We present a general thermodynamic theory that describes phases and phase transitions of ferromagnetic superconductors with spin-triplet electron Cooper pairing. The theory is based on extended Ginzburg-Landau expansion in powers of superconducting and ferromagnetic order parameters. We propose a simple form for the dependence of theory parameters on the pressure that allows correct theoretical outline of the temperature-pressure phase diagram for which at low temperatures a stable phase of coexistence of p-wave superconductivity and itinerant ferromagnetism appears. We demonstrate that the theory is in an agreement with the experimental data for some intermetallic compounds that are experimentally proven to be itinerant ferromagnetic exhibiting spin-triplet superconductivity. Some basic features of quantum phase transitions in such systems are explained and clarified. We propose to group the spin-triplet ferromagnetic superconductors in two different types of thermodynamic behavior, on the basis of quantitative criterion deduced from the present theory and the analysis of experimental data.
Hund's coupling in multiorbital systems allows for the possibility of even-parity orbital-antisymmetric spin-triplet pairing, which can be stabilized by spin-orbit coupling (SOC). While this pairing expressed in the orbital basis is uniform and spin-triplet, it appears in the band basis as a pseudospin-singlet, with the momentum dependence determined by the SOC and the underlying triplet character remaining in the form of interband pairing active away from the Fermi energy. Here, we examine the role of momentum-dependent SOC in generating nontrivial pairing symmetries, as well as the hidden tr…
Recent experiments in quantum critical heavy fermion metals have pushed to the fore the question about whether antiferromagnetic fluctuations can promote both spin-singlet and spin-triplet superconductivity. Here we address the issue through non-perturbative calculations in antiferromagnetically correlated Kondo systems. We identify Kondo-destruction quantum critical points in both the SU(2) symmetric and Ising-anisotropic cluster Bose-Fermi Anderson models. The spin-singlet pairing correlations are significantly enhanced near the quantum critical point in the SU(2) case; however, with adequat…
Searching for triplet superconductivity has been pursued intensively in a broad field of material science and quantum information for decades. Nevertheless, these novel states remain rare. Within a simplified effective three-orbital model, we reveal a spin triplet pairing in doped MoS$_2$ by employing both the finite temperature determinant quantum Monte Carlo approach and the ground state constrained-phase quantum Monte Carlo method. In a wide filling region of $\avg{n}=0.60-0.80$ around charge neutrality $\avg{n}=2/3$, the $f$-wave pairing dominates over other symmetries. The pairing suscept…
We investigate the twisted bilayer graphene by a two-orbital Hubbard model on the honeycomb lattice. The model is studied near 1/4 band filling by using the singular-mode functional renormalization group theory. Spin-triplet $f$-wave pairing is found from weak to moderate coupling limit of the local interactions, and is associated with the Hund's rule coupling and incommensurate spin fluctuations at moderate momenta.
A prime category of superconducting materials in which to look for spin-triplet pairing and topological superconductivity are superconductors without inversion symmetry. It is predicted that the breaking of parity symmetry gives rise to an admixture of spin-singlet / spin-triplet pairing states; a triplet pairing component, being substantial, seems all but guaranteed. However, the experimental confirmation of pair mixing in any particular material remains elusive. In this work, we perform phase-sensitive experiment to examine the pairing state of noncentrosymmetric superconductor $α-$BiPd. The…
Spin-orbit coupling (SOC) plays a crucial role in determining the spin structure of an odd parity psedospin-triplet Cooper pairing state. Here, we present a thorough study of how SOC lifts the degeneracy among different p-wave pseudospin-triplet pairing states in a widely used microscopic model for $\mathrm{Sr_2 Ru O_4}$, combining a Ginzburg-Landau (GL) free energy expansion, a symmetry analysis of the model, and numerical weak-coupling renormalization group (RG) and random phase approximation (RPA) calculations. These analyses are then used to critically re-examine previous numerical results…
The superconducting state in uranium compounds UGe2, URhGe and UCoGe is formed at temperatures far below the Curie temperature pointing on nonconventional nature of superconductivity in these materials - namely the superconductivity with triplet pairing. The emergence of superconductivity is accompanied by the slight magnetization expulsion typical for the type-II superconductors. Following classic Abrikosov paper I develop the theory of type-II superconductivity in application to two-band ferromagnetic metal with equal spin triplet pairing.
