Electronic specific-heat anomalies in two-dimensional systems

The influence of the electron-phonon interaction on the electronic spectral properties in a two-dimensional system is studied within leading-order perturbation theory. We find that the wave-vector dependence of screening in the electron-phonon coupling strength may give rise to a ${\omega }^3\ln \omega$ term in the electronic self-energy at zero temperature, where $\omega$ is the electronic energy relative to the Fermi energy. Implications of such anomalous self-energy corrections for the electronic specific heat are explored. We find that at finite temperature the specific heat will have an anomalous $T^3\ln T$ term in addition to the regular linear $T$ term. The possibility of observing such specific-heat anomalies in actual two-dimensional systems is discussed.