Quantum Conductance Staircase of Edge Hole Channels in Silicon Quantum Wells

Nikolay T. Bagraev, Leonid E. Klyachkin, Andrei A. Kudryavtsev, Anna M. Malyarenko

Ioffe Physical Technical Institute, St. Petersburg, Russia.

DOI: 10.4236/jmp.2012.311220                

Abstract

We present the findings for the quantum conductance staircase of holes that is caused by the edge channels in the ultra-shallow p-type silicon quantum well (Si-QW), 2 nm, confined by the δ-barriers heavily doped with boron on the n-type Si (100) surface. This longitudinal quantum conductance staircase, G_xx, is revealed by the voltage applied to the Hall contacts, V_xy, to a maximum of 4e²/h. In addition to the standard plateau, 2e²/h, the variations of the V_xy voltage appear to exhibit the fractional forms of the quantum conductance staircase with the plateaus and steps that bring into correlation respectively with the odd and even fractional values.

Keywords

Quantum Conductance Staircase; Edge Channels; Silicon Nanosandwich; Odd and Even Fractional Values

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	T. J. Thornton, M. Pepper, H. Ahmed, D. Andrews and G. J. Davies, “One-Dimensional Conduction in the 2D Electron Gas of a GaAs-AlGaAs Heterojunction,” Physical Review Letters, Vol. 56, No. 11, 1986, pp. 1198-1201. doi:10.1103/PhysRevLett.56.1198
[2]	D. A. Wharam, T. J. Thornton, R. Newbury, M. Pepper, H. Ahmed, J. E. F. Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie and G. A. C. Jones, “One-Dimensional Transport and the Quantisation of the Ballistic Resistance,” Journal of Physics C: Solid State Physics, Vol. 21, No. 8, 1988, pp. L209-L214. doi:10.1088/0022-3719/21/8/002
[3]	B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel and C. T. Foxon, “Quantized Conductance of Point Contacts in a Two-Dimensional Electron Gas,” Physical Review Letters, Vol. 60, No. 9, 1988, pp. 848-850. doi:10.1103/PhysRevLett.60.848
[4]	A. Yacoby, H. L. Stormed, Ned S. Wingreen, L. N. Pfeiffer, K. W. Baldwin and K. W. West, “Nonuniversal Conductance Quantization in Quantum Wires,” Physical Review Letters, Vol. 77, No. 11, 1996, pp. 4612-4615. doi:10.1103/PhysRevLett.77.4612
[5]	K. J. Thomas, J. T. Nicholls, M. Y. Simmons, M. Pepper, D. R. Mace and D. A. Ritchie, “Possible Spin Polarization in a One Dimensional Electron Gas,” Physical Review Letters, Vol. 77, No. 1, 1996, pp.135-138. doi:10.1103/PhysRevLett.77.135
[6]	L. P. Rokhinson, L. N. Pfeiffer and K. W. West, “Spontaneous Spin Polarization in Quantum Point Contacts,” Physical Review Letters, Vol. 96, No. 15, 2006, Article ID: 156602.
[7]	O. Klochan, W. R. Clarke, R. Danneau, A. P. Micolich, L. H. Ho, A. R. Hamilton, K. Muraki, Y. Hirayama, “Ballistic Transport in Induced One-Dimensional Hole Systems,” Applied Physics Letters, Vol. 89, No. 9, 2006, Article ID: 092105.
[8]	N. T. Bagraev, A. D. Bouravleuv, L. E. Klyachkin, A. M. Malyarenko, W. Gehlhoff, V. K. Ivanov and I. A. Shelykh, “Quantized Conductance in Silicon Quantum Wires,” Semiconductors, Vol. 36, No. 4, 2002, pp. 439- 460. doi:10.1134/1.1469195
[9]	N. T. Bagraev, V. K. Ivanov, L. E. Klyachkin and I. A. Shelykh, “Spin Depolarization in Quantum Wires Polarized Spontaneously in a Zero Magnetic Field,” Physical Review B, V. 70, No. 15, 2004, Article ID: 155315.
[10]	N. T. Bagraev, N. G. Galkin, W. Gehlhoff, L. E. Klyachkin and A. M. Malyarenko, “Phase and Amplitude Response of the ‘0.7 Feature’ Caused by Holes in Silicon One-Dimensional Wires and Rings,” Journal of Physics: Condensed Matter, Vol. 20, 2008, Article ID: 164202.
