SPECIFIC HEAT OF Mg11B2 IN MAGNETIC FIELDS: TWO ENERGY GAPS IN THE SUPERCONDUCTING STATE

Abstract

SPECIFIC HEAT OF Mg 11 B 2 IN MAGNETIC FIELDS: TWO ENERGY GAPS IN THE SUPERCONDUCTING STATE R. A. FISHER, F. BOUQUET, N. E. PHILLIPS Lawrence Berkeley National Laboratory and Chemistry Department, University of California, Berkeley, CA 94720, USA D. G. HINKS AND J. D. JORGENSEN Argonne National Laboratory, Argonne, IL 60439, USA We present specific-heat measurements on Mg 11 B 2 in magnetic fields to 9 T. The anomaly at T c is rapidly broadened and attenuated in fields, as expected for an anisotropic, randomly oriented superconductor. At low temperature there is a strongly field-dependent feature that shows the existence of a second energy gap. The Sommerfeld constant, γ , increases rapidly and non- linearly with magnetic field, which cannot be accounted for by anisotropy. It approaches γ n = 2.6 mJ K -2 mol -1 , the coefficient of the normal-state electron contribution, asymptotically for fields greater than 5 T. In zero magnetic field the data can be fitted with a phenomenological two-gap model, a generalization of a semi-empirical model for single-gap superconductors. Both of the gaps close at the same T c ; one is larger and one smaller than the BCS weak coupling limit, in the ratio ~ 4:1, and each accounts for ~ 50% of the normal-state electron density of states. The parameters characterizing the fit agree well with those from theory and are in approximate agreement with some spectroscopic measurements. Soon after the discovery of superconductivity in MgB 2 with T c ~ 40 K [1], it was shown that the specific heat, C, provides compelling evidence for the existence of two distinctly different energy gaps. In this paper we will describe briefly how specific-heat measurements in magnetic fields, H, can be used to identify and quantify these energy gaps [2-4]. The electronic specific heat, C e (H), for various H is plotted in Fig. 1 as C e (H)/T vs. T for a polycrystalline sample of Mg 11 B 2 , where C e (H) was evaluated from the difference C(H) – C(9 T) [2-4]. The anomaly at T c is rapidly broadened and attenuated in H, as expected for an anisotropic, randomly oriented superconductor in the mixed state. In addition, two things are striking about the plot: 1). For H = 0 C e increases much more rapidly with T than for a BCS superconductor. 2). At low T and H ≠ 0, there is a very