Pairing Symmetry Research Articles

Characterizing two-dimensional superconductivity via nanoscale noise magnetometry with single-spin qubits

We propose nanoscale magnetometry via isolated single-spin qubits as a probe of superconductivity in two-dimensional materials. We characterize the magnetic field noise at the qubit location, arising from current and spin fluctuations in the sample and leading to measurable polarization decay of the qubit. We show that the noise due to transverse current fluctuations studied as a function of temperature and sample-probe distance can be used to extract useful information about the transition to a superconducting phase and the pairing symmetry of the superconductor. Surprisingly, at low temperatures, the dominant contribution to the magnetic noise arises from longitudinal current fluctuations and can be used to probe collective modes such as monolayer plasmons and bilayer Josephson plasmons. We also characterize the noise due to spin fluctuations, which allows probing the spin structure of the pairing wave function. Our results provide a non-invasive route to probe the rich physics of two-dimensional superconductors.

Revealing sign-reversal s+− -wave pairing by quasiparticle interference in the heavy-fermion superconductor CeCu2Si2

Recent observations of two nodeless gaps in superconducting CeCu$_2$Si$_2$ have raised intensive debates as to its exact gap structure of either sign-reversal ($s^{+-}$) or sign-preserving ($s^{++}$) pairing. Here we investigate the quasiparticle interference (QPI) using realistic Fermi surface topology for both weak and strong interband impurity scatterings. Our calculations of the QPI and integrated antisymmetrized local density of states reveal qualitative distinctions between $s^{+-}$ and $s^{++}$ pairing states, which include the intragap impurity resonance and a significant energy-dependence difference between two gap energies. Our predictions provide a guide for phase-sensitive QPI measurements to uncover decisively the true pairing symmetry in the heavy-fermion superconductor CeCu$_2$Si$_2$.

Rotational Cryptanalysis of MORUS

MORUS is one of the finalists of the CAESAR competition. This is an ARX construction that required investigation against rotational cryptanalysis. We investigated the power of rotational cryptanalysis against MORUS. We show that all the operations in the state update function of MORUS maintain the rotational pairs when the rotation distance is set to a multiple of the sub-word size. Our investigation also confirms that the rotational pairs can be used as distinguishers for the full version of MORUS if the constants used in MORUS are rotational-invariant. However, the actual constants used in MORUS are not rotational-invariant. The introduction of such constants in the state update function breaks the symmetry of the rotational pairs. Experimental results show that rotational pairs can be used as distinguishers for only one step of the initialization phase of MORUS. For more than one step, there are not enough known differences in the rotational pairs of MORUS to provide an effective distinguisher. This is due to the XOR-ing of the constants that are not rotational-invariant. Therefore, it is unlikely for an adversary to construct a distinguisher for the full version of MORUS by observing the rotational pairs.

Anomalous inverse proximity effect in unconventional superconductor junctions

We investigate the effects of Andreev bound states due to the unconventional pairing on the inverse proximity effect of ferromagnet/superconductor junctions. Utilizing quasiclassical Eilenberger theory, we obtain the magnetization penetrating into the superconductor. We show that in a wide parameter range the direction of the induced magnetization is determined by two factors: whether Andreev bound states are present at the junction interface and the sign of the spin-mixing angle. In particular, when Andreev bound states appear at the interface, the direction of the induced magnetization is opposite to that without Andreev bound states. We also clarify the conditions under which the inverted induced magnetization appears. Applying this novel effect helps distinguishing the pairing symmetry of a superconductor.

Higgs-mode signature in ultrafast electron dynamics in superconducting graphene

We theoretically investigate the effect of superconductivity on the ultrafast electron dynamics in graphene interacting with an ultrashort linearly polarized optical pulse. The optical pulse, with frequency greater than 1 THz, quadratically couples to the Higgs (amplitude) mode and therefore can excite the Higgs-mode oscillations in superconductors, leading to quenching superconducting excitation energy, even in $s$-wave pairing symmetry. Since the duration of the used pulse is less than the electron scattering time in graphene (10--100 fs), the electron dynamics driven by the electric field of pulse remains coherent and is described within the tight-binding model of graphene. We show that the electron-electron and hole-hole transitions from valence to conduction bands are substantially irreversible, with a large residual population of the conduction band, which implies quantum electron dynamics being highly nonadiabatic. Such a feature of the system allows us to clearly project the effect of Higgs oscillations on the electric dipole moment created by the electric field of the pulse between the conduction and valence bands. In particular, we study the impact of the superconducting pair potential on the conduction band population, where the strong pulse causes electronlike and holelike quasiparticles transitions between the conduction and valence bands. The conduction band electron redistribution in honeycomb Dirac points results in almost asymmetric hot spots in two different $K$ and ${K}^{\ensuremath{'}}$ valleys after the pulse ends, which may be interpreted as the valley polarization effect due to the presence of superconductivity. The redistribution of hot spots around Dirac points is in good agreement with the Higgs-mode oscillations (corresponding to the electric dipole moment pattern), and the number of spots weakly depends on the superconducting gap, whereas it has a strong dependence on the ultrashort-pulse intensity.

