Triplet Pairing Correlations Research Articles

Magnetic Field-Induced "Mirage" Gap in an Ising Superconductor.

Superconductivity is commonly destroyed by a magnetic field due to orbital or Zeeman-induced pair breaking. Surprisingly, the spin-valley locking in a two-dimensional superconductor with spin-orbit interaction makes the superconducting state resilient to large magnetic fields. We investigate the spectral properties of such an Ising superconductor in a magnetic field taking into account disorder. The interplay of the in-plane magnetic field and the Ising spin-orbit coupling leads to noncollinear effective fields. We find that the emerging singlet and triplet pairing correlations manifest themselves in the occurrence of "mirage" gaps: at (high) energies of the order of the spin-orbit coupling strength, a gaplike structure in the spectrum emerges that mirrors the main superconducting gap. We show that these mirage gaps are signatures of the equal-spin triplet finite-energy pairing correlations and due to their odd parity are sensitive to intervalley scattering.

Triplet p-wave pairing correlation in low-doped zigzag graphene nanoribbons

We reveal an edge spin triplet p–wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrained-path quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling.

Triplet p-wave pairing correlation in low-doped zigzag graphene nanoribbons

We reveal an edge spin triplet p-wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrained-path quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling.

Inverse proximity effect at superconductor-ferromagnet interfaces: Evidence for induced triplet pairing in the superconductor

Considerable evidence for proximity-induced triplet superconductivity on the ferromagnetic side of a superconductor-ferromagnet (S-F) interface now exists; however, the corresponding effect on the superconductor side has hardly been addressed. We have performed scanning tunneling spectroscopy measurements on NbN superconducting thin films proximity coupled to the half-metallic ferromagnet La2/3Ca1/3MnO3 (LCMO) as a function of magnetic field. We have found that at zero and low applied magnetic fields the tunneling spectra on NbN typically show an anomalous gap structure with suppressed coherence peaks and, in some cases, a zero-bias conductance peak. As the field increases to the magnetic saturation of LCMO where the magnetization is homogeneous, the spectra become more BCS-like and the critical temperature of the NbN increases, implying a reduced proximity effect. Our results therefore suggest that triplet-pairing correlations are also induced in the S side of an S-F bilayer.

Zero-energy peak and triplet correlations in nanoscale superconductor/ferromagnet/ferromagnet spin valves

Using a self-consistent Bogoliubov-de Gennes approach, we theoretically study the proximity-induced density of states (DOS) in clean SFF spin-valves with noncollinear exchange fields. Our results clearly demonstrate a direct correlation between the presence of a zero energy peak (ZEP) in the DOS spectrum and the persistence of spin-1 triplet pair correlations. By systematically varying the geometrical and material parameters governing the spin-valve, we point out to experimentally optimal system configurations where the ZEPs are most pronounced, and which can be effectively probed via scanning tunneling microscopy. We complement these findings in the ballistic regime by employing the Usadel formalism in the full proximity limit to investigate their diffusive SFF counterparts. We determine the optimal normalized ferromagnetic layer thicknesses which result in the largest ZEPs. Our results can serve as guidelines in designing samples for future experiments.

Magnetic field dependence of the proximity-induced triplet superconductivity at ferromagnet/superconductor interfaces

Long-ranged superconductor proximity effects recently found in superconductor-ferromagnetic (S-F) systems are generally attributed to the formation of triplet-pairing correlations due to various forms of magnetic inhomogeneities at the S-F interface. In order to investigate this conjecture within a single F layer coupled to a superconductor, we performed scanning tunneling spectroscopy on bilayers of La${}_{2/3}$Ca${}_{1/3}$MnO${}_{3}$ (LCMO) ferromagnetic thin films grown on high-temperature superconducting films of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ or Pr${}_{1.85}$Ce${}_{0.15}$CuO${}_{4}$ under various magnetic fields. We find a strong correlation between the magnitude of superconductor-related spectral features measured on the LCMO layer and the degree of magnetic inhomogeneity controlled by the external magnetic field. This corroborates theoretical predictions regarding the role played by magnetic inhomogeneities in inducing triplet pairing at S-F interfaces.