Motivated by the possible non-spin-singlet superconductivity in the magic-angle twisted trilayer graphene experiment, we investigate the triplet-pairing superconductivity arising from a correlation-induced spin-fermion model on a honeycomb lattice. We find that the $f$-wave pairing is favored due to the valley-sublattice structure, and the superconducting state is time-reversal symmetric, fully gapped, and non-topological. With a small in-plane magnetic field, the superconducting state becomes partially polarized, and the transition temperature can be slightly enhanced. Our results apply quali…
We investigate superconducting pairing driven by electron-electron interactions in a theoretical model for monolayer MoS$_2$ with the temperature-flow functional renormalization group(fRG). At low doping, the dominant instability is toward odd-parity pairing with $f$-wave Mo-nearest-neighbor structure. We compute the fRG phase diagram versus electron doping below the van Hove filling of the conduction band. In the superconducting regime, the critical temperature grows with doping, comparable to the experiments. Near van Hove filling the system favors a ferromagnetic state. We demonstrate that …
We study the possible superconducting pairing symmetry mediated by spin and charge fluctuations on the honeycomb lattice using the extended Hubbard model and the random-phase-approximation method. From $2\%$ to $20\%$ doping levels, a spin-singlet $d_{x^{2}-y^{2}}+id_{xy}$-wave is shown to be the leading superconducting pairing symmetry when only the on-site Coulomb interaction $U$ is considered, with the gap function being a mixture of the nearest-neighbor and next-nearest-neighbor pairings. When the offset of the energy level between the two sublattices exceeds a critical value, the most fav…
The heavy-fermion system $\mathrm{UTe_2}$ is a candidate for spin-triplet superconductivity, which is of considerable interest to quantum engineering. Among the outstanding issues is the nature of the pairing state. A recent surprising discovery is the observation of a resonance in the spin excitation spectrum at an antiferromagnetic wavevector [C. Duan {\it et al.}, Nature \textbf{600}, 636 (2021)], which stands in apparent contrast to the ferromagnetic nature of the interactions expected in this system. We show how the puzzle can be resolved by a multiorbital spin-triplet pairing constructed…
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 anal…
Triplet pairing, orbital selectivity and correlations in Iron-based superconductors
University of Cincinnati（辛辛那提大学）；Max-Planck-Institut für Festkörperforschung（马克斯·普朗克固体研究所）；Rutgers University（罗格斯大学）；Royal Holloway, University of London（伦敦大学皇家霍洛威学院）
The spin-triplet state is most likely realized in uranium ferromagnetic superconductors, UGe2, URhGe, UCoGe. The microscopic coexistence of ferromagnetism and superconductivity means that the Cooper pair should be realized under the strong internal field due the ferromagnetism, leading to the spin-triplet state with equal spin pairing. The field-reinforced superconductivity, which is observed in all three materials when the ferromagnetic fluctuations are enhanced, is one of the strong evidences for the spin-triplet superconductivity. We present here the results of a newly discovered spin-tripl…
We construct minimum effective models to investigate the pairing symmetry in the newly discovered quasi-one-dimensional superconductor K$_2$Cr$_3$As$_3$. We show that a minimum three-band model based on the $d_{z^2}$, $d_{xy}$ and $d_{x^2-y^2}$ orbitals of one Cr sublattice can capture the band structures near Fermi surfaces. In both weak and strong coupling limits, the standard random phase approximation (RPA) and mean-field solutions consistently yield the triplet $p_z$-wave pairing as the leading pairing symmetry for physically realistic parameters. The triplet pairing is driven by the ferr…
The theory of triplet superconductivity in ferromagnetic metals based on electron-electron interaction by spin fluctuation exchange is developed. The equations for the upper critical field temperature dependence are derived. In contrast to the similar equations for the superconductivity in two band metals they contain the pairing amplitudes and the Fermi velocities depending on magnetic field. The critical field behaviour near the critical temperature and at T = 0 is established analytically.
We theoretically predict proximity-induced odd-frequency (odd-$ω$) pairing on the surface of a Weyl nodal loop semimetal, characterized by a nodal loop Fermi surface and drumhead-like surface states (DSSs), attached to conventional spin-singlet $s$-wave superconducting leads. Due to the complete spin polarization of the DSS, odd-$ω$ equal-spin triplet pairing is present, and we show that it gives rise to a finite Josephson current. Placing an additional ferromagnet in the junction can also generate odd-$ω$ mixed-spin triplet pairing, but the pairing and current is not affected if the magnetiza…
