OFFPRINT Photoproduction in semiconductors by onset of magnetic field

The energy bands of a semiconductor are lowered by an external magnetic field. When a field is switched on, the straight-line trajectories near the top of the occupied valence band are curved into Landau orbits and Bremsstrahlung is emitted until the electrons have settled in their final Fermi distribution. We calculate the radiated energy, which should be experimentally detectable, and suggest that a semiconductor can be cooled by an oscillating magnetic field. Copyright c © EPLA, 2008 Introduction. – Valence and conduction electrons near the Fermi sphere of a semiconductor have many similarities with the Dirac electrons in the vacuum. In fact, the hole state as a missing state in the valence band is completely analogous to a positron in Dirac’s sea of occupied negative-energy electrons. The band width ∆ of a superconductor, which is typically of the order of 0.1 eV, corresponds to the energy gap ∆= 2mec 2 ≃ 1.04MeV in Dirac’s vacuum, above which electron-positron pairs can be produced. As a consequence, the electromagnetic behavior of a semiconductor at and below room temperature with kBT ≃ 0.024eV (kB =Boltzmann constant) can be studied by the same field-theoretic techniques as a Dirac vacuum for kBT ≪ 2mc. In particular, one can transfer the results found by Heisenberg and Euler [1,2] for electrons and positron to electrons and holes. A strong electric field larger than Ec =m 2 ec /e ≃ 1.3 · 10V/m leads to electron-hole pair production. A magnetic fieldH lowers the energy of the ground state since the electrons are curved into Landau orbits [3]. This should produce synchrotron radiation. For the magnetic field switched on in the vacuum, this was pointed out in ref. [4] as a consequence of the Euler-Heisenberg calculation [1,2]. However, this effect could become observable only for extremely large magnetic fields which cannot be attained in present-day laboratories. It will play a role mainly in astrophysical events, such as supernova explosions, and during the formation of neutron stars, where (a)E-mail: [email protected] (b)E-mail: [email protected] magnetic fields reach Hc =m 2 ec /e = 4.3× 10 gauss. It may also account for the emission of an anomalous X-ray pulsar [5]. The purpose of this note is to suggest observing this type of synchrotron radiation at presently available magnetic fields of 10 gauss by placing a semiconductor in a magnetic field. Moreover, we point out that this may give rise to a novel cooling technique for semiconductors. Electron and hole states. – The electrons in the highest valence band of a semiconductor occupy Bloch states which look like free-particle states ψk(r, t) = e kψk(r), where k is the Bloch momentum and ξk the energy measured from the Fermi surface between the bands. Near the top of the band, the energy can be expanded as [6]