Spin-singlet Superconductivity Research Articles

Light-induced switching between singlet and triplet superconducting states

While the search for topological triplet-pairing superconductivity has remained a challenge, recent developments in optically stabilizing metastable superconducting states suggest a new route to realizing this elusive phase. Here, we devise a testable theory of competing superconducting orders that permits ultrafast switching to an opposite-parity superconducting phase in centrosymmetric crystals with strong spin-orbit coupling. Using both microscopic and phenomenological models, we show that dynamical inversion symmetry breaking with a tailored light pulse can induce odd-parity (spin triplet) order parameter oscillations in a conventional even-parity (spin singlet) superconductor, which when driven strongly can send the system to a competing minimum in its free energy landscape. Our results provide new guiding principles for engineering unconventional electronic phases using light, suggesting a fundamentally non-equilibrium route toward realizing topological superconductivity.

Unequivocal Identification of Spin-Triplet and Spin-Singlet Superconductors with Upper Critical Field and Flux Quantization.

Spin-triplet superconductors play central roles in Majorana physics and quantum computing but are difficult to identify. We show the methods of kink-point upper critical field and flux quantization in superconducting rings can unequivocally identify spin-singlet, spin-triplet in centrosymmetric superconductors, and singlet-triplet admixture in noncentrosymmetric superconductors, as realized in γ-BiPd, β-Bi_{2}Pd, and α-BiPd, respectively. Our findings are essential for identifying triplet superconductors and exploring their quantum properties.

Impurity and hybridization effects on the symmetry classification and magnetic response function of a two-band superconductor with interband pairing order

Abstract The effects of hybridization and impurity (magnetic and nonmagnetic) potentials on the pairing symmetries and magnetic response of a two-band superconductor with an equal-time s-wave interband pairing order parameter in the framework of Green’s function technique are investigated theoretically. First, the effects of spin-independent and spin-dependent hybridization on the generation of even- or odd-frequency Cooper pairs which determines the symmetry classification and the response of the superconductor are studied. Next, the impurity effect on creating different symmetry classes and the kernel response function of a two-band superconductor are discussed. By separating the contributions of even- and odd-frequency pairing to the Meissner kernel, it is shown that the competition between these two terms determines the total Meissner effect of the superconductor. For a two-band spin-singlet superconductor, nonmagnetic impurity scatterings do not change transition temperature according to Anderson’s theorem, while both intra- and interband magnetic impurity scattering cause superconducting transition temperature suppression with the rate following the Abrikosov–Gor’kov theory. For spin-triplet pairing, interband magnetic scattering has no impact on pair breaking, whereas intraband magnetic scattering acts as a pair breaker and suppresses the transition temperature in the Born limit. In this case, the odd-frequency superconducting pairs can be induced in the simultaneous presence of both intra- and interband magnetic impurities. Thus, by controlling the concentration of magnetic impurities, it is possible to engineer triplet-pairing odd-frequency superconductors with a total diamagnetic Meissner response which stabilizes the superconducting state. This technique opens up an avenue for designing stable odd-frequency superconductors.

Synthetic complex Weyl superconductors, chiral Josephson effect and synthetic half-vortices

We show that the most generic form of spin-singlet superconducting order parameter for chiral fermions in systems with broken time reversal symmetry and inversion symmetry is of the Delta _s+igamma ^5Delta _5 where Delta _s is the usual order parameter and Delta _5 is the pseudo-scalar order parameter. After factoring out the U(1) phase e^{iphi }, this form of superconductivity admits yet additional complex structure in the plane of (Delta _s,Delta _5). The polar angle chi in this plane, which we call the chiral angle, can be controlled by the external flux bias. We present a synthetic setup based on stacking of topological insulators (TIs) and superconductors (SCs). Alternatively flux biasing the superconductors with a fluxes pm Phi leads to Delta _5=Delta _0 sin (chi ), where Delta _0 is the superconducting order parameter of the SC layers, and the chiral angle chi ={2pi }Phi /Phi _0 is directly given by the flux Phi in units of the flux quantum Phi _0=h/(2e). This can be used as a building block to construct a two-dimensional Josephson array. In this setup chi will be a background field defining a pseudoscalar Delta _5 that can be tuned to desired configuration. While in a uniform background field Delta _5 the dynamics of phi is given by standard XY model and its associated vortices, a staggered background pm Delta _5 (or equivalently chi and chi +pi in alternating lattice sites) creates a new set of minima for the phi field that will support half-vortex excitations. An isolated single engineered “half-vortex” in the chi field in an otherwise uniform background will bind a phi -half-vortex. This is similar to the way a p-wave superconducting vortex core binds a Majorana fermion.

