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The temperature dependence of the London penetration depth, λ(T ), was measured in both single crystal and polycrystalline MgB2 samples by a high-resolution, radio frequency technique. A clear exponential temperature dependence of λ(T ) was observed at low temperature, indicating s-wave pairing. A BCS fit to the lowest temperature data gives an in-plane energy gap ∆ of 30 ± 2 K (2∆/Tc = 1.5 ± 0.1), which is significantly smaller than the standard BCS weak coupling value of 3.5. We find that the data are best described by a two-gap model.

Tunneling and theoretical studies have suggested that Andreev bound states form at certain surfaces of unconventional superconductors. Through studies of the temperature and field dependence of the in-plane magnetic penetration depth λ ab at low temperature, we have found strong evidence for the presence of these states in clean single crystal YBCO and BSCCO. Crystals cut to expose a [110] interface show a strong upturn in λ ab at around 7 K, when the field is oriented so that the supercurrents flow around this surface. In YBCO this upturn is completely suppressed by a field of ∼ 0.1 T.PACS numbers: 74.25.NfThe low temperature behavior of the magnetic penetration depth (λ) has played an important role in identifying the bulk order parameter in the high T c cuprates. Within the usual BCS quasiparticle picture, the temperature and field dependence of λ are determined by the energy dependence of the quasiparticle density of states N (E), and hence give information about the magnitude of the energy gap, but not its phase. Recently however, it has been suggested that there is another contribution to λ which arises from current carrying, zero energy, surface Andreev bound states (ABS) [1], which form if there is π phase shift between the different lobes of the order parameter [2][3][4]. The observation of these states provides a key piece of evidence backing the d-wave scenario in the cuprates. In addition, this extra contribution has important consequences for the interpretation of all surface impedance measurements in non-conventional superconductors.The zero bias conductance peak (ZBCP) observed in tunneling measurements has been interpreted as resulting from ABS [5,2] . This has been interpreted as resulting from surface roughness and/or nanofaceting [2]. The contribution of the ABS to λ can be understood simply by noting the increase in the penetration depth ∆λ due to thermally excited quasiparticles is given bywhere f is the Fermi function. For a d-wave superconductor N (E) ∼ |E|, which gives ∆λ(T )/λ(0) = αT , where α depends on the angular slope of the energy gap near the nodes [6]. Surface bound states add a singular contribution δ(E) to N (E) which when substituted into Eq. (1) adds a divergent 1/T term to ∆λ(T ). The relative size of 1/T term depends on the orientation of the surface and the band structure of the material [4]. The ABS contribution to λ is highly non-linear in field, as the superflow Doppler shifts of the position of the bound state peaks. It is therefore expected that the 1/T term is suppressed with a relatively weak magnetic field. In this letter, we report measurements of the temperature and field dependence of the in-plane penetration depth of high quality YBa 2 Cu 3 O 6.9 and Bi 2 Sr 2 CaCu 2 O 8 single crystals which provide strong evidence of the existence of ABS in these materials. Evidence for an ABS contribution to λ have previously been identified from studies of irradiated thin films [3] and grain boundary junctions [7]. Here, we have been able to investigate the ABS more fully ...

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