Modified electron-boson coupling in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ nanocrystals

The coupling between electrons and bosons is thought to underlie a variety of unusual behavior in the cuprates. Here we present optical evidence that the electron-boson coupling is strongly modified in mechanically-exfoliated Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ nanocrystals. Through an extended Drude analysis of the mid-infrared optical conductivity, we demonstrate that the electron-boson spectral function is blue-shifted and enhanced in thin Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ nanocrystals. Taken together with complementary Raman and Laue diffraction data, our results provide further evidence that the bosons relevant to the electrodynamics of the normal state are magnetic.