Optical conductivity of superconducting Sr2RuO4

– We compute the optical conductivity of 2D f-wave superconductors and also of the multigap model proposed recently by Zhitomirsky and Rice at T = 0K in the Born limit. The presence of interband impurity scattering was found to play an important role: the contributions from the two bands mix up, and new structures are seen in the tunneling density of states and in the optical spectrum as well, corresponding to interband transitions. This will provide a sensitive test in selecting the competing models for the triplet superconductivity in Sr2RuO4. Introduction. – The discovery of superconductivity in Sr2RuO4 in 1994 has generated much interest since it is a perovskite with the same crystal structure as La2CuO4 [1]. From analogy with superfluid He Rice and Sigrist [2,3] proposed the spin triplet p-wave superconductor with order parameter ∆(k) = d∆p(T )(k̂x ± ik̂y) (1) Here d is the spin vector parallel to z. The triplet pairing has been confirmed by the presence of spontaneous magnetization seen by μSR [4], which revealed that the superconducting state breaks the time-reversal symmetry, and a flat O Knight shift seen by NMR [5] showed no change in the spin susceptibility when passing through the superconducting transition temperature. However the large density of states (N(0)) in the gapless region was somewhat surprising [6], since eq. (1) has the full energy gap [7]. Furthermore, as sample quality improved, the characteristics of nodal superconductors became clearly visible in the specific heat (∝ T ) [8], the magnetic penetration depth (∝ T ) [9], NMR relaxation rate (∝ T ) [10], the thermal conductivity (∝ T ) [11, 12] and the ultrasonic attenuation [13]. Therefore a variety of 2D f-wave models have been proposed c © EDP Sciences 2 EUROPHYSICS LETTERS [14, 15, 16]. Since all these f-wave models have the same quasiparticle density of states, the specific heat and the magnetic penetration depth etc. are described equally well by any of these 2D f-wave models [16]. On the other hand, the angular dependent magnetothermal conductivity data by Izawa et al. [17] can exclude all 2D f-wave models with nodes lying in the a− b plane [16, 18]. Therefore it singles out the most consistent f-wave as ∆(k) = d∆f (T )(k̂x ± ik̂y) cos(ckz). (2) The nodal lines are horizontal. Also the pair correlation takes the maximum value for the relative separation of the pair at ±c. However in quasi-two dimensional systems with paramagnon (i.e. the ferromagnetic fluctuation), the ground state of p-wave superconductors is given by eq. (1) [3]. This is why Zhitomirsky and Rice (ZR) [19] proposed the multigap model: there is p-wave superconductor attached the active γ band, which induces another f-wave like order parameter in the passive α+ β bands through Cooper pair scattering given by ∆2(k) = d∆2(T )(k̂x ± ik̂y) cos(ckz/2). (3) Since ∆2(k) as given in eq. 3 gives the same quasiparticle density of states as a d-wave superconductor [20], it is not difficult to reproduce the specific heat and the magnetic penetration depth within the multigap model as was shown recently by Kusunose and Sigrist [21]. However a simple analysis suggests that ∆2(k) is incompatible with the angular dependent magnetothermal conductivity data. In fig. (1) we show ∆(k) for p-wave, f-wave and ∆2(k) in quasi 2D systems. p-wave |∆2(k)| f-wave Fig. 1 – The absolute value of the p-wave (left), ∆2(k) (middle) and f-wave gap is shown. Note the presence of horizontal nodes in the latter two. We note here that vc = 0 (i.e. the Fermi velocity in the z direction) on the nodal lines of ∆2(k) which gives rise to a large cos(2φ) term in the angular dependent thermal conductivity [16]. In the following we compute the quasiparticle density of states and the optical conductivity for the f-wave gap and for the multigap model in the Born limit at T = 0K, assuming, that both interand intraband scattering of impurities are important, which was predicted to have strong effect on the superconducting state [22]. The density of states differs significantly in these two models, producing distinct peaks from the active and passive bands in the ZR model, while only one single peak is found in the f-wave case. In the optical conductivity, beyond the intraband resonance peaks another extra feature is found coming from interband scattering. On the other hand, the single broad bump in the f-wave case can clearly be distinguished from Balázs Dóra et al.: Optical conductivity of superconducting Sr2RuO4 3 the three peak structure of ZR’s model, hence both the single particle density of states and the optical conductivity manifest evident signatures of the corresponding model. Density of states. – As already pointed out by Agterberg [22], the effect of interband impurity scattering plays an important role in the multigap model, similarly to the interband scattering of Cooper pairs, which induced ∆2(k) in the passive bands. However, in the f-wave case, we deal with a simple one band model, therefore only intraband impurity scattering is considered. The effect of weak impurities (Born limit) is incorporated in the quasiparticle Green’s function of the multigap model by renormalizing the frequency: ∆2u1 = ω + Γ11 2 π u1