| We construct the low energy theory of a doped Mott insulator, such as the high-temperature superconductors, by explicitly integrating over the degrees of freedom far away from the chemical potential. For either hole or electron doping, a charge 2e bosonic field emerges at low energy. The charge 2e boson mediates dynamical spectral weight transfer across the Mott gap and creates a new charge e excitation by binding a hole. The presence of a new low-energy charge e excitation represents a fundamental breakdown of Fermi liquid theory as this excitation has no correspondence with the spectrum in the free system. As a result of this new excitation, a bifurcation of the electron dispersion below the chemical potential obtains as is observed recently in angle-resolved photoemission on Pb-doped Bi2Sr2CaCu2O8+δ (Pb2212). In addition, we show that the 1) mid-infrared band in the optical conductivity, 2) the T2 contribution to the thermal conductivity, 3) the pseudogap, 4)insulating behaviour away from half-filling, 5) the high and low-energy kinks in the electron dispersion and 6) T-linear resistivity all derive from the charge 2e boson. |
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