İki Farklı Metalik Kapı Yöntemiyle Oluşturulan Hall Bar’daki Sıkıştırılamaz Şeritlerin Kalınlıkları ve Elektron Hızı

Yıl 2023, Cilt: 13 Sayı: 1, 278 - 284, 01.03.2023

Deniz Ekşi

https://doi.org/10.21597/jist.1155664

Öz

Bu çalışmada, üç boyutlu hetero yapılarda oluşturulan iki boyutlu elektron sistemi üzerinde metalik kapılar kullanılarak tanımlanabilen Hall bar geometrisi, iki farklı kapı yöntemi için incelenmiştir. Hesaplamalarda üç boyutlu Poisson denklemi, kendinden tutarlı çözülerek elektron yoğunluğunun ve potansiyel profilinin iki boyutlu uzaysal dağılımları belirlenmiştir. Dik bir manyetik alan varlığında, her iki kapı yöntemi ile elde edilen elektron dağılımlarında oluşan sıkıştırılamaz şeritlerin yerleri, kalınlıkları ve bu bölgelerdeki elektronların hızları manyetik alanın bir fonksiyonu olarak sunulmuştur. Manyetik alanın artması ile Sıkıştırılamaz Şeritlerin kalınlıklarının arttığı ve bu bölgelerdeki elektronların hızlarının azaldığı görülmektedir. Yapılan hesaplamaların sonuçları, daha önce yapılmış çalışmalar ile uyumludur. Aynı zamanda, çalışmanın, kuantum sensörler ve bilgisayarlar alanında katkı sunacağı düşünülmektedir.

Anahtar Kelimeler

Kuantum Hall etkisi, İki boyutlu elektron sistemi, Sıkıştırılamaz şerit

Destekleyen Kurum

Yok

Proje Numarası

Yok

Thicknesses and Electron Velocity of Incompressible Strips in The Hall Bar Formed by The Two Different Metallic Gate Method

Öz

In this study, Hall bar Geometry, which can be defined using metallic gates on a two-dimensional electron system formed in three-dimensional heterostructures, was investigated for two different gate methods. In the calculations, the two-dimensional spatial distributions of the electron density and potential profile were determined by solving the three-dimensional Poisson equation in a self-consistent manner. In the presence of a perpendicular magnetic field, the locations of the incompressible strips formed in the electron distributions obtained by both gate methods, thicknesses and velocities of the electrons in these regions has been presented as a function of the magnetic field. It is seen that the thickness of the Incompressible Strips increases with the increase of the magnetic field and the velocity of the electrons in these regions decreases. The results of the calculations are in agreement with previous studies. At the same time, it is thought that the study will contribute in the field of quantum sensors and computers.

