Quantum tunneling of vortices in a MgB$_2$ superconductor
  Magnetic relaxation in a MgB$_2$ superconductor was measured. The temperature dependence of the normalized relaxation rate was determined for three different magnetic fields. By extrapolating these rates to T=0 K, we find that these extrapolations do not approach zero, indicating quantum tunneling of vortices in the superconductor. A quantum correction of the relaxation rate, followed by the correction of the magnetic moment, is proposed. Using the quantum correction, we find that $U_0$ increases with decreasing temperature and approaches a maximum at T=0. 
Y. Z. Zhang, R. Deltour, H.H. Wen, C. Q. Jin, Y. M. Ni, S. L Jia,   G.C.Che, and Z. X. Zhao