Evidence for non-s-wave symmetry of theπgap inMgB2from intermodulation distortion measurements

Abstract

We present low-temperature low-power intermodulation-distortion ͑IMD͒ measurements of high-quality MgB 2 thin films that are inconsistent with presumed s-wave symmetry of the order parameter. The measurements were carried out in a stripline resonator at approximately 2 GHz between 1.8 K and T c . The IMD arises from the nonlinear Meissner effect in which the penetration depth is dependent on the RF magnetic field. Specifically, the observed IMD vs temperature T for T Ӷ T c / 2 varies as T −2 , while for an s-wave gap symmetry in the clean limit, the low-temperature IMD decreases exponentially with decreasing temperature. We calculate the IMD from first principles for different order-parameter symmetries using a Green's function approach and compare the results with the measured data. We propose that the observed upturn in the low-temperature IMD implies an admixture of an order parameter with nodal lines into the energy gaps of MgB 2 . Most likely, this admixture is prominent for the gap. Within the constraints of the hexagonal crystal symmetry of MgB 2 , the best fit with our IMD measurements is obtained with a gap ⌬͑ , T͒ = ⌬ 0 ͑T͒sin͑6͒, where is the azimuthal angle in the ab plane, and ⌬ 0 ͑T͒ is the amplitude, weakly temperature dependent at low temperatures. This gap symmetry entails six nodal lines. We also present low-temperature penetration-depth measurements that are consistent with the proposed nodal gap symmetry. To relate our proposition with existing literature, we review other low-temperature probes of the order-parameter symmetry. The literature presents conflicting results, some of which are in direct support of the symmetry proposed here.

Current-phase relation in a short clean josephson junction model: application to MgB2

“…This signature been observed in the cuprate YBCO which indeed has a nodal (d-wave) energy-gap. The measured low-temperature IMD of MgB 2 is strikingly similar to that of YBCO, which strongly suggests a nodal p energy gap, specifically with i-wave symmetry [15]. Other observables, such as the low-temperature penetration-depth anomaly and the temperature dependence of the microwave surface resistance provide additional support for the i-wave symmetry [13].…”

“…From a physics point of view MgB 2 is interesting in at least two respects. It has two energy gaps that are susceptible only to weak coupling by non-magnetic impurities and, allegedly, these two energy gaps have distinct symmetries [12][13][14][15]. By convention, the two energy gaps are labelled as the s (larger) and the p gap (smaller).…”

MgB2nonlinear properties investigated under localized high rf magnetic field excitation

“…When the excitation field approaches the critical field, the mechanism of intrinsic nonlinearity is still similar to the NLME and becomes more significant. For example, around T c , this nonlinearity comes from the backflow of excited quasiparticles in a current-carrying superconductor, which results in an effective decrease of the superfluid density [7,8,18]. A two-band quasiparticle backflow calculation has been applied to the MgB 2 intrinsic nonlinearity.…”

“…Although MgB 2 is commonly believed to be a conventional s-wave superconductor, Agassi, Oates, and Moeckly claim that MgB 2 has line nodes in the superconducting gap, and they claim further that the gap has six nodes, as Áð; TÞ ¼ Á 0 ðTÞ Ã sinð6Þ where is the azimuthal angle in the c ab plane of the hexagonal crystal, and Á 0 ðTÞ is the weakly temperature-dependent amplitude of the gap function at low temperatures [8]. From their IMD measurement on MgB 2 films, the temperature-dependent P IMD ðTÞ shows an upturn around T < 10 K and increases as 1=T 2 [9].…”

“…In this paper, we report the MgB 2 experimental nonlinearity data from localized areas. These data will be interpreted as a combination of several nonlinear mechanisms including intrinsic nonlinear responses [7,8] and vortex nonlinearity [5].…”