Pairing symmetries in the Zeeman-coupled extended attractive Hubbard model

By introducing the possibility of equal- and opposite-spin pairings concurrently, we show that the ground state of the extended attractive Hubbard model (EAHM) exhibits rich phase diagrams with a variety of singlet, triplet, and mixed parity superconducting orders. We study the competition between these superconducting pairing symmetries invoking an unrestricted Hartree–Fock–Bogoliubov–de Gennes (HFBdG) mean-field approach, and we use the d-vector formalism to characterize the nature of the stabilized superconducting orders. We discover that, while all other types of orders are suppressed, a non-unitary triplet order dominates the phase space in the presence of an in-plane external magnetic field. We also find a transition between a non-unitary to unitary superconducting phase driven by the change in average electron density. Our results serve as a reference for identifying and understanding the nature of superconductivity based on the symmetries of the pairing correlations. The results further highlight that EAHM is a suitable effective model for describing most of the pairing symmetries discovered in different materials.

Dispersion of neutron spin resonance mode in Ba0.67K0.33Fe2As2 * *Project supported by the National Key Research and Development Program of China (Grant Nos. 2018YFA0704200, 2018YFA0305602, 2017YFA0303100, and 2017YFA0302900), the National Natural Science Foundation of China (Grant Nos. 11822411 and 11961160699), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (CAS) (Grant Nos. XDB25000000 and XDB07020300), K.C.Wong Education

We report an inelastic neutron scattering investigation on the spin resonance mode in the optimally hole-doped iron-based superconductor Ba0.67K0.33Fe2As2 with Tc= 38.2 K. Although the resonance is nearly two-dimensional with peak energy E R ≈ 14 meV, it splits into two incommensurate peaks along the longitudinal direction ([H,0,0]) and shows an upward dispersion persisting to 26 meV. Such dispersion breaks through the limit of total superconducting gaps Δ tot = |Δk | + |Δ k+Q | (about 11–17 meV) on nested Fermi surfaces measured by high resolution angle resolved photoemission spectroscopy (ARPES). These results cannot be fully understood by the magnetic exciton scenario under s±-pairing symmetry of superconductivity, and suggest that the spin resonance may not be restricted by the superconducting gaps in the multi-band systems.

Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems

Quantum anomalous Hall insulator (QAH)/$s$-wave superconductor (SC) hybrid systems are known to be an ideal platform for realizing two-dimensional topological superconductors with chiral Majorana edge modes. In this paper we study QAH/unconventional SC hybrid systems whose pairing symmetry is $p$-wave, $d$-wave, chiral $p$-wave, or chiral $d$-wave. The hybrid systems are a generalization of the QAH/$s$-wave SC hybrid system. In view of symmetries of the QAH and pairings, we introduce three topological numbers to classify topological phases of the hybrid systems. One is the Chern number that characterizes chiral Majorana edge modes and the others are topological numbers associated with crystalline symmetries. We numerically calculate the topological numbers and associated surface states for three characteristic regimes that feature an influence of unconventional SCs on QAHs. Our calculation shows a rich variety of topological phases and unveils the following topological phases that are no counterpart of the $s$-wave case: crystalline symmetry-protected helical Majorana edge modes, a line node phase (crystalline-symmetry-protected Bogoliubov Fermi surface), and multiple chiral Majorana edge modes. The phenomena result from a nontrivial topological interplay between the QAH and unconventional SCs. Finally, we discuss tunnel conductance in a junction between a normal metal and the hybrid systems, and show that the chiral and helical Majorana edge modes are distinguishable in terms of the presence/absence of zero-bias conductance peak.

Spectroscopic evidence of mixed angular momentum symmetry in non-centrosymmetric Ru_7B_3

Superconducting crystals with a lack of inversion symmetry can potentially host unconventional pairing. However, till today, no direct conclusive experimental evidence of such unconventional order parameters in non-centrosymmetric superconductors has been reported. In this paper, through direct measurement of the superconducting energy gap by scanning tunnelling spectroscopy, we report the existence of both s-wave (singlet) and p-wave (triplet) pairing symmetries in non-centrosymmetric Ru_7B_3. Our temperature and magnetic field-dependent studies also indicate that the relative amplitudes of the singlet and triplet components change differently with temperature.

Nature of Unconventional Pairing in the Kagome Superconductors AV_{3}Sb_{5} (A=K,Rb,Cs).

