Large temperature renormalization of anomalous Luttinger exponent in $Li_{0.9}Mo_{6}O_{17}$

$Li_{0.9}Mo_{6}O_{17}$ is unique as a quasi-1 dimensional metal for which both photoemission spectroscopy (PES) [1] and tunneling [2] find Luttinger liquid (LL) power law behaviors in spectra near the Fermi energy $E_{F}$, albeit with differing values of the anomalous exponent $\alpha$, $\approx0.9$ at temperature 300K and $\approx0.6$ below 50K, respectively. New T-dependent PES spectra from T = 300K down to 15K can be well fit by finite-T LL theory, with $\alpha$ varying continuously from $\approx0.9$ to $\approx0.6$, showing consistency of PES and tunneling. We find that its incommensurate Fermi wavevector would preclude such a large renormalization of $\alpha$ with T for $Li_{0.9}Mo_{6}O_{17}$ were it not for interband dynamics and residual interaction scattering that can occur only because there are two (nearly degenerate) bands crossing $E_{F}$. We also discuss implications of the theory for further experiments. [1] G.-H. Gweon et al, Phys. Rev. B $\bf {68}$, 195117 (2003). [2] J. Hager et al, Phys. Rev. Lett. $\bf {95}$, 186402 (2005).