arXiv:cond-mat/0111409v1 [cond-mat.dis-nn] 21 Nov 2001 Optically induced coherent intra–band dynamics in disordered semiconductors C. Schlichenmaier, 1 I. Varga, 1, 2 T. Meier, 1 P. Thomas, 1 and S. W. Koch 1 1 Fachbereich Physik und Wissenschaftliches Zentrum f¨ ur Materialwissenschaften, Philipps–Universit¨ at, Renthof 5, D–35032 Marburg, Germany 2 Elm´ eleti Fizika Tansz´ ek, Fizikai Int´ ezet, Budapesti M˝ uszaki ´ es Gazdas´ agtudom´ anyi Egyetem, H–1521 Budapest, Hungary (Dated: October 24, 2018) On the basis of a tight–binding model for a strongly disordered semiconductor with correlated conduction- and valence band disorder a new coherent dynamical intra–band effect is analyzed. For systems that are excited by two, specially designed ultrashort light–pulse sequences delayed by τ relatively to each other echo–like phenomena are predicted to occur. In addition to the inter–band photon echo which shows up at exactly t =2τ relative to the first pulse, the system responds with two spontaneous intra–band current pulses preceding and following the appearance of the photon echo. The temporal splitting depends on the electron–hole mass ratio. Calculating the population relaxation rate due to Coulomb scattering, it is concluded that the predicted new dynamical effect should be experimentally observable in an interacting and strongly disordered system, such as the Quantum–Coulomb–Glass. PACS numbers: 72.40.+w; 78.47.+p; 72.80.Ng I. INTRODUCTION Echo phenomena, the prototype being the Hahn spin echo 1 for spin–1/2–systems, rely on the generation of a coherent ensemble of excitations with a continuous distri- bution of frequencies. After pulsed excitation the macro- scopic response of the ensemble decays as a consequence of destructive interference effects in the continuum of ex- cited frequencies. A second, delayed excitation pulse in- duces a rephasing of the individual excited species such that at twice the delay time the ensemble shows a spon- taneous macroscopic response, the echo. A necessary re- quirement for the observability of this coherent dynamics are sufficiently weak dephasing interactions on the time scale of the pulse delay. The microscopic reason for the appearance of an echo is that the second pulse causes phase conjugation of the coherent excitation generated by the first pulse. In close analogy to the spin echo also photon echoes have been observed in ensembles of two–level absorbers 2 . There are also phonon echoes 3 and temperature echoes 4 , even classical mechanic ensembles of pendulums can show echo phenomena 5 . Photon echoes have also been studied in more compli- cated systems, such as ordered 6 and disordered 7 semicon- ductors. The optically excited inter–band transitions in a semiconductor cannot be considered as an ensemble of independent two–level absorbers due to the strong inter- action of the electron–hole pairs. Photon echoes there- fore may show a decay as a function of the delay time due to the Coulomb interactions, due to disorder, and due to combined interaction–disorder effects 6,8,9,10 . In Ref. 11 a new echo phenomenon has been proposed for disordered conductors or Anderson insulators. On the basis of a non–interacting one–dimensional tight–binding band with diagonal disorder filled with a low density of carriers the current response to short externally applied voltage pulses was calculated. Assuming excitation with two short voltage pulses at t = 0 and t = τ , where τ was chosen larger than the typical elastic scattering time τ el , it was predicted that the system spontaneously responds with a current pulse exactly at time t =2τ . In contrast to spin echoes and photon echoes this current echo is not related to phase conjugation. The influence of Coulomb interactions on the current echo was investigated in Ref. 12 . The numerically exact calculation for a small tight–binding system showed that the current echo should remain visible in the presence of the many–body interaction, however so far no experi- mental observation has been reported. In a series of papers van Driel, Sipe, and coworkers have shown that in semiconductors currents can be in- duced optically on an ultra–short time scale using a co- herent control scheme 13 . In addition, a resulting current pulse could possibly be observed using THz–detection techniques. Stimulated by these results, we studied optically in- duced current phenomena in disordered model systems 14 . By solving the equation of motion for the intra–band current in a noninteracting tight–binding model we con- cluded that on the basis of the coherent control scheme it should be indeed possible to generate a current pulse also in a strongly disordered semiconductor. The current pulse decays due to elastic scattering. In addition, the current traces show signatures of Anderson localization (in a one–dimensional noninteracting disordered system all states are localized). The application of two delayed optical pulses, both generating a current pulse, was found to result in a sizable echo in the intra–band current, that appears at t =2τ . At the same time the inter–band polarization shows the conventional photon echo. Continuing our earlier work 14 and making our model more realistic we were surprised to discover that the opti- cally induced intra–band dynamics in a disordered semi- conductor with correlated conduction- and valence–band disorder shows features that differ profoundly from both the photon and the current echo. By allowing the ef-