Finite Capacitive Response at the Quantum Hall Plateau
-
Abstract
We study ultra-high-mobility two-dimensional (2D) electron/hole systems with high precision capacitance measurement. It is found that the capacitance charge appears only at the fringe of the gate at high magnetic field when the 2D conductivity decreases significantly. At integer quantum Hall effects, the capacitance vanishes and forms a plateau at high temperatures T≳300 mK, which surprisingly disappears at T≲100 mK. This anomalous behavior is likely a manifestation that dilute particles/vacancies in the top-most Landau level form Wigner crystals, which have finite compressibility and can host polarization current. -
-
References
[1] Prange R E and Girvin S M 1987 The Quantum Hall Effect New York: Springer[2] Sarma S D and Pinczuk A 1997 Perspectives in Quantum Hall Effects New York: Wiley[3] Jain J K 2007 Composite Fermions Cambridge: Cambridge University Press[4] Jiang H W, Willett R L, Stormer H L, Tsui D C, Pfeiffer L N, and West K W 1990 Phys. Rev. Lett. 65 633[5] Goldman V J, Santos M, Shayegan M, and Cunningham J E 1990 Phys. Rev. Lett. 65 2189[6] See articles by Fertig H A and by Shayegan M in Ref.[2].[7] Chen Y, Lewis R M, Engel L W, Tsui D C, Ye P D, Pfeiffer L N, and West K W 2003 Phys. Rev. Lett. 91 016801[8] Liu Y, Pappas C G, Shayegan M, Pfeiffer L N, West K W, and Baldwin K W 2012 Phys. Rev. Lett. 109 036801[9] Hatke A T, Liu Y, Magill B A, Moon B H, Engel L W, Shayegan M, Pfeiffer L N, West K W, and Baldwin K W 2014 Nat. Commun. 5 4154[10] Myers S A, Huang H, Pfeiffer L N, West K W, and Csáthy G A 2021 Phys. Rev. B 104 045311[11] Kaplit M and Zemel J N 1968 Phys. Rev. Lett. 21 212[12] Voshchenkov A M and Zemel J N 1974 Phys. Rev. B 9 4410[13] Smith T P, Goldberg B B, Stiles P J, and Heiblum M 1985 Phys. Rev. B 32 2696[14] Mosser V, Weiss D, Klitzing K, Ploog K, and Weimann G 1986 Solid State Commun. 58 5[15] Ashoori R C, Stormer H L, Weiner J S, Pfeiffer L N, Pearton S J, Baldwin K W, and West K W 1992 Phys. Rev. Lett. 68 3088[16] Smith T P, Wang W I, and Stiles P J 1986 Phys. Rev. B 34 2995[17] Yang M J, Yang C H, Bennett B R, and Shanabrook B V 1997 Phys. Rev. Lett. 78 4613[18] Eisenstein J P, Pfeiffer L N, and West K W 1994 Phys. Rev. B 50 1760[19] Zibrov A A, Kometter C, Zhou H, Spanton E M, Taniguchi T, Watanabe K, Zaletel M P, and Young A F 2017 Nature 549 360[20] Irie H, Akiho T, and Muraki K 2019 Appl. Phys. Express 12 063004[21] Eisenstein J P, Pfeiffer L N, and West K W 1992 Phys. Rev. Lett. 68 674[22] Deng H, Pfeiffer L N, West K W, Baldwin K W, Engel L W, and Shayegan M 2019 Phys. Rev. Lett. 122 116601[23] Jo J, Garcia E A, Abkemeier K M, Santos M B, and Shayegan M 1993 Phys. Rev. B 47 4056[24] Zibrov A A, Rao P, Kometter C, Spanton E M, Li J I A, Dean C R, Taniguchi T, Watanabe K, Serbyn M, and Young A F 2018 Phys. Rev. Lett. 121 167601[25] Tomarken S L, Cao Y, Demir A, Watanabe K, Taniguchi T, Jarillo-Herrero P, and Ashoori R C 2019 Phys. Rev. Lett. 123 046601[26] Zhao L, Lin W, Fan X, Song Y, Lu H, and Liu Y 2022 Rev. Sci. Instrum. 93 053910[27] In samples A, B and C, our measured capacitance approaches a constant value ≃60 fF when the particles form incompressible integer quantum Hall liquid. This is likely the parasitic capacitance CP induced by the bonding wires, gates, etc. In sample D, CP is reduced to ≃15 fF because we add one impedance matching network at the input of the bridge at the sample stage. We have subtracted CP in all figures. -
