Mesoscopic effects in tunneling between parallel quantum wires

Physical Review B - Condensed Matter and Materials Physics

Volumn 64, Issue 8, 2001, Pages

  Boese, Daniel ^a   Governale, Michele ^a   Zülicke, Ulrich ^a   Rosch, Achim ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CONDUCTANCE; DIFFUSION; ELECTRIC POTENTIAL; MAGNETIC FIELD; MATHEMATICAL ANALYSIS; QUANTUM MECHANICS;

EID: 0035880821     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.085315     Document Type: Article

References (61)

1. E.L. Wolf, Principles of Electron Tunneling Spectroscopy, International Series of Monographs in Physics Vol. 71 (Oxford University Press, New York, 1985);F. Capasso, Physics of Quantum Electron Devices, Springer Series in Electronics and Photonics Vol. 28 (Springer, Berlin, 1990).
2. J. Smoliner, E. Gornik, and G. Weimann, Appl. Phys. Lett. 52, 2136 (1988);
3. Appl. Phys. Lett.J.P. Eisenstein, L.N. Pfeiffer, and K.W. West, 58, 1497 (1991).
4. J. Smoliner, W. Demmerle, G. Berthold, E. Gornik, G. Weimann, and W. Schlapp, Phys. Rev. Lett. 63, 2116 (1989);
5. W. Demmerle, J. Smoliner, G. Berthold, E. Gornik, G. Weimann, and W. Schlapp, Phys. Rev. B 44, 3090 (1991).
6. J.P. Eisenstein, T.J. Gramila, L.N. Pfeiffer, and K.W. West, Phys. Rev. B 44, 6511 (1991);
7. Phys. Rev. BL. Zheng and A.H. MacDonald, 47, 10 619 (1993).
8. S.Q. Murphy, J.P. Eisenstein, L.N. Pfeiffer, and K.W. West, Phys. Rev. B 52, 14 825 (1995);
9. Phys. Rev. BT. Jungwirth and A.H. MacDonald, 53, 7403 (1996).
10. J. Smoliner, W. Demmerle, F. Hirtler, E. Gornik, G. Weimann, M. Hauser, and W. Schlapp, Phys. Rev. B 43, 7358 (1991);
11. Phys. Rev. BW. Demmerle, J. Smoliner, E. Gornik, G. Böhm, and G. Weimann, 47, 13 574 (1993);
12. B. Kardynał, C.H.W. Barnes, E.H. Linfield, D.A. Ritchie, K.M. Brown, G.A.C. Jones, and M. Pepper, Phys. Rev. Lett. 76, 3802 (1996);
13. B. Kardynał, C.H.W. Barnes, E.H. Linfield, D.A. Ritchie, J.T. Nicholls, K.M. Brown, G.A.C. Jones, and M. Pepper, Phys. Rev. B 55, R1966 (1997).
14. U. Zülicke and A.H. MacDonald, Phys. Rev. B 54, R8349 (1996);
15. A. Altland, C.H.W. Barnes, F.W.J. Hekking, and A.J. Schofield, Phys. Rev. Lett. 83, 1203 (1999).
16. L. Pfeiffer, K.W. West, H.L. Stormer, J.P. Eisenstein, K.W. Baldwin, D. Gershoni, and J. Spector, Appl. Phys. Lett. 56, 1697 (1990);
17. M. Grayson, Ç. Kurdak, D.C. Tsui, S. Parihar, S. Lyon, and M. Shayegan, Solid-State Electron. 40, 233 (1996).
18. A. Yacoby, H.L. Stormer, N.S. Wingreen, L.N. Pfeiffer, K.W. Baldwin, and K.W. West, Phys. Rev. Lett. 77, 4612 (1996).
19. O. M. Auslaender and A. Yacoby (unpublished).
20. J. Voit, Rep. Prog. Phys. 57, 977 (1994).
21. D. Carpentier, C. Peça, and L. Balents, cond-mat/0103193 (unpublished);
22. U. Zülicke and M. Governale, cond-mat/0105066 (unpublished).
23. Parallel quantum wires have been fabricated before using a split-gate technique. See K.J. Thomas, J.T. Nicholls, M.Y. Simmons, W.R. Tribe, A.G. Davies, and M. Pepper, Phys. Rev. B 59, 12 252 (1999). In this experiment, 1D–to–1D tunneling transport was not measured directly. Instead, the two-terminal conductance of the two wires in parallel was used for spectroscopy of the tunnel-split 1D subbands.
24. R. de Picciotto, H. Stormer, A. Yacoby, L.N. Pfeiffer, K.W. Baldwin, and K.W. West, Phys. Rev. Lett. 85, 1730 (2000).
25. C.C. Eugster, J.A. del Alamo, M.J. Rooks, and M.R. Melloch, Appl. Phys. Lett. 64, 3157 (1994).
26. J.A. del Alamo and C.C. Eugster, Appl. Phys. Lett. 56, 78 (1990).
27. M. Macucci, A. Galick, and U. Ravaioli, Phys. Rev. B 52, 5210 (1995);
28. Phys. Rev. BM. Governale, M. Macucci, and B. Pellegrini, 62, 4557 (2000).
29. A. Bertoni, P. Bordone, R. Brunetti, C. Jacoboni, and S. Reggiani, Phys. Rev. Lett. 84, 5912 (2000).
30. D. Rogovin and D.J. Scalapino, Ann. Phys. (N.Y.) 86, 1 (1974).