Violation of the orbital depairing limit in a nonunitary state: High-field phase in the heavy fermion superconductor UTe2

A theoretical study is reported on the origin of an extremely high upper critical field $\ensuremath{\sim}70$ T observed in ${\mathrm{UTe}}_{2}$ with the transition temperature ${T}_{\mathrm{c}}=1.6$--2 K, which exceeds the conventional orbital depairing limit set by the Fermi velocity and ${T}_{\mathrm{c}}$ for a superconductor (SC) in the clean limit. We investigate possible violation of the orbital limit in terms of a spin-triplet nonunitary state, which is effectively coupled to the underlying magnetization induced by an external field. This produces the reduced internal field by canceling it via magnetization. We formulate a theory within the Ginzburg-Landau framework to describe this orbital limit violation and analyze experimental data on the upper critical fields for various field orientations in ${\mathrm{UTe}}_{2}$. We show that the orbital limit violation for a spin-triplet SC, as well as the Pauli-Clogston limit violation for a spin-singlet SC, constitutes a complete and useful framework for examining the high field physics of superconductors in the clean limit.

Spin-singlet topological superconductivity in the attractive Rashba-Hubbard model

Fully gapped, spin-singlet superconductors with antisymmetric spin-orbit coupling in a Zeeman magnetic field provide a promising route to realize superconducting states with non-Abelian topological order and therefore fault-tolerant quantum computation. Here we use a quantum Monte Carlo dynamical cluster approximation to study the superconducting properties of a doped two-dimensional attractive Hubbard model with Rashba spin-orbit coupling in a Zeeman magnetic field. We generally find that the Rashba coupling has a beneficial effect towards $s$-wave superconductivity. In the presence of a finite Zeeman field, when superconductivity is suppressed by Pauli pair breaking, the Rashba coupling counteracts the spin imbalance created by the Zeeman field by mixing the spins, and thus restores superconductivity at finite temperatures. We show that this favorable effect of the spin-orbit coupling is traced to a spin-flip driven enhancement of the amplitude for the propagation of a pair of electrons in time-reversed states. Moreover, by inspecting the Fermi surface of the interacting model, we show that for sufficiently large Rashba coupling and Zeeman field, the superconducting state is expected to be topologically nontrivial.

Stabilizing Fluctuating Spin-Triplet Superconductivity in Graphene via Induced Spin-Orbit Coupling.

A recent experiment showed that a proximity-induced Ising spin-orbit coupling enhances the spin-triplet superconductivity in Bernal bilayer graphene. Here, we show that, due to the nearly perfect spin rotation symmetry of graphene, the fluctuations of the spin orientation of the triplet order parameter suppress the superconducting transition to nearly zero temperature. Our analysis shows that both an Ising spin-orbit coupling and an in-plane magnetic field can eliminate these low-lying fluctuations and can greatly enhance the transition temperature, consistent with the recent experiment. Our model also suggests the possible existence of a phase at small anisotropy and magnetic field which exhibits quasilong-range ordered spin-singlet charge 4e superconductivity, even while the triplet 2e superconducting order only exhibits short-ranged correlations. Finally, we discuss relevant experimental signatures.

Majorana vortex modes in spin-singlet chiral superconductors with noncollinear spin ordering: Local density of states study

In the present study topologically nontrivial edge and vortex bound states are described in the coexistence phase of chiral spin-singlet superconductivity and noncollinear spin ordering on a triangular lattice in the presence of few (up to four) vortices. We consider the topological phase transition induced by the magnetic order between the phase hosting Majorana modes and the initial phase of the chiral d-wave superconductivity supporting non-Majorana modes which is also topologically nontrivial. The change of the excitation spectrum at the critical point is obtained in both cases of open and periodic boundary conditions in the presence of vortices. It is proved that zero energy Majorana modes localized at vortex cores are caused by noncollinear long-range magnetic ordering. Even though nearby excitation energies of subgap states including the edge-localized and vortex-localized states are very close to each other, the energy difference between different vortex bound states is an order of magnitude higher. This difference determines the energy gap for Majorana vortex modes separating them from other vortex bound states. It is found that even in the presence of noncollinear spin ordering its value can be estimated from the excitation energy of vortex bound states in the pure chiral d-wave state for the nonmagnetic case. By studying local density of states near the vortex cores the possibility to experimentally detect the described Majorana vortex modes by scanning tunneling microscopy is discussed. It is demonstrated that Majorana vortex modes and Majorana antivortex modes induced by noncollinear magnetism have different features in energy and spatially resolved density of states due to the chiral symmetry on the superconducting order parameter.

