Isotropic superconducting gap and electron-boson coupling in MgB2 multiband superconductor

MgB$_2$ is a prototype multiband BCS/Elishberg superconductor with high transition temperature T$_C$ $\sim$39K. In this talk, we will present electronic properties of this compounds measured by tunable laser ARPES. Momentum dependent gap structure on two $\sigma$ Fermi surface around $\Gamma$ is nearly isotropic with $\Delta_0$$\sim$7meV, directly proving its s-wave pairing symmetry. Our data reveals a strong renormalization of the dispersion (kink) at $\sim$65 meV, which is caused by coupling of electrons to E$_{2g}$ phonon mode. In contrast to cuprates, the 65 meV kink in MgB$_2$ does not change significantly across T$_C$. More interestingly, we observe strong coupling to a second, low energy collective mode at 10 meV. This excitation vanishes above T$_C$ and is likely a signature of the elusive Leggett mode.