31. Our modeling of electrostatics using the single parameter (Formula presented) is a first approximation to the real situation where, e.g., coupling to reservoirs leads to a nonuniform distribution of electron density as well as charge transfer between reservoirs and the wire. See, e.g., V.A. Sablikov, S.V. Polyakov, and M. Büttiker, Phys. Rev. B 61, 13 763 (2000).
32. Here, in contrast to the situation considered in Refs. 2223242526, the external voltage does not drive a net current flow within a single quantum wire.
33. D.L. Maslov and M. Stone, Phys. Rev. B 52, R5539 (1995).
34. V. Ponomarenko, Phys. Rev. B 52, R8666 (1995).
35. I. Safi and H.J. Schulz, Phys. Rev. B 52, R17 040 (1995).
36. R. Egger and H. Grabert, Phys. Rev. Lett. 77, 538 (1996);
37. Phys. Rev. Lett.R. EggerH. Grabert80, 2255(E) (1998).
38. R. Egger and H. Grabert, Phys. Rev. B 58, 10 761 (1998).
39. In contrast to the familiar single-particle density of levels, the thermodynamic DOS contains exchange-correlation contributions.
40. M. Büttiker, H. Thomas, and A. Prêtre, Phys. Lett. A 180, 364 (1993);
41. M. Büttiker, J. Phys.: Condens. Matter 5, 9361 (1993);
42. M. Büttiker and T. Christen, in Mesoscopic Electron Transport, edited by L.L. Sohn, L.P. Kouwenhoven, and G. Schön (Kluwer Academic, Dordrecht, 1997), pp. 259-289.
43. See, e.g., M.A. Kastner, Rev. Mod. Phys. 64, 849 (1992);
44. Single Charge Tunneling, edited by H. Grabert and M.H. Devoret (Plenum Press, New York, 1992). Within the language used in the literature studying single-electron effects, the parameter (Formula presented) corresponds to the ratio of charging energy to the single-particle level spacing.
45. S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950);
46. J.M. Luttinger, J. Math. Phys. 4, 1154 (1963).
47. F.D.M. Haldane, J. Phys. C 14, 2585 (1981).
48. Y.M. Blanter, F.W.J. Hekking, and M. Büttiker, Phys. Rev. Lett. 81, 1925 (1998);
49. R. Egger and H. Grabert, Phys. Rev. B 55, 9929 (1997);
50. Phys. Rev. BR. EggerH. Grabert58, 13 275(E) (1998).
51. The characteristic length scale above which LL effects will be important can be roughly estimated by (Formula presented). Here, (Formula presented) is a cut-off wave number that can be much smaller than (Formula presented) We expect quantum wires in CEO structures to be at the borderline of this criterion; see O.M. Auslaender, A. Yacoby, R. de Picciotto, K.W. Baldwin, L.N. Pfeiffer, and K.W. West, Phys. Rev. Lett. 84, 1764 (2000).
52. K. Schönhammer and V. Meden, Phys. Rev. B 48, 11 390 (1993).
53. M. Governale, M. Grifoni, and G. Schön, Phys. Rev. B 62, 15 996 (2000).
54. This neglects the finite size of the wires in z direction.
55. The range of magnetic fields that need to be applied to map out the interesting features in the linear, or differential, tunneling conductance implies the condition (Formula presented) for safe neglect of Zeeman splitting. Here, g is the Landé factor, (Formula presented) the electron mass in vacuum, and n the (in general, voltage-dependent) electron density in the wire. Typically, this condition will be violated only in the band-filling limit around the point where one of the wires is empty.
56. G. D. Mahan, Many-Particle Physics (Plenum Press, New York, 1990).
57. Elastic scattering by impurities is taken into account by introducing a finite life-time broadening for the single-electron spectral functions (Formula presented).
58. R. Landauer, IBM J. Res. Dev. 1, 223 (1957);
59. IBM J. Res. Dev.M. Büttiker, 32, 317 (1988);
60. S. Datta, Electron Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, UK, 1995).
61. In Figs. 556677, we give (Formula presented) in units of (Formula presented) which is independent of magnetic field due to our gauge choice.