title: Measurements of the electric field of zero-point optical phonons in GaAs quantum wells support the Urbach rule for zero-temperature lifetime broadening.
abstract: We study a specific type of lifetime broadening resulting in the well-known exponential "Urbach tail" density of states within the energy gap of an insulator. After establishing the frequency and temperature dependence of the Urbach edge in GaAs quantum wells, we show that the broadening due to the zero-point optical phonons is the fundamental limit to the Urbach slope in high-quality samples. In rough analogy with Welton's heuristic interpretation of the Lamb shift, the zero-temperature contribution to the Urbach slope can be thought of as arising from the electric field of the zero-point longitudinal-optical phonons. The value of this electric field is experimentally measured to be 3  kV cm-1, in excellent agreement with the theoretical estimate.
authors: Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Nadia 741246, West Bengal, India.
authors: Rupak
authors: R
authors: Bhattacharya
authors: Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Nadia 741246, West Bengal, India.
authors: Richarj
authors: R
authors: Mondal
authors: Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Nadia 741246, West Bengal, India.
authors: Pradip
authors: P
authors: Khatua
authors: Laboratory of Physics of Nanostructures, Ecole Polytechnique Fédédrale de Lausanne, CH-1015 Lausanne, Switzerland.
authors: Alok
authors: A
authors: Rudra
authors: Laboratory of Physics of Nanostructures, Ecole Polytechnique Fédédrale de Lausanne, CH-1015 Lausanne, Switzerland.
authors: Eli
authors: E
authors: Kapon
authors: University of Erlangen-Nürnberg (FAU), Applied Physics, D-91058, Erlangen, Germany.
authors: Stefan
authors: S
authors: Malzer
authors: Max Planck Institute for the Science of Light, Günther-Scharowsky-Strasse 1, Bau 24, 91058 Erlangen, Germany.
authors: Gottfried
authors: G
authors: Döhler
authors: Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Nadia 741246, West Bengal, India.
authors: Bipul
authors: B
authors: Pal
authors: Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Nadia 741246, West Bengal, India.
authors: Bhavtosh
authors: B
authors: Bansal