[11]	K. J. Thomas, J. T. Nicholls, N. J. Appleyard, M. Y. Simmons, M. Pepper, D. R. Mace, W. R. Tribe and D. A. Ritchie, “Interaction Effects in a One-Dimensional Constriction,” Physical Review B, Vol. 58, No. 8, 1998, pp. 4846-4852. doi:10.1103/PhysRevB.58.4846
[12]	K. J. Thomas, J. T. Nicholls, M. Pepper, W. R. Tribe, M. Y. Simmons and D. A. Ritchie, “Spin Properties of Low Density One-Dimensional Wires,” Physical Review B, Vol. 61, No. 20, 2000, pp. R13365-R13368. doi:10.1103/PhysRevB.61.R13365
[13]	E. Lieb and D. Mattis, “Theory of Ferromagnetism and the Ordering of Electronic Energy Levels,” Physical Review, Vol. 125, No. 1, 1962, pp. 164-172. doi:10.1103/PhysRev.125.164
[14]	R. Crook, J. Prance, K. J. Thomas, S. J. Chorley, I. Farrer, D. A. Ritchie, M. Pepper and C. G. Smith, “Conductance Quantization at a Half-Integer Plateau in a Symmetric GaAs Quantum Wire,” Science, Vol. 312, No. 5778, 2006, pp. 1359-1362. doi:10.1126/science.1126445
[15]	M. Z. Hasan and C. L. Kane, “Colloquium: Topological Insulators,” Reviews of Modern Physics, Vol. 82, No. 4, 2010, pp. 3045-3067. doi:10.1103/RevModPhys.82.3045
[16]	X.-L. Qi and S.-C. Zhang, “Topological Insulators and Superconductors,” Reviews of Modern Physics, Vol. 83, No. 4, 2011, pp. 1057-1110. doi:10.1103/RevModPhys.83.1057
[17]	M. Buttiker, “Physics. Edge-State Physics without Magnetic Fields,” Science, Vol. 325, No. 5938, 2009, pp. 278- 279. doi:10.1126/science.1177157
[18]	N. T. Bagraev, L. E. Klyachkin, A. A. Kudryavtsev, A. M. Malyarenko and V. V. Romanov, “Superconductor Properties for Silicon Nanostructures,” In: A. Luiz, Ed., Superconductivity—Theory and Applications, SCIYO International Offices, Rijeka Croatia, 2010, Chap. 4, pp. 69-92.
[19]	C. Weisbuch and B. Winter, “Quantum Semiconductor Structures,” Academic Press, New York, 1991, p. 252.
[20]	A. K. Geim and K. S. Novoselov, “The Rise of Graphene,” Nature Materials, Vol. 6, 2007, pp. 183-191. doi:10.1038/nmat1849
[21]	N. T. Bagraev, E. Yu. Danilovskii, L. E. Klyachkin, A. M. Malyarenko and V. A. Mashkov, “Spin Interference of Holes in Silicon Nanosandwiches,” Semiconductors, Vol. 46, No. 1, 2012, pp. 75-86. doi:10.1134/S1063782612010034
[22]	P. Jarillo-Herrero, J. A. van Dam, L. P. Kouwenhoven, “Quantum Supercurrent Transistors in Carbon Nanotubes,” Nature, Vol. 439, No. , 2006, pp. 953-956. doi:10.1038/nature04550
[23]	J. Xiang, A. Vidan, M. Tinkham, R. M. Westervelt and C. Lieber, “Ge-Si Nanowire Mesoscopic Josephson Junctions,” Nature-Nanotechnology, Vol. 1, 2006, pp. 208- 214.
[24]	M. Rosenau da Costa, I. A. Shelykh and N. T. Bagraev, “Fractional Quantization of Ballistic Conductance in One-Dimensional Hole Systems,” Physical Review B, Vol. 76, No. 20, 2007, Article ID: R201302.
[25]	C.-K. Wang and K. F. Berggren, “Spin Splitting of Subbands in Quasi-One-Dimensional Electron Quantum Channels,” Physical Review B, Vol. 54, No. 20, 1996, pp. R14257-R14260. doi:10.1103/PhysRevB.54.R14257
[26]	A. A. Starikov, I. I. Yakimenko and K. F. Berggren, “Scenario for the 0.7-Conductance Anomaly in Quantum Points Contacts,” Physical Review B, Vol. 67, No. 23, 2003, Article ID: 235319.
[27]	R. Landauer, “Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction,” IBM Journal of Research and Development, Vol. 1, No. 3, 1957, pp. 223-231. doi:10.1147/rd.13.0223
[28]	M. Buttiker, “Four-Terminal Phase-Coherent Conductance,” Physical Review Letters, Vol. 57, No. 14, 1986, pp. 1761-1764. doi:10.1103/PhysRevLett.57.1761
[29]	V. J. Goldman, “Superperiods and quantum statistics of Laughlin quasiparticles,” Physical Review B, Vol. 75, No. 4, 2007, Article ID: 045334.