Triplet pair correlations and nonmonotonic supercurrent decay with Cr thickness in Nb/Cr/Fe/Nb Josephson devices

Supercurrents carry charge but not spin in the vast majority of superconductors. This is because the charge carriers are Cooper pairs which are formed of electrons with antiparallel spins (singlet pairs). It is now established that if singlet pairs propagate through a superconductor interface with an inhomogeneous ferromagnet, triplet pair correlations form so the supercurrents can acquire a net spin component. Although the spins at sputter-deposited Fe/Cr interfaces can be frustrated due to surface roughness and interdiffusion, an antiferromagnetic spin density wave (SDW) state can still form in Cr close to the interface. Here, we show evidence for triplet pair correlations in Josephson junctions with Cr/Fe and Cr/Fe/Cr barriers. Although the exact mechanism of pair conversion is unknown, we propose a simple model in which a SDW state in Cr and frustrated spins at the Cr/Fe interfaces serve as spin-mixers for generating triplet supercurrents and so provide a potential means to generating large superconducting spin current densities.

Supra-oscillatory critical temperature dependence of Nb-Ho bilayers

We investigate the critical temperature Tc of a thin s-wave superconductor (Nb) proximity coupled to a helical rare-earth ferromagnet (Ho). As a function of the Ho layer thickness, we observe multiple oscillations of Tc superimposed on a slow decay, that we attribute to the influence of the Ho on the Nb proximity effect. Because of the inhomogeneous magnetization in Ho, singlet and triplet pair correlations are present in the bilayers. We take both into consideration when solving the self-consistent Bogoliubov-de Gennes equations, and we find a reasonable agreement with the experiments. We also observe non-trivial transitions into the superconducting state, the zero resistance state being attained after two successive transitions which appear to be associated with the magnetic structure of Ho.

Triplet Pair Correlations ins-Wave Superfluids as a Signature of the Fulde-Ferrell-Larkin-Ovchinnikov State

We show that antiparallel triplet pairing correlations are generated in superfluids with purely s-wave interactions whenever population imbalance enforces anisotropic Fulde-Ferrell (FF) or inhomogeneous Larkin-Ovchinikov (LO) states. These triplet correlations appear in the Cooper pair wave function, while the triplet part of the gap remains zero. The same set of quasiparticle states contributes to the triplet component and to the polarization, thus spatially correlating them. In the LO case, this set forms a narrow band of Andreev states centered on the nodes of the s-wave order parameter. This picture naturally provides a unifying explanation of previous findings that attractive p-wave interaction stabilizes FFLO states. We also study a similar triplet mixing which occurs when a balanced two-component system displays FFLO-type oscillations due to a spin-dependent optical lattice. We discuss how this triplet component can be measured in systems of ultracold atoms using a rapid ramp across a p-wave Feshbach resonance. This should provide a smoking gun signature of FFLO states.

Superconductive proximity in a topological insulator slab and excitations bound to an axial vortex

We consider the proximity effect in a topological insulator (TI) sandwiched between two conventional superconductors by comparing $s$-wave spin singlet superconducting pairing correlations and odd-parity triplet pairing correlations with a zero spin component orthogonal to the slab (``polar'' phase). A superconducting gap opens in the Dirac dispersion of the surface states existing at the interfaces. An axial vortex is included, piercing the slab along the normal to the interfaces with the superconductors. It is known that, when proximity is $s$-wave, quasiparticles in the gap are Majorana bound states, localized at opposite interfaces. We report the full expression for the quantum field associated to the midgap neutral fermions, as derived in the two-orbital band model for the TI. When proximity involves odd-parity pairing, midgap modes are charged surface Andreev bound states, and they originate from interfacial circular states of definite chirality, centered at the vortex singularity and decaying in the TI film with oscillations. When the chemical potential is moved away from midgap, extended states along the vortex axis are also allowed. Their orbital structure depends on the symmetry of the bulk band from where the quasiparticle level splits off.

Spin–triplet current in half metal/conical helimagnet/superconductor heterojunctions

The BTK theory is extended to investigate spin–triplet current and differential conductance spectrum in the half metal/conical helimagnet (Holmium)/s-wave superconductor heterojunctions. We show that the effective spin–split and spin–flip scatterings of the Holmium layer control the conversion efficiency between the spin–singlet and equal-spin triplet pair correlations, leading to a tunneling current oscillation with the thickness of the Holmium layer. This can provide qualitative explanations on the current oscillation in Ho/Co/Ho-based Josephson junction experiment. The differential conductance spectrum confirms spin–flip Andreev reflection induced long-ranged equal-spin triplet pair correlations.

Emergence of triplet correlations in superconductor/half-metallic nanojunctions with spin-active interfaces

We study triplet pairing correlations induced in an SFS trilayer (where F is a ferromagnet and S an ordinary $s$-wave superconductor) by spin-flip scattering at the interfaces, via the derivation and self-consistent solution of the appropriate Bogoliubov--de Gennes equations in the clean limit. We find that the spin-flip scattering generates $m=\ifmmode\pm\else\textpm\fi{}1$ triplet correlations, odd in time and study the general spatial behavior of these and of $m=0$ correlations as a function of position and of spin-flip strength, ${H}_{spin}$, concentrating on the case where the ferromagnet is half-metallic. For certain values of ${H}_{spin}$, the triplet correlations pervade the magnetic layer and can penetrate deeply into the superconductor. The behavior we find depends very strongly on whether the singlet order parameter is in the 0 or $\ensuremath{\pi}$ state, which must in turn be determined self-consistently. We also present results for the density of states (DOS) and for the local magnetization, which, due to spin-flip processes, is not in general aligned with the magnetization of the half-metal, and near the interfaces, rotates as a function of position and ${H}_{spin}$. The average DOS in both F and S is shown to exhibit various subgap bound states positioned at energies that depend strongly on the particular junction state and the spin-flip scattering strength.

Induced triplet pairing in cleans-wave superconductor/ferromagnet layered structures

We study induced triplet pairing correlations in clean ferromagnet/superconductor/ferromagnet heterostructures. The pairing state in the superconductor is the conventional singlet $s$ wave, and the angle $\ensuremath{\alpha}$ between the magnetizations of the two ferromagnetic layers is arbitrary. We use a numerical fully self-consistent solution of the microscopic equations and obtain the time-dependent triplet correlations via the Heisenberg equations of motion. We find that in addition to the usual singlet correlations, triplet correlations, which are odd in time as required by the Pauli principle, are induced in both the ferromagnets and the superconductor. These time-dependent correlations are largest at times of order of the inverse of the Debye cutoff frequency ${\ensuremath{\omega}}_{D}$, and we find that within that time scale, they are often spatially very long ranged. We discuss the behavior of the characteristic penetration lengths that describe these triplet correlations. We also find that the ferromagnets can locally magnetize the superconductor near the interface and that the local magnetization then undergoes strongly damped oscillations. The local density of states exhibits a variety of energy signatures, which we discuss, as a function of ferromagnetic strength and $\ensuremath{\alpha}$.

Odd Triplet Pairing in Clean Superconductor/Ferromagnet Heterostructures

We study triplet pairing correlations in clean ferromagnet (F)/superconductor (S) nanojunctions, via fully self-consistent solution of the Bogoliubov-de Gennes equations. We consider FSF trilayers, with S being an s-wave superconductor, and an arbitrary angle alpha between the magnetizations of the two F layers. We find that contrary to some previous expectations, triplet correlations, odd in time, are induced in both the S and F layers in the clean limit. We investigate their behavior as a function of time, position, and alpha. The triplet amplitudes are largest at times on the order of the inverse Debye frequency, and at that time scale they are long-ranged in both S and F. The zero temperature condensation energy is found to be lowest when the magnetizations are antiparallel.

Supercurrent pumping by ferromagnetic resonance in ferromagnetic Josephson junctions

We theoretically study the Josephson current through a half-metallic ferromagnet between two singlet superconductors. The magnon-assisted electron tunneling across the interface induces a triplet pairing correlation in the half-metallic ferromagnet through which the Josephson current flows between the superconductors. It is shown that the Josephson current is pumped by the coherent precession of the magnetization, and is controllable by use of ferromagnetic resonance effect in a ferromagnetic Josephson junction.

Signatures of retroreflection and induced triplet electron-hole correlations in ferromagnet–s-wave-superconductor structures

We present a theoretical study of a ferromagnet--$s$-wave-superconductor junction to investigate the signatures of induced triplet correlations in the system. We apply the extended Blonder-Tinkham-Klapwijk formalism and allow for an arbitrary magnetization strength and direction of the ferromagnet, a spin-active barrier, Fermi-vector mismatch, and different effective masses in the two systems. It is found that the phase associated with the $xy$ components of the magnetization in the ferromagnet couples with the superconducting phase and induces spin triplet pairing correlations in the superconductor, if the tunneling barrier acts as a spin filter. This feature leads to an induced spin-triplet pairing correlation in the ferromagnet, along with a spin-triplet electron-hole coherence due to an interplay between the ferromagnetic and superconducting phases. As our main result, we investigate the experimental signatures of retrorelection, manifested in the tunneling conductance of a ferromagnet--$s$-wave-superconductor junction with a spin-active interface.

Spin-triplet superconductivity in the double-chain Hubbard model with ferromagnetic exchange interaction

We study possible occurrence of spin-triplet superconductivity in the model of two Hubbard chains coupled with ferromagnetic exchange interaction. We use the analytical bozonization method as well as the numerical exact-diagonalization and density-matrix renormalization group methods. We show that, in the low electron density region, the complete ferromagnetic state occurs and the triplet pairing correlation is most dominant, where we find that the gap function behavior is p y -wave like. We also show that, in the high electron density regions, the spin-singlet superconductivity anticipated by the weak coupling analysis is most dominant, where the gap function behavior is d xy -wave like.

Superconducting proximity effect through a magnetic domain wall

We study the superconducting proximity effect in a superconductor-ferromagnet-superconductor heterostructure containing a domain wall in the ferromagnetic region. For the ferromagnet we assume an alloy with an exchange splitting of the conduction bands comparable to the superconducting gaps. We calculate the modification of the density of states in the center of the domain wall as a result of the proximity effect. We show that the density of states is sensitive to domain-wall parameters due to triplet-pairing correlations created in the vicinity of the domain wall. We present a theoretical tool which in a very effective way enables retaining the full spatially dependent spin-space structure of the problem.

Effect of an inhomogeneous exchange field on the proximity effect in disordered superconductor-ferromagnet hybrid structures

We investigate the effect of an inhomogeneous exchange field on the proximity effect in superconductor-ferromagnet hybrid structures within the quasi-classical theory of superconductivity. As an example we study the proximity effect in a superconductor-ferromagnet bilayer with an in-plane spiral magnetic order in the ferromagnet. This model simulates a multiple magnetic domain structure where the domain walls of the N\'{e}el type are of equal size as the domains. Triplet correlations are induced in the bilayer by the superconducting proximity effect, which are sensitive to the local quantization axis of the exchange field in the ferromagnet. The coexistence of singlet and triplet pair correlations in the bilayer results into a sensitivity of the superconducting transition temperature on the spatial variation of the exchange field in the ferromagnetic layer. We show that the inhomogeneity tends to suppress the oscillating behavior of the pair amplitudes in the ferromagnet. As a result, the superconducting critical temperature is found to be strongly dependent on the spiral wavevector. We study the spin-dependent local density of states and the effect of an induction of a spin magnetization in the superconductor.

Pairing and density correlations of stripe electrons in a two-dimensional antiferromagnet

We study a one-dimensional electron liquid embedded in a 2D antiferromagnetic insulator, and coupled to it via a weak antiferromagnetic spin exchange interaction. We argue that this model may qualitatively capture the physics of a single charge stripe in the cuprates on length- and time scales shorter than those set by its fluctuation dynamics. Using a local mean-field approach we identify the low-energy effective theory that describes the electronic spin sector of the stripe as that of a sine-Gordon model. We determine its phases via a perturbative renormalization group analysis. For realistic values of the model parameters we obtain a phase characterized by enhanced spin density and composite charge density wave correlations, coexisting with subleading triplet and composite singlet pairing correlations. This result is shown to be independent of the spatial orientation of the stripe on the square lattice. Slow transverse fluctuations of the stripes tend to suppress the density correlations, thus promoting the pairing instabilities. The largest amplitudes for the composite instabilities appear when the stripe forms an antiphase domain wall in the antiferromagnet. For twisted spin alignments the amplitudes decrease and leave room for a new type of composite pairing correlation, breaking parity but preserving time reversal symmetry.