9 N ov 2 00 1 Superconducting energy gaps , low temperature specific heat , and quasiparticle spectra of MgB 2

Hyoung Joon Choi, David Roundy, Hong Sun, Marvin L. Cohen, & Steven G. Louie Department of Physics, University of California at Berkeley, Berkeley, CA 94720, USA. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. Magnesium diboride is remarkable not only for its unusually high transition temperature of 39K for a sp-bonded metal [1] and its reduced isotope-effect exponent [2,3], but also for its unusual superconducting gap behavior [4–16]. Some earlier experiments seem consistent with conventional single-gap superconductivity [4–8], but recent measurements indicate the existence of more than one gap [9–16]. For example, specific heat measurements show an anomalous large bump at low temperature, inconsistent with single-gap BCS theory. Moreover, there is a significant variation in the measured values for the gaps. Here, we report first-principles calculations of the kand T -dependent superconducting gap ∆(~k, T ) in MgB2 and its manifestation in various measured quantities. Because its Fermi surface has disconnected sheets with very different electron-phonon coupling strengths, our calculations show that near T = 0, the values of ∆(~k) cluster into two groups: large values (∼ 6.5 to 7.5 meV) on the strongly coupled sheets and small values (∼ 1 to 3 meV) on the weakly coupled sheets. The calculated gap, quasiparticle density of states, and specific heat and their temperature dependences are in agreement with the recent measurements which support that MgB2 is a multiple gap superconductor. In fact, theory predicts four prominent values for the gap at low T . Most theoretical work on MgB2 has been focused on the electronic structure, the phonon structure, and the electron-phonon interaction [17–23]. It is shown that the electron-phonon