Semiconductor analog of the Dirac equation and Sauter-Schwinger pair creation

There is an analogy between E-field-induced tunneling of Dirac-sea electrons to the upper energy continuum in Dirac theory (Sauter-Schwinger effect) and electron-hole pair creation in direct-gap semiconductors via interband (Landau-Zener) tunneling due to external E fields. In this talk, we show that in 1+1 spacetime dimensions, the Bloch electrons in the vicinity of the band gap obey a Dirac equation with effective physical constants in arbitrary external fields E(t,x), provided the fields predominantly stimulate tunneling-type excitations (low photon energies, large wavelengths). Condensed-matter analogs of relativistic quantum physics could be useful to study high-energy effects in the laboratory.