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These properties of solid metals and ultra-cold gases, respectively, are connected by the BCS-BEC crossover. Here we investigate the band dispersions in FeTe$_{0.6}$Se$_{0.4}$($T_c$ = 14.5 K $\\sim$ 1.2 meV) in an accessible range below and above the Fermi level($E_F$) using ultra-high resolution laser angle-resolved photoemission spectroscopy. 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