The recent discovery of AV_{3}Sb_{5} (A=K,Rb,Cs) has uncovered an intriguing arena for exotic Fermi surface instabilities in a kagome metal. Among them, superconductivity is found in the vicinity of multiple van Hove singularities, exhibiting indications of unconventional pairing. We show that the sublattice interference mechanism is central to understanding the formation of superconductivity in a kagome metal. Starting from an appropriately chosen minimal tight-binding model with multiple van Hove singularities close to the Fermi level for AV_{3}Sb_{5}, we provide a random phase approximation analysis of superconducting instabilities. Nonlocal Coulomb repulsion, the sublattice profile of the van Hove bands, and the interaction strength turn out to be the crucial parameters to determine the preferred pairing symmetry. Implications for potentially topological surface states are discussed, along with a proposal for additional measurements to pin down the nature of superconductivity in AV_{3}Sb_{5}.

Quasiparticle on Bogoliubov Fermi Surface and Odd-Frequency Cooper Pair

We discuss a close relationship between a quasiparticle on the Bogoliubov Fermi surface and an odd-frequency Cooper pair in a superconductor in which a Cooper pair consisting of two j=3/2 electrons forms the pseudospin-quintet even-parity pair potential with breaking time-reversal symmetry. It has been established in a single-band superconductor that a low-energy quasiparticle below the superconducting gap accompanies an odd-frequency Cooper pair. In this paper, we show that an odd-frequency pair characterized by chirality coexists with a quasiparticle on the Bogoliubov Fermi surface. The symmetry of odd-frequency Cooper pairs is analyzed in detail by taking realistic pair potentials into account in a cubic superconductor.

Symmetry, nodal structure, and Bogoliubov Fermi surfaces for nonlocal pairing

Multiband effects can lead to fundamentally different electronic behavior of solids, as exemplified by the possible emergence of Fermi surfaces of Bogoliubov quasiparticles in centrosymmetric superconductors which break time-reversal symmetry. We extend the analysis of possible pairing symmetries, the corresponding nodal structure, and the Bogoliubov Fermi surfaces in two directions: We include nonlocal pairing and we consider internal degrees of freedom other than the effective angular momentum of length $j=3/2$ examined so far. Since our main focus is on the Bogoliubov Fermi surfaces we concentrate on even-parity pairing. The required symmetry analysis is illustrated for several examples, as a guide for the reader. We find that the inclusion of nonlocal pairing leads to a much larger range of possible pairing symmetries. For infinitesimal pairing strength, we find a simple yet powerful criterion for nodes in terms of a scalar product of form factors.

Higher angular momentum pairings in interorbital shadowed-triplet superconductors: Application to Sr2RuO4

Even-parity interorbital spin-triplet pairing emerges as an intriguing candidate in multiorbital superconductors with significant Hund's and spin-orbit coupling. Within such a state, the pairing is dominated by the intraband pseudospin-singlet component via the spin-orbit coupling, distinguishing it from a pure spin triplet and motivating the name, shadowed triplet. With atomic spin-orbit coupling, it was shown that this pairing exhibits an anisotropic $s$-wave character, while higher angular momentum pairing symmetries such as $d$- or $g$-wave have been proposed based on phenomenological analyses in candidate systems. A natural question is then whether higher angular momentum pairings may arise with this form of spin-triplet pairing. Here, we examine the interplay between spin-orbit coupling and the electronic dispersions in correlated metals and demonstrate how they can be realized. We apply this idea to Sr$_{2}$RuO$_{4}$ and determine the competition among different pairing states as multiple spin-orbit coupling parameters are tuned. The presence of both $d$- and $g$-wave pairings, including a $d+ig$ state, are found when momentum-dependent spin-orbit coupling with $d$-wave character is increased. Implications of the theory and future directions are also discussed.

Topological defect states in mesoscopic superconductors with mixed pairing symmetries

Topological defect states in mesoscopic superconductors with mixed pairing symmetries

Impurity effect on order modulations in superconducting systems with mixed singlet-triplet pairing

Based on a model Hamiltonian including the on-site repulsive interaction among the electrons, we investigate the effect induced by nonmagnetic impurities in bulk superconducting systems with mixed singlet-triplet pairing by numerically solving the Bogoliubov-de Gennes equations. For the emergent spin-triplet p-wave as well as coexisted spin-singlet s-wave and d-wave pairing symmetries, the order-parameter patterns for the quantized vortex states with point-like cores can be effectively tuned by the located sites of nonmagnetic impurities. The next-nearest-neighbor hopping effect on the evolution of vortex configurations is also discussed in the presence of vortex pinning by the impurity. Besides the unconventional vortex lattice, several types of topological defects, including the unclosed domain walls and enclosed skyrmionic modes, can be obtained when the impurity position is varied. All these configurations can be resolved by the zero-energy peaks in the local density of states.

