Quantum Hall Effect in Vanishing Magnetic Fields

Transcription

1 Quantum Hall Effect in Vanishing Magnetic Fields Wei Pan Sandia National Labs Sandia is a multi-mission laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy s National Nuclear Security Administration under contract DE-AC04-94AL Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy s National Nuclear Security Administration under contract DE-AC04-94AL SAND NO XXXXP

2 Part I: Anti-levitation of Landau levels in vanishing magnetic fields (Pan et al, PRB (2016)) Part II: Collapse of spin splitting in the quantum Hall regime (Pan et al, PRB (2011))

3 part I outline Background Sample HIGFET (Heterojunction Insulated-Gate Field-Effect Transistor) Results Anti-levitation is observed at low Landau level fillings n=4,5,6. This observation is in good agreement with a recent theoretical prediction (C. Wang et al, PRB 89, (2014)).

4 dn d ħw c E B = 0 B 0 E = (N+1/2)ħw c E

5 Integer quantum Hall effect R xy quantized h R xy = ne 2 R xx zero n n Landau level filling = nh/eb (n density)

6 So ugly and yet so precise Resistance quantized to a few parts in 10 98

7 (source:

8 (by Kwon Park) Cm=1 1 1

9 Chern number never disappears by itself E = (N+1/2)ħw c 0

10 E (or electron density) Floating of Landau levels in vanishing B field Laughlin, PRL 52, 2304 (1984). Khmelnitskii, Phys. Lett. A 106, 182 (1984).

11 Glozman, Johnson, and Jiang PRL 74, 594 (1995)

12 arxiv:

13 Only insulator to N = 1 transition allowed N=2 N=3 N=1 E F

14 Global phase diagram S.A. Kivelson, D.H. Lee, and S.C. Zhang, PRB (1992)

15 However, transition from insulator to high order quantum Hall states has been observed in experiments Insulator to N=3 transition Insulator to N=4 transition C.H. Lee, Y.H. Chang, Y.W. Suen, and H.H. Lin, PRB (1998) S.T. Lo, et al, C.-T. Liang, Solid State Commun. (2010)

16 Liu et al, PRL 76, 975 (1996) Sheng et al, PRL 78, 318 (1997) Yang et al, PRL 76, 1316 (1996) non-floating behavior

17 Anti-levitation of Landau levels Wang, Avishai, Meir, and Wang, PRB 89, (2014)

18 HIGFET (Heterojunction Insulated-Gate Field-Effect Transistor) n+ GaAs (60 nm) Vg AlGaAs (600 nm) 2DEG GaAs (2 mm) AlGaAs/GaAs superlattice GaAs overgrowth layer n+ GaAs AlGaAs GaAs GaAs substrate 2DES Kane, Pfeiffer, West, and Harnett, APL,1993

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20 Straight sidewall is important Vg n+ GaAs AlGaAs GaAs 2DES

21 Mesa gate contact 2DEG

22 Mesa Annealed Ni/Ge/Au contact device works!

23 Very large density range ~ 1x10 9 to ~ 7.5x10 11 cm -2

24 Linear I-V at very low densities

25

26 s xx = r xx /(r xx2 +r xy2 ) s xy = r xy /(r xx2 +r xy2 )

27 n = nh/eb n = ne/h B B = 500 mt

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29 n = nh/eb n=nh/eb n=16 n = ne/h B

30 <dn> cm-2

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32 Wang et al, PRB 89, (2014)

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34 Wang et al, PRB 89, (2014)

35 Observation of anti-floating in vanishing B field 0-1 n=6 n=5 n=4 n (10 8 cm -2 ) Magnetc Field (T)

36

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38 part I conclusion In a high-quality HIGFET, anti-levitation of Landau levels is observed in vanishing magnetic fields. This observation is in a good agreement with the theoretical prediction (C. Wang et al, PRB 2014).

39 part II outline (Collapse of spin splitting in the quantum Hall regime) Background Sample HIGFET (Heterojunction Insulated-Gate Field-Effect Transistor) Result Landau level number N displays a power-law dependence on 2DEG density n, where the spin splitting collapses. N = n 0.64±0.01 (n is in units of cm 2 ). This power-law dependence is in good agreement with the theoretical prediction in the low-density regime.

40 dn d ħw c B 0 E

41 Spin degeneracy lifted hw c gm B B DOS E

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43 hw c gm B B DOS E odd Landau level filling states ~ gm B B g = 0.44, m B = 0.67K/Tesla, B = 5Tesla, ~ 1.5K

44 However, odd Landau level filling states >> gm B B gm B B Huang et al, Physica E 12 (2002)

45 g factor enhancement E ex is the exchange parameter n, n are the occupation factors of the spin levels. n = 2 n = n n = 3 n > n

46 disorder-induced destruction of exchange enhancement Fogler and Shklovskii [PRB 52, (1995)] n=2n+3/2 n=2n+1/2 width of Landau level << s n = 1 width of Landau level ~ s n 0 n = the Landau level filling between spin-up and spin-down bands

47 a second-order phase transition r(0) = E 0 ħw c r(0)e 0 (mb) 1/2 0

48 theoretical prediction In high mobility GaAs/AlGaAs heterostructures: Fogler and Shklovskii [PRB 52, (1995)] low density regime: N c n 2/3

49 previous experimental work Wong, Jiang, Palm, and Schaff, PRB 55, R7343 (1997). sample peak mobility < 10 6 cm 2 /Vs

50 HIGFET high mobility down to low densities n+ GaAs (60 nm) AlGaAs (600 nm) 2DEG GaAs (2 mm) AlGaAs/GaAs superlattice GaAs overgrowth layer n+ GaAs AlGaAs GaAs Vg GaAs substrate 2DES Kane, Pfeiffer, West, and Harnett, APL,1993

51 B = 0.197T T ~ 15 mk

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53 n=2n+1 (theoretical prediction) Pan et al, PRB (2011)

54 n+ GaAs (60 nm) AlGaAs (600 nm) n i GaAs (2 mm) AlGaAs/GaAs superlattice GaAs overgrowth layer GaAs substrate

55 Fogler and Shklovskii [PRB 52, (1995)]

56 part II conclusion In a high-quality HIGFET, the Landau level number N follows a power-law dependence on the 2DEG electron density n, where the spin splitting collapses. N = n 0.64±0.01 This power-law dependence is in a good agreement with the theoretical prediction in the low-density regime.

57 Thank you for your attention