Electron-phonon coupling is large for localized states

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 squared 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.