Abstract
We investigate bifurcation and stability of nonuniform current states at a voltage-controlled current instability. We consider a model which exhibits bulk negative differential conductivity due to Bragg scattering of hot electrons. The system is described by balance equations for momentum and energy densities of the carriers. These transport fields are coupled to Maxwell's equations. The uniform stationary current state is unstable against long-wavelength dielectric relaxation modes at a critical field. We find that the softening of these modes gives rise to a family of periodic travelling waves and to a solitary solution (dipole domain). We show that the periodic travelling waves are unstable, wheras the dipole domain can be stabilized by coupling the sample to a suitable external circuit, if the static impedance of the sample in the domain state is negative. The model describes therefore a discontinuous nonequilibrium transition to a large amplitude domain state.
Similar content being viewed by others
References
Büttiker, M., Thomas, H. In: Solitons and Condensed Matter Physics p. 321, Bishop A.R., Schneider T. (eds.) Berlin, Heidelberg, New York: Springer 1978
Gerber, P.R., Büttiker, M.: Z. Physik B33, 219 (1979)
Clever, R.M., Busse, F.: J. Fluid Mech.65, 625 (1974)
Haken, H.: Rev. of Mod. Physics47, 67 (1975)
Büttiker, M., Thomas, H.: Z. Physik B33, 275 (1979)
Büttiker, M., Thomas, H.: Phys. Rev. Lett.38, 78 (1977)
Büttiker, M., Thomas, H.: Solid State Electr.21, 95 (1978)
Butcher, P.N., Facett, W., Hilsum, C.: Brit. J. Appl. Phys.17, 841 (1966)
Knight, B.W., Peterson, G.A.: Phys. Rev.155, 393 (1967)
Gunn, J.B.: IBM J. Res. Dev.13, 591 (1969)
Copeland, J.A.: J. Appl. Phys.37, 3602 (1969)
Volkov, A.F., Kogan, Sh.: Sov. Phys. Usp.11, 881 (1969)
Gunn, J.B.: IBM J. Res. Dev.8, 141 (1966)
Gunn, J.B.: IBM J. Res. Dev.10, 300 (1966)
Coddington, E.A., Levinson, N.: Theorie of Ordinary Differential equations, New York: Mc Graw-Hill 1955
Naknamura, K.: J. Phys. Soc. Jap.38, 46 (1973)
Esaki, L.: Rev. Mod. Phys.46, (1970)
Esaki, L., Tsu, R.: IBM J. Res. Dev.14, 61 (1970)
Esaki, L., Chang, L.L.: Phys. Rev. Lett.33, 495 (1974)
Dingle, R., Wiegemann, W., Henry, C.H.: Phys. Rev. Lett.33, 827 (1974)
Author information
Authors and Affiliations
Additional information
Work Supported by the Swiss National Science Foundation
Rights and permissions
About this article
Cite this article
Büttiker, M., Thomas, H. Bifurcation and stability of dynamical structures at a current instability. Z Physik B 34, 301–311 (1979). https://doi.org/10.1007/BF01325626
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01325626