Anderson-Higgs transition in quantum spin ice Yb$_{2}$Ti$_{2}$O$_{7}$

We have carried out polarized elastic neutron-scattering experiments on single crystals Yb$_{2}$Ti$_{2}$O$_{7}$ from 1 K to 0.04 K. The results reveal that the diffuse [111]-rod scattering [1] is suppressed below T$_{c}$ $\sim $ 0.21 K, where magnetic Bragg peaks and a full depolarization of neutron spins are observed with the thermal hysteresis, indicating a first-order ferromagnetic transition. Theoretically, a quantum spin ice state [2] above T$_{c }$ has been realized from an effective classical model where $<$111$>$ Ising moments, i.e., pseudospin-1/2 interact mainly through a magnetic dipolar interaction [3], and a transition from magnetic Coulomb phase to Higgs phase has emerged at T$_{c }$ in Yb$_{2}$Ti$_{2}$O$_{7}$. [1] K. A. Ross \textit{et al.}, Phys. Rev. Lett. \textbf{103}, 227202 (2009). [2] S. Onoda \textit{et al.}, J. Phys.: Conf. Series, in press. [3] S. T. Bramwell and M. J. P. Gingras, Science \textbf{294}, 1495 (2001).