Momentum dependence of the superconducting gap and in-gap states in ${\mathrm{MgB}}_2$ multiband superconductor

We use tunable laser-based angle-resolved photoemission spectroscopy to study the electronic structure of the multiband superconductor ${\mathrm{MgB}}_2$. These results form the baseline for detailed studies of superconductivity in multiband systems. We find that the magnitude of the superconducting gap on both $\sigma$ bands follows a BCS-like variation with temperature with ${\mathrm{\Delta }}_0\sim 7\mathrm{meV}$. The value of the gap is isotropic within experimental uncertainty and in agreement with a pure $s$-wave pairing symmetry. We also observe in-gap states confined to $k_F$ of the $\sigma$ band that occur at some locations of the sample surface. The energy of this excitation, $\sim 3$ meV, is somewhat larger than the previously reported gap on $\pi$ Fermi sheet and therefore we cannot exclude the possibility of interband scattering as its origin.

Figure 1

Temperature dependence of the superconducting gap in ${\mathrm{MgB}}_2$. (a) Sketched FS topology from calculation. Inset shows the measured FS intensity map close to the Brillouin zone center. (b)–(d) ARPES intensity divided by the Fermi function along cut1 ($\mathrm{\Gamma }-M$ direction) at 18, 27, and 40 K, respectively. (e) ARPES intensity divided by the Fermi function along cut2 measured at 22 K. Locations of cuts are illustrated in (a). (f) Temperature dependence of EDCs at $k_F$ of cut1. (g) Symmetrized EDCs from (f). (h) and (i) Symmetrized EDCs at $k_F$ of cut2 for $\sigma 1$ and $\sigma 2$ bands, respectively. (j) Temperature dependence of the superconducting gap extracted from (g) and (f) color/shape coding shown in (a). Solid lines indicate BCS prediction with corresponding ${\mathrm{\Delta }}_0$.

Figure 2

Momentum dependence of the superconducting gap in ${\mathrm{MgB}}_2$. (a) and (b) EDCs at $k_F$ along two $\sigma$ FS sheets. The 19 momentum locations in the Brillouin zone are marked in the left-bottom inset. Data were measured at 25 K. (c) Angle dependence of the superconducting gap. (d) Same data as (c) plotted in polar coordinates after being sixfold symmetrized.

Figure 3

Inside gap state in a superconducting state. (a) Measured band structure of cut1 [as illustrated in Fig. 1] at 18 K. (b) Expanded area close to $E_F$. Color scale is adjusted to highlight structure above $E_F$. (c) EDCs corresponding to data in (b). Bogoliubov quasiparticle peaks and inside gap structures are marked with red and blue arrows, respectively.

Figure 4

Temperature dependence of the in-gap state. (a1)–(a5) ARPES intensity measured at cut1 for various temperatures. (b) EDCs slightly off $k_F$ [location marked with red line in (a1)] for various temperatures along line marked in (a1). Inset shows fitting of the EDC above $E_F$ with two Gaussian peaks to extract value of the two gaps. (c) Extracted temperature dependence of the peak positions of Bogoliubov quasiparticle (red dots) and inside gap structures (blue dots). Two dashed lines are guide to the eye.