Parity Transition of Spin-Singlet Superconductivity Using Sublattice Degrees of Freedom.

Recently, a superconducting (SC) transition from low-field (LF) to high-field (HF) SC states was reported in CeRh_{2}As_{2}, indicating the existence of multiple SC states. It has been theoretically noted that the existence of two Ce sites in the unit cell, the so-called sublattice degrees of freedom owing to the local inversion symmetry breaking at the Ce sites, can lead to the appearance of multiple SC phases even under an interaction inducing spin-singlet superconductivity. CeRh_{2}As_{2} is considered as the first example of multiple SC phases owing to this sublattice degree of freedom. However, microscopic information about the SC states has not yet been reported. In this study, we measured the SC spin susceptibility at two crystallographically inequivalent As sites using nuclear magnetic resonance for various magnetic fields. Our experimental results strongly indicate a spin-singlet state in both SC phases. In addition, the antiferromagnetic phase, which appears within the SC phase, only coexists with the LF SC phase; there is no sign of magnetic ordering in the HF SC phase. The present Letter reveals unique SC properties originating from the locally noncentrosymmetric characteristics.

Theory of criticality for quantum ferroelectric metals

Although ferroelectricity in metals was long considered to be impossible, a large family of materials hosting both states has been discovered in recent years, and these properties are often strongly coupled. The authors investigate here the quantum phase transition between the ferroelectric and paraelectric states in metals. They find unique quantum critical properties stemming from unconventional inversion-breaking fluctuations, along with enhanced tendencies to both spin singlet and triplet superconductivity, and provide protocols for strain control of the quantum state of these systems.

Long-range skin Josephson supercurrent across a van der Waals ferromagnet

The emerging field of superconducting spintronics promises new quantum device architectures without energy dissipation. When entering a ferromagnet, a supercurrent commonly behaves as a spin singlet that decays rapidly; in contrast, a spin-triplet supercurrent can transport over much longer distances, and is therefore more desirable, but so far has been observed much less frequently. Here, by using the van der Waals ferromagnet Fe3GeTe2 (F) and spin-singlet superconductor NbSe2 (S), we construct lateral Josephson junctions of S/F/S with accurate interface control to realize long-range skin supercurrent. The observed supercurrent across the ferromagnet can extend over 300 nm, and exhibits distinct quantum interference patterns in an external magnetic field. Strikingly, the supercurrent displays pronounced skin characteristics, with its density peaked at the surfaces or edges of the ferromagnet. Our central findings shed new light on the convergence of superconductivity and spintronics based on two-dimensional materials.

Spin-orbit coupled superconductivity with spin-singlet nonunitary pairing

An unconventional superconductor is distinguished with two types of gap functions: unitary and non-unitary. This core subject has been concentrated on purely spin-triplet or singlet-triplet mixed superconductors. However, the generalization to a purely spin-singlet superconductor has remained primarily of theoretical interest, which requires at least a multi-orbital correlated electronic systems. In this work, we present a possible establishment of both unitary and non-unitary pairings for spin-singlet superconductors with two atomic orbitals. Then we investigate the effects of atomic spin-orbit coupling and find a new spin-orbit-coupled non-unitary superconductor that supports exotic phenomena. Remarkably, there are mainly three features. Firstly, the atomic spin-orbit coupling locks the electron spins to be out-of-plane, which could give birth to the Type II Ising superconductivity with a large in-plane upper critical field compared to the Pauli limit. Secondly, topological chiral or helical Majorana edge state could be realized even in the absence of external magnetic fields or Zeeman fields. In addition, a spin-polarized superconducting state could even be generated by spin-singlet non-unitary pairings with spontaneous time-reversal breaking, which severs as a smoking gun to detect this exotic state by measuring the spin-resolved density of states. Therefore, our work might pave a new avenue to spin-orbit-coupled superconductors with spin-singlet non-unitary pairing symmetries.

Inter-valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral trilayer graphene

Superconductivity was recently discovered in rhombohedral trilayer graphene (RTG) in the absence of a moiré potential. Superconductivity is observed proximate to a metallic state with reduced isospin symmetry, but it remains unknown whether this is a coincidence or a key ingredient for superconductivity. Using a Hartree-Fock analysis and constraints from experiments, we argue that the symmetry breaking is inter-valley coherent (IVC) in nature. We evaluate IVC fluctuations as a possible pairing glue, and find that they lead to chiral unconventional superconductivity when the fluctuations are strong. We further elucidate how the inter-valley Hund’s coupling determines the spin-structure of the IVC ground state and breaks the degeneracy between spin-singlet and triplet superconductivity. Remarkably, if the normal state is spin-unpolarized, we find that a ferromagnetic Hund’s coupling favors spin-singlet superconductivity, in agreement with experiments. Instead, if the normal state is spin-polarized, then IVC fluctuations lead to spin-triplet pairing.

Magneto-topological transitions in multicomponent superconductors

Multi-component spin-singlet superconductors with competing 0- and $\pi$-pairing couplings, as in $s_{++}$ and $s_{\pm}$ phases, are close to instabilities with a spontaneous breaking of time-reversal symmetry. We demonstrate that the modification of the kinetic energy of superconducting electrons in a doubly connected superconducting cylinder, determined by the applied flux, generally drives transitions from chiral superconducting states to configurations that are time-reversal symmetric. This magneto-topological-induced changeover is investigated by means of a Ginzburg-Landau approach for a two-band superconductor with interband interactions and impurity scattering investigated for the case of a sample in the form of a mesoscopically thin-walled cylinder. We find that the application of a magnetic flux can convert a chiral $s_{\pm}+is_{++}$ state into a $s_{\pm}$ configuration and vice versa or tune the energy splitting of chiral states having inequivalent pairing amplitudes. We discuss signatures for the detection of these phases and of the corresponding transitions in mesoscopic superconducting loops.

Colossal Orbital Edelstein Effect in Noncentrosymmetric Superconductors.

In superconductors that lack inversion symmetry, the flow of supercurrent can induce a nonvanishing magnetization, a phenomenon which is at the heart of nondissipative magnetoelectric effects, also known as Edelstein effects. For electrons carrying spin and orbital moments, a question of fundamental relevance deals with the orbital nature of magnetoelectric effects in conventional spin-singlet superconductors with Rashba coupling. Remarkably, we find that the supercurrent-induced orbital magnetization is more than 1 order of magnitude greater than that due to the spin, giving rise to a colossal magnetoelectric effect. The induced orbital magnetization is shown to be sign tunable, with the sign change occurring for the Fermi level lying in proximity of avoiding crossing points in the Brillouin zone. In the presence of superconducting phase inhomogeneities, a modulation of the Edelstein signal on the scale of the superconducting coherence length appears, leading to domains with opposite orbital moment orientations. These hallmarks are robust to real-space self-consistent treatment of the superconducting order parameter. The orbital-dominated magnetoelectric phenomena, hence, have clear-cut marks for detection both in the bulk and at the edge of the system and are expected to be a general feature of multiorbital superconductors with inversion symmetry breaking.

Rise and fall of Yu-Shiba-Rusinov bound states in charge-conserving s -wave one-dimensional superconductors

We re-examine the problem of a magnetic impurity coupled to a superconductor focusing on the role of quantum fluctuations. We study in detail a system that consists of a one-dimensional charge conserving spin-singlet superconductor coupled to a boundary magnetic impurity. Our main finding is that quantum fluctuations lead to the destruction of Yu-Shiba-Rusinov (YSR) intragap bound states in all but a narrow region of the phase diagram. We carry out our analysis in three stages, increasing the role of the quantum fluctuations at each stage. First we consider the limit of a classical impurity and study the bulk semiclassically, finding YSR states throughout the phase diagram, a situation similar to conventional BCS superconductors. In the second stage, we reintroduce quantum fluctuations in the bulk and find that the YSR state is suppressed over half of the phase diagram, existing only around the quantum critical point separating the unscreened and the partially screened phases. In the final stage we solve exactly the full interacting model with arbitrary coupling constants using the Bethe ansatz. We find that including both the quantum fluctuating bulk and quantum impurity destabilizes the YSR state over most of the phase diagram allowing it to exist only in a small region, the YSR regime, between a Kondo-screened and an unscreened regime. Within the YSR regime a first-order phase transition occurs between a spin singlet and doublet ground state. We also find that for large-enough impurity spin exchange interaction a renormalized Kondo-screened regime is established. In this regime, not found for BCS superconductors, there is no YSR state and a renormalized Kondo temperature scale is generated.

Superconducting spin smecticity evidencing the Fulde-Ferrell-Larkin-Ovchinnikov state in Sr2RuO4.

Translational symmetry breaking is antagonistic to static fluidity but can be realized in superconductors, which host a quantum-mechanical coherent fluid formed by electron pairs. A peculiar example of such a state is the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, induced by a time-reversal symmetry-breaking magnetic field applied to spin-singlet superconductors. This state is intrinsically accompanied by the superconducting spin smecticity, spin density-modulated fluidity with spontaneous translational-symmetry breaking. Detection of such spin smecticity provides unambiguous evidence for the FFLO state, but its observation has been challenging. Here, we report the characteristic "double-horn" nuclear magnetic resonance spectrum in the layered superconductor Sr2RuO4 near its upper critical field, indicating the spatial sinusoidal modulation of spin density that is consistent with superconducting spin smecticity. Our work reveals that Sr2RuO4 provides a versatile platform for studying FFLO physics.

Orbital vortices in s -wave spin-singlet superconductors in zero magnetic field

Breaking of time-reversal and point-group spatial symmetries can have a profound impact on superconductivity. One of the most extraordinary effects, due to the application of a magnetic field, is represented by the Abrikosov vortices with charged supercurrents circulating around their cores. Whether a similar phenomenon can be obtained by exploiting spatial symmetry breaking, e.g. through electric fields or mechanical strain, is a fundamentally relevant but not yet fully settled problem. Here, we show that in two-dimensional spin-singlet superconductors with unusually low degree of spatial symmetry content, vortices with supercurrents carrying angular momentum around the core can form and be energetically stable. The vortex has zero net magnetic flux since it is made up of counter-propagating Cooper pairs with opposite orbital moments. By solving self-consistently the Bogoliubov - de Gennes equations in real space, we demonstrate that the orbital vortex is stable and we unveil the spatial distribution of the superconducting order parameter around its core. The resulting amplitude has a characteristic pattern with a pronounced angular anisotropy that deviates from the profile of conventional magnetic vortices. These hallmarks guide predictions and proposals for the experimental detection.

Topological superconductivity induced by magnetic texture crystals

We present a detailed investigation of the topological phases and Majorana fermion (MF) excitations that arise from the bulk interplay between (un)conventional one/two-band spin-singlet superconductivity and a number of magnetic texture crystals. The latter define inhomogeneous magnetization profiles which consist of a periodically-repeating primitive cell. Here we focus on magnetic texture crystals with a primitive cell of the helix, whirl, and skyrmion types, which feature distinct symmetry properties. We identify a multitude of accessible topological phases which harbor flat, uni- or bi-directional, (quasi-)helical, or chiral MF edge modes. This rich variety originates from the interplay between topological phases with gapped and nodal bulk energy spectra. The types of the emerging topological superconducting phases and the features of the arising MFs are solely determined by the properties and compatibility of the so-called magnetic and pairing point/space groups. Our analysis is general and does not rely on specific parameters of the models employed here to exemplify the topological scenarios which become accessible. Therefore, our results can be extended to systems with multiple bands, are relevant for a wide range of layered materials and hybrid devices, and provide predictions for strong, weak and crystalline topological phases.

Se77 -NMR evidence for spin-singlet superconductivity with exotic superconducting fluctuations in FeSe

Although the nature of the superconducting state has been intensively studied in FeSe, many fundamental issues including the pairing symmetry and superconducting fluctuations are still highly controversial. Here, we report a revised $^{77}\mathrm{Se}$-nuclear magnetic resonance (NMR) study on the superconducting state of $^{77}\mathrm{Se}$-enriched bulk FeSe. Below the superconducting temperature (${T}_{c}$), by carefully avoiding the rf heating effect, a remarkable linewidth broadening and obvious reduction of the Knight shift are observed under external magnetic field along both in-plane and out-of-plane directions, suggesting an intrinsic superconducting nature. These exotic results unambiguously rule out the possibility of chiral $p$-wave pairing, and favor a pairing scenario with the mixing of ${s}^{\ifmmode\pm\else\textpm\fi{}}$ and $d$ wave. A slight decrease of the Knight shift well above ${T}_{c}$ is also revealed under a moderated external magnetic field, suggesting exotic superconducting fluctuations beyond phase fluctuations in the two-dimensional limit. These renewed NMR results provide valuable constraints for the theoretical models on the exotic superconductivity in FeSe.