We study a resistively shunted semiconductor superlattice subject to a high-frequency electric field. Using a balance equation approach that incorporates the influence of the electric circuit, we determine numerically a range of amplitude and frequency of the ac field for which a dc bias and current are generated spontaneously and show that this region is likely accessible to current experiments. Our simulations reveal that the Bloch frequency corresponding to the spontaneous dc bias is approximately an integer multiple of the ac field frequency. [S0031-9007(98)05660-9] PACS numbers: 72.20.Ht, 05.45. + b, 73.20.Dx In 1928 Bloch demonstrated [1] that electrons in a periodic lattice potential with period a subject to a dc electric field E dc undergo oscillations with characteristic frequency v B eaE dc ͞h. In naturally occurring solids, observations of Bloch oscillations are precluded by the need for very high applied electric fields to reduce the Bloch oscillation period below the dephasing times arising from the ever-present scattering due to impurities and phonons. In 1970, Esaki and Tsu [2] recognized that due to their longer spatial periods, semiconductor superlattices (SSLs) can support Bloch oscillations in the terahertz (THz) domain-comparable to or faster than the corresponding scattering frequencies-even for modest field strengths (ϳ1 kV͞cm). Thus, not only should the Bloch oscillations be observable in SSLs, but SSLs could also serve as devices to produce THz radiation [2]. When, in addition to the static field E dc , an SSL is subjected to an ac field of frequency V, the static current-voltage characteristic can exhibit structures at v B nV (where n is an integer) [3,4]. In the presence of dissipation, multiphoton transitions involving different n can lead to a Bloch oscillator capable of producing radiation from almost zero to the THz frequencies. Recently, experiments involving novel electromagnetic radiation sources and coupling techniques have revealed additional effects of THz radiation fields on the dc conductivity of an SSL [5-8], including (i) THz multiphoton-assisted tunneling [5], (ii) ac-field-induced reduction of the dc current [6], (iii) absolute negative conductance [7], and (iv) resonant changes in conductivity [8].In the present Letter, we examine a question that is roughly the converse of the Bloch oscillations in an SSL: namely, can a purely ac external field applied to an appropriately configured (but unbiased) SSL create a dc bias and corresponding dc current? In technical terms, this corresponds to a spontaneous breaking of spatial reflection symmetry. Using the methods of nonlinear dynamics, we show that the answer to this question is "yes" and find the condition for spontaneous dc current generation in the circuit consisting of the SSL shunted by an external resistance. We observe that the Bloch frequency corresponding to the spontaneously generated bias across the SSL is approximately an integer multiple of the frequency of the external ac field and explain the origin of this...

We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field.We use the semi-classical balance-equation approach which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free electron lasers, chaos may be observable in SSLs. We clarify the nature of this novel nonlinear dynamics in the superlattice-external field system by exploring analogies to the Dicke model of 1 an ensemble of two-level atoms coupled with a resonant cavity field and to Josephson junctions.

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