  From density functional calculations, we show that localized states stemming
from defects or topological disorder exhibit an anomalously large
electron-phonon coupling. We provide a simple analysis to explain the
observation and perform a detailed study on an interesting system: amorphous
silicon. We compute first principles deformation potentials (by computing the
sensitivity of specific electronic eigenstates to individual classical normal
modes of vibration). We also probe thermal fluctuations in electronic
eigenvalues by first principles thermal simulation. We find a strong
correlation between a static property of the network [localization, as gauged
by inverse participation ratio (IPR)] and a dynamical property (the amplitude
of thermal fluctuations of electron energy eigenvalues) for localized electron
states. In particular, both the electron-phonon coupling and the variance of
energy eigenvalues are proportional to the IPR of the localized state. We
compare the results for amorphous Si to photoemission experiments. While the
computations are carried out for silicon, very similar effects have been seen
in other systems with disorder.
