248 nm, and one-color ion images at the REMPI wavelengths of ∼304 nm and ∼280 nm. Analysis of the ion images shows that, regardless of iodine spin-orbit state, ∼20% of the available energy is partitioned into translation E(T) at all excitation wavelengths indicating that the CH2I co-fragment is formed highly internally excited. The translational energy distributions comprise a slow, "statistical" component that peaks near zero and faster components that peak away from zero. The slow component makes an increasingly large contribution to the distribution as the excitation wavelength is decreased. The C-I bond dissociation energy of D0 = 2.155 ± 0.008 eV is obtained from the trend in the E(T) release of the faster components with increasing excitation energy. The I and I* ion images are anisotropic, indicating prompt dissociation, and are characterized by β parameters that become increasingly positive with increasing E(T). The decrease in β at lower translational energies can be attributed to deviation from axial recoil. MRCI calculations including spin-orbit coupling have been performed to identify the overlapping features in the absorption spectrum and characterize one-dimensional cuts through the electronically excited potential energy surfaces. The excited states are of significantly mixed singlet and triplet character. At longer wavelengths, excitation directly accesses repulsive states primarily of B1 symmetry, consistent with the observed 〈β〉, while shorter wavelengths accesses bound states, also of B1 symmetry that are crossed by repulsive states.

Domain walls in superconductors: Andreev bound states and tunneling features

Domain walls can be formed in superconductors with a discrete degeneracy of the ground state, for instance, due to the breaking of time reversal symmetry. We study all cases where the formation of domain walls is possible in a tetragonal superconductor with the point group ${D}_{4h}$. We discuss both triplet and mixed singlet order parameters. It is found that in all cases the domain walls support subgap Andreev bound states, whose energies strongly depend on the direction of semiclassical propagation. The bound state contribution to the density of quasiparticle states exhibits peculiar features, which can be observed in tunneling experiments.

Transport signatures of superconducting hybrids with mixed singlet and chiral triplet states

We propose a model for a superconductor where both spin-singlet and chiral triplet pairing amplitudes can coexist. By solving the Bogoliubov--de Gennes equations with a general pair potential that accounts for both spin states we study experimental signatures of normal metal and superconductor hybrids. The interplay between the spin-singlet and triplet correlations manifests in the appearance of two effective gaps. When the amplitude of the spin-triplet component is stronger than that of the spin singlet, a topological phase transition into a nontrivial regime occurs. As a result, the normal metal--superconductor conductance evolves from a conventional gap profile onto an unconventional zero-bias peak. Additionally, in the topologically nontrivial phase, Andreev bound states formed at Josephson junctions present zero-energy modes; the number of those modes depends on the relative chirality of the junction. Finally, we present results for the current-phase relation and the temperature dependence of the Josephson critical current within both topological phases for several system parameters.

Effects of the Rashba-like spin–orbit coupling in ferromagnetic superconductors

Interplay between ferromagnetism and superconductivity in ferromagnetic superconductors has been studied by considering the Rashba-like spin–orbit coupling (RSOC). The electron band is splited into two pseudospin bands due to the RSOC and intrinsic magnetization. Quasiparticles in the pseudospin bands are assumed to form A1-phase-like p-wave Cooper pairs, and thus a mixed spin singlet–triplet superconducting state is induced. The singlet and triplet superconducting gaps in electron representation can be obtained from the quasiparticles pairing order parameters. It suggests that the magnetization is suppressed by the RSOC, whereas both the spin-singlet gap and the ratio of the singlet- to triplet-gaps are enhanced with increasing RSOC.

Fermion pairing across a dipolar interaction induced resonance.

It is known from the solution of the two-body problem that an anisotropic dipolar interaction can give rise to s-wave scattering resonances, which are named dipolar interaction induced resonances (DIIR). In this Letter, we study the zero-temperature many-body physics of a two-component Fermi gas across a DIIR. In the low-density regime, it is very striking that the resulting pairing order parameter is a nearly isotropic singlet pairing and the physics can be well described by an s-wave resonant interaction potential with finite range conditions, despite the anisotropic nature of the dipolar interaction. The pairing energy is as strong as a unitary Fermi gas near a magnetic Feshbach resonance. In the high-density regime, the anisotropic effect plays an important role. We find phase transitions from singlet pairing to a state with mixed singlet and triplet pairing and then from mixed pairing to pure triplet pairing. The state with mixed pairing spontaneously breaks the time-reversal symmetry.

Probing Anisotropic Superfluidity in Atomic Fermi Gases with Rashba Spin-Orbit Coupling

Motivated by the prospect of realizing a Fermi gas with a synthetic non-Abelian gauge field, we investigate theoretically a strongly interacting Fermi gas in the presence of a Rashba spin-orbit coupling. As the twofold spin degeneracy is lifted by spin-orbit interaction, bound pairs with mixed singlet and triplet components emerge, leading to an anisotropic superfluid. We calculate the relevant physical quantities, such as the momentum distribution, the single-particle spectral function, and the spin structure factor, that characterize the system.