Anahtar Kelimeler

Quantum Hall effect, two-dimensional electron system, incompressible strip

Proje Numarası

Yok

Kaynakça

• Ahlswede, E., Weis, J., Klitzing, K. v., Eberl, K. (2002). Hall potential distribution in the quantum Hall regime in the vicinity of a potential probe contact. Physica E, 12(1-4), 165-168.
• Arslan, S., Cicek, E., Eksi, D., Aktas, D., Weichselbaum, A., Siddiki, A. (2008). Modeling of quantum point contacts in high magnetic fields and with current bias outside the linear response regime. Physical Review B, 78, 125423.
• Camino, F. E., Zhou, W., Goldman, V. J. (2005). Aharonov-Bohm electron interferometer in the integer quantum Hall regime. Physical Review B, 72, 155313.
• Chklovskii, D. B., Shklovskii, B. I. ve Glazman, L. I. (1992). Electrostatics of edge channels. Physical Review B, 46, 4026.
• Eksi, D., Cicek, E., Mese, A. I., Aktas, S., Siddiki, A., Hakioğlu, T. (2007). Theoretical investigation of the effect of sample properties on the electron velocity in quantum Hall bars. Physical Review B, 76, 075334.
• Eksi, D., Kilicoglu, O., Göktas, O., Siddiki, A. (2010). Screening model of metallic nonideal contacts in the integer quantized Hall regime. Physical Review B, 82, 165308.
• Eksi, D. ve Siddiki, A. (2022). Investigating the current distribution of parallel-configured quantum point contacts under quantum Hall conditions. Journal of Computational Electronics, 21, 1–9.
• Gaury, B., Weston, J. ve Waintal, X. (2014). Stopping electrons with radio-frequency pulses in the quantum Hall regime. Physical Review B, 90, 161305(R).
• Güven, K. ve Gerhardts, R. R. (2003). Self-consistent local equilibrium model for density profile and distribution of dissipative currents in a Hall bar under strong magnetic fields. Physical Review B, 67, 115327.
• Ilani, S., Martin, J., Teitelbaum, E., Smet, J. H., Mahalu, D., Umansky, V., Yacoby, A. (2004). The microscopic nature of localization in the quantum Hall effect. Nature, 427, 328-332.
• Klitzing, K. v., Dorda, G. ve Pepper, M. (1980). New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance. Physical Review Letters, 45, 494.
• Kramer, T. (2006). A heuristic quantum theory of the integer quantum hall effect. International Journal of Modern Physics B, 20, 1243-1260.
• Litvin, L. V., Helzel, A., Tranitz, H. -P., Wegscheider, W., Strunk, C. (2008). Edge-channel interference controlled by Landau level filling. Physical Review B, 78, 075303.
• McClure, D. T., Zhang, Y., Rosenow, B., Levenson-Falk, E. M., Marcus, C. M., Pfeiffer, L. N., West, K. W. (2009). Edge-State Velocity and Coherence in a Quantum Hall Fabry-Pérot Interferometer. Physical Review Letters, 103, 206806.
• Neder, I., Heiblum, M., Levinson, Y., Mahalu, M., Umansky, V. (2006). Unexpected Behavior in a Two-Path Electron Interferometer. Physical Review Letters, 96, 016804.
• Oh, J. H. ve Gerhardts, R. R. (1997). Self-consistent Thomas-Fermi calculation of potential and current distributions in a two-dimensional Hall bar geometry. Physical Review B, 56, 13519.
• Ping, V. L., Camino, F. E ve Goldman, V. J. (2009). Electron interferometry in the quantum Hall regime: Aharonov-Bohm effect of interacting electrons. Physical Review B, 80, 125310.
• Roulleau, P., Portier, F., Roche, P., Cavanna, A., Faini, G., Gennser, U., Mailly, D. (2008). Noise Dephasing in Edge States of the Integer Quantum Hall Regime. Physical Review Letters, 101, 186803.
• Siddiki, A., Eksi, D., Cicek, E., Mese, A. I., Aktas, S., Hakioğlu, T. (2008). Theoretical investigation of the electron velocity in quantum Hall bars, in the out of linear response regime. Physica E, 40, 1217-1219.
• Siddiki, A. ve Gerhardts R. R. (2003). Thomas-Fermi-Poisson theory of screening for laterally confined and unconfined two-dimensional electron systems in strong magnetic fields. Physical Review B, 68, 125315.
• Siddiki, A. ve Gerhardts, R. R. (2004). Incompressible strips in dissipative Hall bars as origin of quantized Hall plateaus. Physical Review B, 70, 195335.
• Sohrmann, C. ve Römer, R. A. (2007). Compressibility stripes for mesoscopic quantum Hall samples. New Journal of Physics, 9, 97.
• Weichselbaum, A. ve Ulloa, S. E. (2006). Tunability of qubit Coulomb interaction: Numerical analysis of top-gate depletion in two-dimensional electron systems. Physical Review B, 74, 085318.
• Wulf, U., Gudmundsson, V. ve Gerhardts, R. R. (1988). Screening properties of the two-dimensional electron gas in the quantum Hall regime. Physical Review B, 38, 4218.
• Zhang, Y., McClure, D. T., Levenson-Falk, E. M., Marcus, C. M., Pfeiffer, L. N., West, K. W. (2009). Distinct signatures for Coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Perot interferometers. Physical Review B, 79, 241304(R).