PRL 95, 189702 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending28 OCTOBER 2005

Murzin and Jansen Reply: In our Letter [1] we describethe observation of oscillatory variations of the Hall (Gxy)conductance in view of topological scaling effects givingrise to the quantum Hall effect. Such oscillations areexperimentally observed in disordered GaAs layers in theextreme quantum limit of applied magnetic field. Theyoccur in a field range without oscillations of the densityof states due to Landau quantization and are, therefore,totally different from the Shubnikov–de Haas oscillations.In a more detailed analysis of the observed oscillations, wehave made a quantitative comparison with conceptuallydifferent theories based on a phenomenological approach[2] and on a microscopic description [3] of the scalingproblem. In the preceding Comment [4], Pruisken andBurmistrov question the microscopic justification of thephenomenological approach and the applicability of themicroscopic theory to our experimental data.

Certainly, the phenomenological approach [2] is hypo-thetical and does not have microscopic justifica-tion. However, this does not mean that the results of thisapproach cannot be valid and experimental comparisonwill be of interest. The phenomenological approach [2]has been developed for macroscopic samples at finitetemperatures. Our derived results for the Hall-conductanceoscillation amplitudes from the general expressions ofthe unified scaling theory [2] hold in the limitexp��2�Gxx� � 1 for the case of small amplitudes ofthe oscillations of Gxx and Gxy with respect to both 1 (inunits e2=h) andGsm

xx �T� �G0xx, whereGsm

xx �T� is the smoothpart of diagonal conductance and G0

xx is the bare diagonalconductance. These conditions are valid in our experi-ments. The oscillations of Gxy are quantitatively welldescribed by this theoretical approach.

In our discussion of the ‘‘dilute instanton gas’’ approxi-mation (DIGA) [1] we did not consider the differencebetween the macroscopic conductances measured at finitetemperature and the ensemble averaged conductances atT � 0 used in this microscopic approach [3]. The verylarge difference (up to 10 times) in the oscillation ampli-tudes between experiment and theory [extracted fromRef. [3] using the ensemble averaged conductance atT � 0] has led us to the conclusion that the DIGA resultsdiffer quantitatively from the experimental data. Morerecently [5], Pruisken and Burmistrov obtained a roughly5 times smaller topological oscillatory term (presented inthe Comment) than that derived in Ref. [3] which would be

0031-9007=05=95(18)=189702(1)$23.00 18970

in line with our conclusion concerning the smallness of themeasured amplitude oscillations with respect to the result[3] as known at the moment of publication. Since anexplicit computation of the function fH�g0� has not beendone [4], we cannot give a quantitative comparison of theoscillation amplitudes with our experimental data consid-ering the DIGA approach for the measured conductance.

Note that in our experiments Gsmxx is a logarithmic func-

tion of the temperature with the same coefficient close to1=� in front of the logarithm for all four samples in the 2Dregime (T < 1 K). Such behavior is in line with the theoryof the quantum corrections due to dominant electron-electron interactions, although for Gsm

xx � 1 one wouldexpect higher order contributions beyond the logarithmictemperature dependence. Using Eq. (2) of the � function[4] for the range of values of our experimental data, thesmooth part of the ensemble averaged conductance �0 isessentially outside the quantum corrections limit withlogarithmic temperature dependence because, for �0 � 1,the term / 1=�0 becomes comparable with the first con-stant term in this equation assigning the logarithmicbehavior.

S. S. Murzin1 and A. G. M. Jansen2

1Institute of Solid State Physics RAS142432, ChernogolovkaMoscow DistrictRussia

2Service de Physique StatistiqueMagnetisme, et SupraconductiviteDepartement de Recherche Fondamentale sur la MatiereCondenseeCEA-Grenoble38054 Grenoble Cedex 9France

Received 31 August 2005; published 25 October 2005DOI: 10.1103/PhysRevLett.95.189702PACS numbers: 73.43.Nq, 73.43.Qt, 73.50.Jt

2-1

[1] S. S. Murzin, A. G. M. Jansen, and I. Claus, Phys. Rev.Lett. 92, 016802 (2004).

[2] B. P. Dolan, Nucl. Phys. B554, 487 (1999).[3] A. M. M. Pruisken and M. A. Baranov, Europhys. Lett.

31, 543 (1995).[4] A. M. M. Pruisken and I. S. Burmistrov, preceding

Comment, Phys. Rev. Lett. 95, 189701 (2005).[5] A. M. M. Pruisken and I. S. Burmistrov, cond-mat/

0502488.

© 2005 The American Physical Society