Related Articles
[1] Ran Tao, Lin Li, Li-Jun Zhu, Yue-Dong Yan, Lin-Hai Guo, Xiao-Dong Fan, Chang-Gan Zeng. Giant-Capacitance-Induced Wide Quantum Hall Plateaus in Graphene on LaAlO$_{3}$/SrTiO$_{3}$ Heterostructures [J]. Chin. Phys. Lett., 2020, 37(7): 077301. doi: 10.1088/0256-307X/37/7/077301 [2] M. R. Setare, D. Jahani. Quantum Hall Effect and Different Zero-Energy Modes of Graphene [J]. Chin. Phys. Lett., 2011, 28(9): 097302. doi: 10.1088/0256-307X/28/9/097302 [3] HUANG Wei, WANG Zhao-Long, YAN Mu-Lin. Noncommutative Chern-Simons Description of the Fractional Quantum Hall Edge [J]. Chin. Phys. Lett., 2010, 27(6): 067304. doi: 10.1088/0256-307X/27/6/067304 [4] LV Wei-Guo, CHU Zhao-Tan, ZHAO Xiao-Qing, FAN Yu-Xiu, SONG Ruo-Long, HAN Wei. Simulation of Electromagnetic Wave Logging Response in Deviated Wells Based on Vector Finite Element Method [J]. Chin. Phys. Lett., 2009, 26(1): 014102. doi: 10.1088/0256-307X/26/1/014102 [5] TU Tao, ZHAO Yong-Jie, HAO Xiao-Jie, WANG Cheng-You, GUO Guang-Can, GUO Guo-Ping. Localization Exponent for the Second Landau Level in the Quantum Hall Effect [J]. Chin. Phys. Lett., 2008, 25(3): 1083-1086. [6] TU Tao, ZHAO Yong-Jie, GUO Guo-Ping, HAO Xiao-Jie, GUO Guang-Can. Form of Scaling Function in Quantum Hall Plateau Transitions [J]. Chin. Phys. Lett., 2007, 24(5): 1346-1349. [7] SHU Qiang, LIN Yao-Wang, XING Xiao-Dong, YAO Jiang-Hong, PI Biao, SHU Yong-Chun, WANG Zhan-Guo, XU Jing-Jun. Effect of Small-Angle Scattering on the Integer Quantum Hall Plateau [J]. Chin. Phys. Lett., 2006, 23(2): 436-438. [8] DUAN Yi-Shi, ZHANG Xiu-Ming, TIAN Miao. The Branch Process of Skyrmions in the Fractional Quantum Hall Effect [J]. Chin. Phys. Lett., 2005, 22(8): 2047-2051. [9] CHEN Yingjian. RELATION BETWEEN THE EFFECTS OF FINITE THICKNESS AND TILTED MAGNETIC FIELDS IN THE FRACTIONAL QUANTUM HALL EFFECT [J]. Chin. Phys. Lett., 1990, 7(11): 514-517. [10] HUANG Fengyi. POSSIBLE EXPLANATION OF THE PLATEAU WIDTH IN THE QUANTUM HALL EFFECT AT FINITE TEMPERATURE [J]. Chin. Phys. Lett., 1989, 6(12): 541-545. -
Cited by
Periodical cited type(6)
1. Myers, S.A., Huang, H., Hussain, W. et al. Thermal activation signatures of the Anderson insulator and the Wigner solid forming near ν=1. Physical Review Research, 2024, 6(2): L022056. DOI:10.1103/PhysRevResearch.6.L022056 2. Liu, X., Wu, M., Wang, R. et al. Interaction between Surface Acoustic Wave and Quantum Hall Effects. Chinese Physics Letters, 2024, 41(4): 047301. DOI:10.1088/0256-307X/41/4/047301 3. Lin, W., Fan, X., Zhao, L. et al. Metastable charge distribution between degenerate Landau levels. Physical Review B, 2024, 109(3): 035305. DOI:10.1103/PhysRevB.109.035305 4. Huang, H., Hussain, W., Myers, S.A. et al. Density Dependence of the Phases of the v = 1 Integer Quantum Hall Plateau in Low Disorder Electron Gases. Physica Status Solidi - Rapid Research Letters, 2024. DOI:10.1002/pssr.202400376 5. Zhao, L., Lin, W., Chung, Y.J. et al. Dynamic Response of Wigner Crystals. Physical Review Letters, 2023, 130(24): 246401. DOI:10.1103/PhysRevLett.130.246401 6. Li, J.-K., Wang, H.-Z., Zhang, J.-Y. et al. Quantum capacitance properties of the holes in planar germanium. Applied Physics Letters, 2023, 122(6): 063102. DOI:10.1063/5.0137292 Other cited types(0)
DownLoad: