Search for time reversal symmetry effects in disordered conductors and insulators beyond weak localization. Marc Sanquer CEA/DRF/INAC & UGA

Transcription

1 Search for time reversal symmetry effects in disordered conductors and insulators beyond weak localization. Marc Sanquer CEA/DRF/INAC & UGA 40 years of Mesoscopics Physics: Colloquium in memory of Jean-Louis Pichard June 25-26, 2018

2 G. Bergmann 1984

3 (Image by Yang-Zhi Chou and Matthew Foster/Rice University) JLPichard PhD (Orsay, 1984) Contribution à une théorie quantique des phénomènes de transport par études numériques de systèmes désordonnés: localisation d Anderson

4 JLP and G. Sarma, Journal of Physics C-solid state physics, L , (1981) JLP obtains the electronic localization length in 2D ribbons or 3D bars ( beyond the strict 1D case) Lt (under special conditions, Lt= cross section of the ribbon) at a time where computers are not very efficient

5 First report of reproducible mesoscopic conductance fluctuations («fingerprint») Conductance in Restricted-Dimensionality Accumulation Layers A. B. Fowler, A. Hartstein, and R. A. Webb Phys. Rev. Lett. 48, 196 (1982) Long ( few microns) and narrow channel

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7 Random Matrix Theory and mesoscopic conductance fluctuations

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9 M a eigenvalues of the X matrix: g measures the numbers of a between 0 and 1. If the { a } are randomly distributed, then var(g) <g>, But var(g) 1 (UCF) Therefore there are correlations between the { a }

10 Time reversal symmetry effects =1 =2 Muttalib, Pichard,Stone PRL 59 (1987) ensemble of Hermitian matrices with random matrix elements Spectral Rigidity Level repulsion p(s=0)= 0 p(s<<1) s =1,2,4 =1 Porter-Thomas distribution

11 =1, Porter-Thomas distribution Eigenvalues repulsion in various physical problems: nuclear physics, chaos-logy (from Pier Mello, Les Houches)

12 TESTING the DEPENDENCE OF THE UCF ON TIME REVERSAL SYMMETRY

13 L=10 m, L =2.8 m, W=90nm GaAs:Si (10 18 cm -3 ) without a gate D. Mailly & M. Sanquer, J. Phys 1, 357 (1992) =1 =2 P.A. Mello, PRL60, 1089 ( 88)

14 =1 =2: 1/f noise reduction Prediction by Feng, Lee, Stone PRL 56, 1960 (1986) L=10 m, L =2.8 m, W=90nm GaAs:Si ( cm -3 ) with an Al-gate D. Mailly & M. Sanquer, J. Phys 1, 357 (1992)

15 Bi-films (thickness 11-90nm, size few m 2 up to 10 m 100 m ) N. O. Birge B. Golding, W. H. Haemmerle PRL62, 195 (1989)

16 Sensitivity of the localization length to time reversal symmetry acroscopic films RH regime GaAs:Si W/O SOC Nl a:y x Si 1-x With SOC JLP, MS et al. PRL 65, 1812 (1990)

17 Sensitivity of the localization length to time reversal symmetry = ( N + 2- )l (quasi 1D bar) GaAs:Si, w/o SOC JLP, MS et al. PRL 65, 1812 (1990)

18 GaAs:Si, w/o SOC =1 2 N 7 Khavin, Gershenson, Bogdanov PRB 58 ( 98)

19 Agreement w/o SOC but Controversy with SOC: Is there an increase of the localization length under application Of a magnetic field (resminiscent os weak antilocalization) or not? PRL 66, 1517 ( 92) With SOC diffusive loops / forward directed path analysis Problem of ergodicity Bouchaud J.-P., 1991, J. Phys. France, 1, 985 (w/o SOC) Lerner Imry Europhys. Lett., 29 (l), pp (1995) Medina Kardar PRB (92)

20 Forward directed path analysis (Nguyen Spivak Shklovskii JETP Lett. 41,42 (85)) Medina Kardar PRB (92)

21 Bouchaud J.-P., 1991, J. Phys. France, 1, 985 (w/o SOC) J-P Bouchaud, D. Sornette Europhys. Lett. 17, 721 (92) (with SOC)

22 J-P Bouchaud, D. Sornette Europhys. Lett. 17, 721 (92) (with SOC)

23 Magneto-conductance of small MESFETs ( L= nm) W. Poirier, MS, D. Mailly, Phys. Rev. B59, (1999)

24 Magneto-conductance of small MESFETs ( L= nm) N 1 N 8 Nguyen,Spivak, Shklovskii, JETP Lett. 41,42 (85) W. Poirier, MS, D. Mailly, Phys. Rev. B59, (1999) [Fit parameters L=160nm, l =20nm]

25 Magneto-conductance of small MESFETs ( L= nm) W. Poirier, MS, D. Mailly, Phys. Rev. B59, (1999)

26 Silicon nanodevices? Smaller, larger carrier density, smaller mean-free path [Compared to GaAs ] Design of doped silicon bars of various lengths and cross-sections L=200nm comparable to L l = 4-8nm k F l 1 N l L Issue: Coulomb Blockade?

27 1989: first report on periodic conductance oscillations in semi-conductors Conductance Oscillations Periodic in the Density of a One-Dimensional Electron Gas Scott-Thomas, J.H.F., S.B. Field, M.A. Kastner, H.I. Smith, and D.A. Antonadis, 1989, Phys. Rev. Lett. 62, 583. Abstract: By use of x-ray lithography Si inversion layers have been fabricated with width 25 nm and mobility cm2/v s. These display oscillations in their conductance that are periodic in the number of electrons per unit length, even in zero magnetic field. The oscillations reflect an oscillatory activation energy of the conductance and are accompanied by unusual nonlinearities suggestive of pinned charge-density waves.

28 2006: Silicon quantum dot based on the FDSOI technology M. Hofheinz, X. Jehl, M. Sanquer, G. Molas, M. Vinet and S. Deleonibus, A simple and controlled single electron transistor based on doping modulation in silicon nanowires, Applied Physics Letters vol.89, (2006).

29 The MOS-SET One gate Underlapped NW R= 100kW Ec= e 2 /C =12 mev Tsi=10nm, spacers 15nm, L*W=40*20nm CEA Ec=30meV, 20*20*10nm 3, C=6aF R 1 MW (Prati et al. Nanotechnology 2011) Simulation INAC+LETI Ec=85meV, C=2aF R= 5 MW (Deshpande et al. IEDM2012) journée nanosciences 27Nov M. Sanquer Size down to 3,5nm 10nm Lavieville et al Nano Lett (2015)

30 Quantum dots; statistics of the conductance for CB peaks (and valleys) ( Jalabert, Stone, Alhassid et PRL 68, 3468, 1992) =1 =2: First, breaking TR symmetry reduces amplitude of fluctuations Second, breaking TR symmetry increases the mean amplitude =4 =2 (Ahmadian, Aleiner PRB 73, (2006) the average peak height is reduced in the case [ =2]. With SOC, the application of the magnetic field causes the average peak conductance to drop by a factor 1.37, similar to antilocalization for bulk systems.

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