Universal Frequency Dependence of the Hopping AC Conductance in p-Ge/GeSi Structures in the Integer Quantum Hall Effect Regime


The hopping ac conductance, which is realized at the transverse conductance minima in the regime of the integer Hall effect, has been measured using a combination of acoustic and microwave methods. Measurements have been made in the p-GeSi/Ge/GeSi structures with quantum wells in a wide frequency range (30–1200 MHz). The experimental frequency dependences of the real part of ac conductance σ1 have been interpreted on the basis of the model presuming hops between localized electronic states belonging to isolated clusters. At high frequencies, dominating clusters are pairs of close states; upon a decrease in frequency, large clusters that merge into an infinite percolation cluster as the frequency tends to zero become important. In this case, the frequency dependences of the ac conductance can be represented by a universal curve. The scaling parameters and their magnetic-field dependence have been determined.

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  1. 1.

    The Quantum Hall Effect, Ed. by R. E. Prange and S. M. Girvin (Springer, New York, 1987).

    Google Scholar 

  2. 2.

    B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors (Springer, Heidelberg, 1984).

    Google Scholar 

  3. 3.

    Y. M. Galperin, V. L. Gurevich, and D. A. Parshin, in Hopping Transport in Solids, Ed. by B. Shklovskii and M. Pollak (Elsevier, New York, 1991).

  4. 4.

    A. Wixforth, J. Scriba, M. Wassermeier, J. P. Kotthaus, G. Weimann, and W. Schlapp, Phys. Rev. B 40, 7874 (1989).

    ADS  Article  Google Scholar 

  5. 5.

    I. L. Drichko, A. M. Diakonov, I. Yu. Smirnov, Y. M. Galperin, and A. I. Toropov, Phys. Rev. B 62, 7470 (2000).

    ADS  Article  Google Scholar 

  6. 6.

    I. L. Drichko, A. M. Diakonov, I. Y. Smirnov, G. O. Andrianov, O. A. Mironov, M. Myronov, D. R. Leadley, and T. E. Whall, Phys. Rev. B 71, 045333 (2005).

    ADS  Article  Google Scholar 

  7. 7.

    I. L. Drichko, A. M. Diakonov, V. I. Kozub, I. Yu. Smirnov, Yu. M. Galperin, A. I. Yakimov, and A. I. Nikiforov, Physica E 26, 450 (2005).

    ADS  Article  Google Scholar 

  8. 8.

    L. W. Engel, D. Shahar, Ç. Kurdak, and D. C. Tsui, Phys. Rev. Lett. 71, 2638 (1993).

    ADS  Article  Google Scholar 

  9. 9.

    A. Endo, T. Kajioka, and Y. Iye, J. Phys. Soc. Jpn. 82, 054710 (2013).

    ADS  Article  Google Scholar 

  10. 10.

    I. L. Drichko, A. M. Diakonov, V. A. Malysh, I. Yu. Smirnov, Y. M. Galperin, N. D. Ilyinskaya, A. A. Usikova, M. Kummer, and H. von Känel, J. Appl. Phys. 116, 154309 (2014).

    ADS  Article  Google Scholar 

  11. 11.

    C. Rosenblad, H. R. Deller, A. Dommann, T. Meyer, P. Schroeter, and H. von Känel, J. Vac. Sci. Technol. A 16, 2785 (1998).

    ADS  Article  Google Scholar 

  12. 12.

    V. D. Kagan, Semiconductors 31, 407 (1997).

    ADS  Article  Google Scholar 

  13. 13.

    B. I. Shklovskii and A. L. Efros, Sov. Phys. JETP 54, 218 (1981).

    Google Scholar 

  14. 14.

    J. C. Dyre and T. B. Schrøder, Rev. Mod. Phys. 72, 873 (2000).

    ADS  Article  Google Scholar 

  15. 15.

    I. Zvyagin, in Charge Transport in Disordered Solids with Applications in Electronics (Wiley, 2006).

    Google Scholar 

  16. 16.

    D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1992).

    Google Scholar 

  17. 17.

    D. G. Polyakov and B. I. Shklovskii, Phys. Rev. Lett. 70, 3796 (1993); Phys. Rev. B 48, 1167 (1993); Phys. Rev. Lett. 74, 150 (1995); Phys. Rev. Lett. 73, 1150 (1999).

    ADS  Article  Google Scholar 

  18. 18.

    H. von Känel, M. Kummer, G. Isella, E. Müller, and T. Hackbarth, Appl. Phys. Lett. 80, 2922 (2002).

    ADS  Article  Google Scholar 

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Correspondence to I. L. Drichko.

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Original Russian Text © I.L. Drichko, A.A. Dmitriev, V.A. Malysh, I.Yu. Smirnov, Yu.M. Galperin, H. von Känel, M. Kummer, G. Isella, D. Chrastina, 2018, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2018, Vol. 153, No. 2, pp. 294–303.

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Drichko, I.L., Dmitriev, A.A., Malysh, V.A. et al. Universal Frequency Dependence of the Hopping AC Conductance in p-Ge/GeSi Structures in the Integer Quantum Hall Effect Regime. J. Exp. Theor. Phys. 126, 246–254 (2018). https://doi.org/10.1134/S1063776118010144

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