Fluctuations of electron energy levels in the interger quantum hall effect
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Keywords:
, electron conductivity, critical phenomena, two-dimensional electron gas, quantum Hall effect, critical index, energy level statistics, unitary ensemble.Abstract
The level statistics in the regime of the quantum Hall effect is studied. The critical exponent of the localization length is found by analyzing the lowest Landau band. By scaling procedure for different system sizes we find the spectral compressability at the plateau-plateau transition. It turned out to be scale-invariant. Obtained results are generalized for other special dimensionalities. Our findings are characteristic of the critical unitary class of universality. For two-dimensional systems the tail of the level spacing distribution resembles the Poisson distribution. It is similar to that of three-dimensional systems, although the exponential rate is as twice as large. Fluctuations of the energy levels are distinct from the classical Gaussian unitary ensemble data and reflect the multifractal nature of the electron wave functions
References
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2 Altshuler B. L., Zharekeshev I. Kh., Kotochigova S. A., Shklovskii B. I. Ottalkivanie energeticheskih urovney i perehod metal-dielektrik // Zhurnal Eksperimental‟noy i Teoreticheskoy Fiziki. – 1988. – T. 94, N. 3. – S. 343-355.
3 Efetov K.B. Supersymmetry and theory of disordered metals // Adv. Phys. – 1983. – Vol. 32. N1. – P. 53-127.
4 Zharekeshev I.Kh. Probability of the Level Number in a Given Energy Interval in Disordered Quantum Systems // Eurasian Physical Technical Journal. – 2010. – T. 7, N. 1(13). – S. 56-60.
5 Shklovskii B.I., Shapiro B., Sears B.R., Lambrianides P., Shore H.B. Statistics of spectra of disordered systems near the metal-insulator transition // Phys. Rev. B. – 1993. – V. 47. – P. 11487-11490.
6 Kramer B., MacKinnon A. Localization: theory and experiment // Rep. Prog. Phys. – 1993. – V. 56. – P. 1496-1564.
7 MacKinnon A., Kramer B. One-parameter scaling of localization length and conductance in disordered systems // Phys.Rev.Lett. – 1981. –V. 47. –P. 1546-1549.
8 Hajdu J. Introduction to the Theory of the Quantum Hall Effect. VCH Verlag. 1994. – 308p.; Klitzing von K, Ebert G. Physica 1983. – V. 117B/118B. – P. 682-687.
9 Zhareekeshev I. Kh. Kriticheskaya statistika urovney energii v neuporyadochennyh sistemah: II. Unitarniy klass simmetrii // Vestnik KazNU. Seriya Fizicheskaya. – 2011. – T. 36, N. 1. – S. 46 – 50.
10 Zharekeshev I.Kh. Haos i porzadok v elekronnyh spektrah neuporyadochennyh sistem na perehode metall-izolyator // Bulletin NNC RK. – 2010. – T. 42, N. 2. – S. 164-173.
11 Zharekeshev I.Kh. Localization trajectory and critical index // Vestnik KazNU. Seriya Fizicheskaya. – 2010. – T. 32, N. 1. – S. 51–55.
12 Zharekeshev I.Kh. Kriticheskaya statistika urovney energii v neuporyadochennyh sistemah: II. Ortogonal„nyi klass simmetrii // Vestnik KazNU. Seriya Fizicheskaya. – 2011. – T. 36, N. 1. – S. 37 – 45.
13 Zharekeshev I.Kh. The two-level correlation function and the form-factor // Eurasian Physical Technical Journal. – 2010. – T. 7, N. 1(13). – S. 61-67.
14 Chalker J.T., Lerner I.V., Smith R. Random walks through the ensemble: Linking spectral statistics with wave-function correlations in disordered metals // Phys. Rev. Lett. – 1996. – Vol.77. – P. 554-557.
15 Zharekeshev I.Kh. Spectral rigidity at the mobility edge // Vestnik Evraziyskogo nazional‟-nogo universiteta. – 2010. – T. 77, N. 4. – S. 41-48.
16 Chalker J.T., Kravtsov V.E., Lerner I.V. Spectral rigidity and eigenfunction correlations at the Anderson transition // Pis'ma Zh. Eksp. Teor. Fiz. – 1996. – V. 64, N. 5. – P. 355-360.
17 Zharekeshev I.Kh., Kramer B. Advanced diagonalization in models of quantum disordered systems // Computer Physics Communications. – 1999. – V. 121/122. – P. 502-504.
18 Zharekeshev I.Kh. Universal statistics of energy levels at the metal-insulator transition // Vestnik KazNU. Seriya Fizicheskaya. – 2009. – T. 31, N. 4. – S. 56-60.
19 Zharekeshev I.Kh. Kriticheskaya statistika urovney energii v neuporyadochennyh sistemah: II. Simplekticheskiy klass simmetrii // Vestnik KazNU. Seriya Fizicheskaya. – 2011. – T. 37, N. 2. – S.50 – 55.
20 Schweitzer L., Zharekeshev I.Kh. Scaling of level statistics and critical exponent of disordered twodimensional symplectic systems // J. Phys.: Condens. Matter. – 1997. – V. 9. – P. L441-L446.
21 Zharekeshev I.Kh. Primenenie modeli Andersona dlya opisaniya fazovogo perehoda metal-izolyator // Vestnik Karagandinskogo universiteta. Seriya Fizika. – 2011. – T. 64, N. 1. – S. 17 – 22.
22 Zharekeshev I.Kh. Elektronnye spektry kvantovyh nanostruktur i ih statisticheskie svoystva // Izvestiya NAN RK, seriya fiziko- matematicheskaya. – 2011. – N. 5 (279). – S. 51-56.
23 Zharekeshev I.Kh. Размерностная зависимость фазового перехода от изолятора к проводнику // Izvestiya NAN RK, seriya fiziko-matematicheskaya. – 2012. – N. 6 (286). – S. 36-40.
24 Zharekeshev I.Kh. Iterative calculation of electron wave functions in quantum nanoclusters // Vestnik Karagandinskogo universiteta. Seriya Fizika. – 2010. – T. 58, N. 2. – S. 29-33.
25 Zharekeshev I.Kh. Spectral density of states in quantum nanoclusters // Vestnik KazNU. Seriya Fizicheskaya. – 2010. – T. 32, N. 1. – S. 47-50.
26 Zharekeshev I.Kh. Algoritm deleniya dlya spektral‟nyh korrelyaziy // Vestnik Karagandinskogo universiteta. Seriya Fizika. – 2010. – T. 57, N. 1. – S. 9-13.
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Zharekeshev, I. K. (2013). Fluctuations of electron energy levels in the interger quantum hall effect. Recent Contributions to Physics (Rec.Contr.Phys.), 45(2), 31–37. Retrieved from https://bph.kaznu.kz/index.php/zhuzhu/article/view/81
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Condensed Matter Physics and Materials Science Problems. NanoScience
