Interlayer coupling andp-wave pairing in strontium ruthenate

Abstract

On the basis of a three orbital model and an effective attractive interaction between electrons we investigate the possible superconducting states, with p and f -wave internal symmetry, of Sr2RuO4. For an orbital dependent interaction which acts between in plane and out of plane nearest neighbour Ruthenium atoms we find a state for which the gap in the quasi-particle spectra has a line node on the α and β sheets of the Fermi Surface, but it is complex with no nodes on the γ-sheet. We show that this state is consistent with all the available experimental data. In particular, we present the results of our calculations of the specific heat and penetration depth as functions of the temperature.PACS numbers: 74.70. Pq, 74.20.Rp, 74.25.Bt Ever since triplet pairing was discovered in superfluid 3 He [1], during the early seventies, there has been a constant search for the superconducting analogue of this intriguing macroscopic quantum phenomenon. Although, as yet, there is no metal for which triplet paring has been definitively demonstrated there are a number of good candidates. The evidence that Sr 2 RuO 4 is a triplet superconductor is particularly strong [2,3]. Nevertheless, even in this case the full symmetry of the equilibrium state below T c remains open to debate [2][3][4][5][6][7][8][9][10][11][12].One of the puzzles currently at the centre of attention is the apparent incompatibility between experimental evidence for broken time-reversal symmetry in the superconducting state [13,10] and equally convincing measurements indicating that the order parameter d(k) has a line of nodes on the Fermi Surface [14,15]. The reason why this state of affairs represents a dilemma is that for all odd parity spin triplet pairing states in tetragonal crystals, group theory does not require the simultaneous presence of both broken time-reversal symmetry and line nodes [16]. Consequently, due to their lower condensation energy, line nodes are unlikely. For instance, the pairing state d(k) ∼ (k x + ik y )ê z , proposed by Agterberg et al.[4] on the grounds that it minimizes the free energy, obviously breaks time reversal invariance and has no line nodes. Of course, such states as Graf and Balatsky [7] and other f-wave states [8,9,11] are allowed by symmetry considerations but, the point is that, the nodes are not required by symmetry and hence it is not very attractive ansatz to build a theory on. Under these circumstances it is more advantageous to study physically motivated microscopic models even if the question of the actual mechanism of pairing is to be avoided. In this letter we propose and investigate one such physically motivated model. Our model is prompted by the observation, of Hasegawa et al. [11], that coupling between the Ruthenium layers in Sr 2 RuO 4 leads to convenient, horizontal, k z = ± π c lines of zeros on the Fermi Surface. It features two, intra and inter plane, interaction constants U and U ⊥ respectively, which describe the attraction between electrons each occupying one of three, t 2g , orbitals on Ru...

Coherence Lengths for Superconductivity in the Two-Orbital Negative-U Hubbard Model

“…The system have been modelled by the negative-U Hubbard model on the two dimensional lattice. The obtained two values of the coherence lengths reects the multi-orbital mechanism of superconductivity and could have some consequence in specic spatial properties of such a complex supeconducting state [15,22].…”

Is the anisotropy of the upper critical field of Sr2RuO4consistent with a helicalp-wave state?

“…Although still under debate [33][34][35], the cylindrical γ band is widely considered to be the primary source of p-wave pairing [3,36]. The small c-axis dispersion in this nearly cylindrical γ Fermi surface can be incorporated by treating it as an elongated uniaxial ellipsoid, characterized by the effective mass anisotropy of the quasi-particles m c ≫ m a = m b = m ab .…”

Concealed d -wave pairs in the s ± condensate of iron-based superconductors

“…This stands in stark contrast with almost all other strongly correlated superconductors and superfluids, including the cuprates, heavy fermions, ruthenates, and 3 He (14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28), where the repulsive interaction between fermions drives the formation of higher angular momentum pairs with nodes in the pair wavefunction. Iron-based superconductors are generally believed to have an isotropic s ± gap structure (29) with a sign change between gap function on the electron and hole pockets.…”