Quasiparticle density of states by inversion with maximum entropy method

Abstract

We propose to extract the quasiparticle density of states (DOS) of the superconductor directly from the experimentally measured superconductor-insulator-superconductor junction tunneling data by applying the maximum entropy method to the nonlinear systems. It merits the advantage of model independence with minimum a priori assumptions. Various components of the proposed method have been carefully investigated, including the meaning of the targeting function, the mock function, as well as the role and the designation of the input parameters. The validity of the developed scheme is shown by two kinds of tests for systems with known DOS. As a preliminary application to a ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ sample with its critical temperature ${T}_{c}=89\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, we extract the DOS from the measured intrinsic Josephson junction current data at temperatures of $T=4.2\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, $45\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, $55\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, $95\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, and $130\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. The energy gap decreases with increasing temperature below ${T}_{c}$, while above ${T}_{c}$, a kind of energy gap survives, which provides an angle to investigate the pseudogap phenomenon in high-${T}_{c}$ superconductors. The developed method itself might be a useful tool for future applications in various fields.