Area dependence of interlayer tunneling in strongly correlated bilayer two-dimensional electron systems at νT = 1

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 7, 2008, Pages

  Finck, A D K ^a   Champagne, A R ^a   Eisenstein, J P ^a   Pfeiffer, L N ^b   West, K W ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 49249091474     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.075302     Document Type: Article

References (34)

1. For an early review, see the chapters by S. M. Girvin, A. H. MacDonald, and J. P. Eisenstein, in Perspectives in Quantum Hall Effects, edited by, S. Das Sarma, and, A. Pinczuk, (Wiley, New York, 1997).
2. I. B. Spielman, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5808 84, 5808 (2000)
3. I. B. Spielman, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.036803 87, 036803 (2001).
4. M. Kellogg, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.036801 93, 036801 (2004).
5. E. Tutuc, M. Shayegan, and D. A. Huse, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.036802 93, 036802 (2004).
6. R. D. Wiersma, J. G. S. Lok, S. Kraus, W. Dietsche, K. von Klitzing, D. Schuh, M. Bichler, H.-P. Tranitz, and W. Wegscheider, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.266805 93, 266805 (2004).
7. J. P. Eisenstein and A. H. MacDonald, Nature (London) NATUAS 0028-0836 10.1038/nature03081 432, 691 (2004).
8. J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.3804 69, 3804 (1992).
9. L. Balents and L. Radzihovsky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1825 86, 1825 (2001).
10. A. Stern, S. M. Girvin, A. H. MacDonald, and N. Ma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1829 86, 1829 (2001).
11. M. M. Fogler and F. Wilczek, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1833 86, 1833 (2001).
12. Y. N. Joglekar and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.196802 87, 196802 (2001).
13. H. A. Fertig and J. P. Straley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.046806 91, 046806 (2003).
14. Z. Q. Wang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 136803 92, 136803 (2004).
15. R. L. Jack, D. K. K. Lee, and N. R. Cooper, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.126803 93, 126803 (2004)
16. R. L. Jack, D. K. K. Lee, and N. R. Cooper, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.085310 71, 085310 (2005).
17. Z. Q. Wang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94. 176804 94, 176804 (2005).
18. K. Park and S. Das Sarma, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.035338 74, 035338 (2006).
19. I. B. Spielman, Ph.D. thesis, Caltech, 2004.
20. J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.103882 57, 2324 (1990).
21. J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.105157 58, 1497 (1991).
22. S. Q. Murphy, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.52.14825 52, 14825 (1995).
23. The top gates lie approximately 0.5 μm above the bilayer 2DES, while the back gate is roughly 50 μm below them.
24. The back gate is calibrated by observing Shubnikov-de Haas oscillation in the resistivity of the lower 2DES. The top gates are then calibrated relative to the back gate by observing the tunneling resonances they induce at zero magnetic field; see Fig. 1.
25. We find that there is a weak asymmetry of the tunneling resonance shape at νT =1 when the bilayer is imbalanced. The origin of this asymmetry is not understood, but it may result from residual incoherent tunneling for which imbalance induced asymmetry is both expected and observed.
26. A. R. Champagne, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.096801 100, 096801 (2008).
27. At B=0 the tunneling strengths of the two rectangular regions in sample B are, at the same 2D density, similar but not identical, differing by roughly 8 percent. However, after renormalizing the νT =1 tunneling data to reflect this discrepancy at zero field, the remaining difference in G (0) at νT =1 between the two regions is within experimental uncertainty. The origin of the zero-field tunneling discrepancy between the two rectangular regions is unknown, but we suspect it may be due to a processing defect. This surmise is supported by the observation that the density of the 2DES in the two regions is not precisely the same even at zero gate voltage.
28. A simple estimate shows that only a ∼2 percent increase in the nominal 10 nm thickness of the barrier layer is needed to reduce the tunneling conductance at B=0 by a factor of 2.
29. K. Yang, K. Moon, L. Zheng, A. H. MacDonald, S. M. Girvin, D. Yoshioka, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.732 72, 732 (1994).
30. K. Moon, H. Mori, K. Yang, S. M. Girvin, A. H. MacDonald, L. Zheng, D. Yoshioka, and S.-C. Zhang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.51. 5138 51, 5138 (1995).
31. In our experiments current in one 2DES layer is fed into the tunneling region from one side [say from the left in Fig. 1] and then removed from that same side but in the other 2DES layer.
32. Such a model would presumably predict that the tunneling conductance would be proportional to the width or perimeter of the tunneling region. Neither possibility is consistent with our data.
33. H. A. Fertig and G. Murthy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.156802 95, 156802 (2005).
34. E. Rossi, A. S. Núñez, and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.266804 95, 266804 (2005).