c of the spin-polarized edge channels in a quantum spin Hall insulator. Experimental setup on a sixterminal Hall bar showing pairs of edge states, with spin-up states in blue and spin-down states in red. Spin-dependent scattering near the Hall contact is provided by the varying the Vxy voltage.
quantum conductance staircase of holes, Gxx, that was measured as a function of the Vxy bias voltage in the ptype silicon quantum well confined by the δ-barriers heavily doped with boron, which is prepared in the framework of the Hall geometry. The fractional conductance features observed at the values of, and are evidence of the prevailing ferromagnetic exchange interaction that gives rise to the spin polarization of holes in a zero magnetic field. This quantum conductance staircase measured to a maximum of, with the plateaus and steps that bring into correlation respectively with the odd and even fractional values, seems to reveal the formation of the helical edge channels in the p-type silicon quantum well.
The work was supported by the programme of fundamental studies of the Presidium of the Russian Academy of Sciences “Quantum Physics of Condensed Matter” (grant 9.12); programme of the Swiss National Science Foundation (grant IZ73Z0_127945/1); the Federal Targeted Programme on Research and Development in Priority Areas for the Russian Science and Technology Complex in 2007-2012 (contract No. 02.514.11.4074), the SEVENTH FRAMEWORK PROGRAMME Marie Curie Actions PIRSES-GA-2009-246784 project SPINMET.
- 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
- 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
- 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
- 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
- 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
- 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.
- 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.
- 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
- 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, Vol. 70, No. 15, 2004, Article ID: 155315.
- 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.
- 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
- 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
- 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
- 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
- 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
- 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
- M. Buttiker, “Physics. Edge-State Physics without Magnetic Fields,” Science, Vol. 325, No. 5938, 2009, pp. 278- 279. doi:10.1126/science.1177157
- 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.
- C. Weisbuch and B. Winter, “Quantum Semiconductor Structures,” Academic Press, New York, 1991, p. 252.
- A. K. Geim and K. S. Novoselov, “The Rise of Graphene,” Nature Materials, Vol. 6, 2007, pp. 183-191. doi:10.1038/nmat1849
- 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
- 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
- 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.
- M. Rosenau da Costa, I. A. Shelykh and N. T. Bagraev, “Fractional Quantization of Ballistic Conductance in OneDimensional Hole Systems,” Physical Review B, Vol. 76, No. 20, 2007, Article ID: R201302.
- 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
- 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.
- 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
- M. Buttiker, “Four-Terminal Phase-Coherent Conductance,” Physical Review Letters, Vol. 57, No. 14, 1986, pp. 1761-1764. doi:10.1103/PhysRevLett.57.1761
- V. J. Goldman, “Superperiods and Quantum Statistics of Laughlin Quasiparticles,” Physical Review B, Vol. 75, No. 4, 2007, Article ID: 045334.