Strain-induced time reversal breaking and half quantum vortices near a putative superconducting tetracritical point in Sr2RuO4

Motivated by continuing debate concerning the pairing symmetries of Sr${}_{2}$RuO${}_{4}$, the authors develop a general description of a situation in which superconducting orders are nearly degenerate. They suggest that many seemingly contradictory experimental findings can be reconciled if one assumes this material is near a tetracritical point, where small variations in strain can lead to rich phenomenology. More specifically, the authors characterize possible superconducting domain walls, allowing for spontaneous time-reversal symmetry breaking and the stabilization of half-quantum vortices.

Strong Correlation Between Superconductivity and Ferromagnetism in an Fe-Chalcogenide Superconductor.

The interplay among topology, superconductivity, and magnetism promises to bring a plethora of exotic and unintuitive behaviors in emergent quantum materials. The family of Fe-chalcogenide superconductors FeTexSe1-x are directly relevant in this context due to their intrinsic topological band structure, high-temperature superconductivity, and unconventional pairing symmetry. Despite enormous promise and expectation, the local magnetic properties of FeTexSe1-x remain largely unexplored, which prevents a comprehensive understanding of their underlying material properties. Exploiting nitrogen vacancy (NV) centers in diamond, here we report nanoscale quantum sensing and imaging of magnetic flux generated by exfoliated FeTexSe1-x flakes, demonstrating strong correlation between superconductivity and ferromagnetism in FeTexSe1-x. The coexistence of superconductivity and ferromagnetism in an established topological superconductor opens up new opportunities for exploring exotic spin and charge transport phenomena in quantum materials. The demonstrated coupling between NV centers and FeTexSe1-x may also find applications in developing hybrid architectures for next-generation, solid-state-based quantum information technologies.

Strange metal from incoherent bosons

The breakdown of the celebrated Fermi liquid theory in the strange metal phase is the central enigma of correlated quantum matter. Motivated by recent experiments reporting short-lived carriers, along with the ubiquitous observations of modulated excitations in the phase diagram of cuprates, we propose a model for this phase. We introduce bosons emerging from the remnants of a pair density wave as additional current carriers in the strange metal phase. These bosonic excitations are finite momentum Cooper pairs and thus carry twice the electronic charge, and its net spin can either be zero or one arising from the two spin-$1/2$ electrons. We show that such a model can capture the famous linear relationship of resistivity with temperature and manifests the Drude form of ac-conductivity with a Planckian dissipation rate. Furthermore, such bosons are incoherent and hence do not contribute to the Hall conductivity. The bosons emerging from the electron pairs of spin-triplet symmetry also reproduce the recently observed linear in-field magnetoresistance [P. Giraldo-Gallo et al., Science 361, 479 (2018); J. Ayres et al., arXiv: 2012.01208 (2020)].

Interplay between insulating gap and Zeeman energy on the tunneling spectrum in f-wave superconductor silicene junctions

We theoretically discussed the interplay between the insulating gap and the Zeeman energy on the charge transport in silicene-based N/f-wave superconductor junctions, where N is normal silicene. The modified Blonder-Tinkham-Klapwijk (BTK) formalism is extended to calculate the tunneling conductance. Two pairing potentials f1 and f2 are chosen for f-wave. The results show that the tunneling conductance spectra present distinctly different behaviors for N/f1-wave superconductor (N/f1S) junction and N/f2S junction. For N/f1S junction, a zero-energy peak as well a zero-conductance dip is obtained. The position of the zero-conductance dip can be used as a criterion for the insulating gap. For N/f2S junction, the tunneling conductance controlled by an external magnetic field becomes as a step function of the bias voltage, which means that this system can be considered as a nano switch. These results can also be used as a criterion to determine the pairing symmetry of f-wave.

Precise optical control of gene expression in C elegans using improved genetic code expansion and Cre recombinase.

Synthetic strategies for optically controlling gene expression may enable the precise spatiotemporal control of genes in any combination of cells that cannot be targeted with specific promoters. We develop an improved genetic code expansion system in Caenorhabditis elegans and use it to create a photoactivatable Cre recombinase. We laser-activate Cre in single neurons within a bilaterally symmetric pair to selectively switch on expression of a loxP-controlled optogenetic channel in the targeted neuron. We use the system to dissect, in freely moving animals, the individual contributions of the mechanosensory neurons PLML/PLMR to the C. elegans touch response circuit, revealing distinct and synergistic roles for these neurons. We thus demonstrate how genetic code expansion and optical targeting can be combined to break the symmetry of neuron pairs and dissect behavioural outputs of individual neurons that cannot be genetically targeted.