Electrons on Helium Films
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1 Electrons on Helium Films Paul Leiderer University of Konstanz Okinawa,
2 Experimental Systems B ext colloid sample PS spheres, 5µm superparamagnetic magn. moment µ ~ B ext electrons on liquid helium
3 Outline - Introduction: Electrons on bulk liquid helium - Electrons on helium films - Electrons in confined geometry - Conclusions
4 Electrons on Liquid Helium potential above bulk He (1/z) Hydrogen-like spectrum wave function of ground and first excited state
5 Phase Diagram E E E Kin Pot F ~ T ~ n ~ n E E Pot Kin (thermal) (Coulomb) (Fermi) Wigner crystal Peeters and Platzman, PRL (1983) Coulomb gas n c T c 2.4*10 33 K 16 m 2 But: Wigner on bulk crystallization liquid 4 He, an ehdand instability melting: occurs at n > 2x10 13 m -2 BKTHNY scenario study (dislocations, electronsdisclinations) He films!!
6 Detour: Colloid System Colloid Wigner Polycrystal
7 Phase Diagram E E E Kin Pot F ~ T ~ n ~ n E E Pot Kin (thermal) (Coulomb) (Fermi) Wigner crystal Peeters and Platzman, PRL (1983) Coulomb gas n c T c 2.4*10 33 K 16 m 2 But: Wigner on bulk crystallization liquid 4 He, an ehdand instability melting: occurs at n > 2x10 13 m -2 BKTHNY scenario study (dislocations, electronsdisclinations) He films!!
8 Electron-Surface Interactions - electrostatic pressure - gas atom scattering - ripplon scattering - scattering from surface roughness - polaron formation (self-trapping of the electrons)?
9 Layering of Thin Helium Films on Solid H 2 investigated with surface state electrons D. Cieslikowsk, A.J. Dahm, PL, PRL 58, 1751 (1987)
10 Electron-Surface Interactions - electrostatic pressure - gas atom scattering - ripplon scattering - scattering from surface roughness - polaron formation (self-trapping of the electrons)?
11 Electrohydrodynamic Instability E< E c ( ~ 3kV/cm) E> E c Ripplon softening M. Wanner, PL, PRL 42, 316 (1979)
12 Dynamics of the Dimple Crystal
13 Outline - Introduction: Electrons on bulk liquid helium - Electrons on helium films - Electrons in confined geometry - Conclusions
14 Cyclotron Resonance 10 GHz B ext with V.B. Shikin J. Low Temp. Phys. 122, 451 (2001) i) m SSE = m e ii) two-fraction model: free and localized electrons (roughness-dependent, here n e /n tot = 0.70))
15 Wigner Crystallization and Quantum Melting Drude-like Holding field (V) Absorption (1/ ) crystallization melting? 11-2 Electron density (10 cm ) Electron density Phys. Rev. B56 (1997) Surf. Sci. 361/62, 831 (1996)
16 Influence of Screening For electrons on a helium film the image charges of the solid substrate come into play: SSE image charge He (ε=1.06) nm dielectric substrate (ε 2 5) dipolar contributions to Coulomb interaction Phase diagram
17 Influence of Screening microwave signal for 2 film thicknesses G. Mistura et al., PR B56 (1997) M. Saitoh, PR B40 (1989)
18 Wigner Crystallization and Quantum Melting classical gas Wigner crystal localized states Kosterlitz-Thouless transition degenerate Fermi gas extended states?
19 Wigner Crystallization and Quantum Melting Holding field (V) Absorption (1/ ) crystallization melting? 11-2 Electron density (10 10 cm cm) -2 )
20 Charge density and He film thickness on insulating substrates on glass
21 Charged He Films on Metallic Substrates evaporated gold film (~45 nm) on glass (BK7) prism Heat beam Plasmon 2 ~ 0.1mm Plasmon 2 20 mm Plasmon 1 Plasmon 1 Top view: Heat beam
22 Thickness of Charged Films on Au
23 Electron Density typical decay behaviour
24 Transport between 2 Segments
25 Transport between the 2 Segments 24 mv = 280 K Tunneling through barrier? 40 V gold 0.1 mm glass gold good reproducibility from run to run, but bad reproducibility from substrate to substrate
26 Outline - Introduction: Electrons on bulk liquid helium - Electrons on helium films - Electrons in confined geometry - Conclusions
27
28 dc measurements with the He FET filament collimator to the electrometer U 4 (pick-up) U g U 1 (source) U 2 (gate) U 3 (drain) U g guardring collimator E4 E1 (source) E2 (gate) E2 E3 (drain)
29 Potential Distribution across the channel source - gate - drain Ashari et al., JLTP 2012
30 Charging the He FET pick-up current (pa)
31 Electron Distribution in the Source Area colloid sample substrate tilted to the right schematic distribution
32 Storage of SSE in the Source current pulse after opening the gate for different gate voltages number of stored electrons as a function of the gate voltage M. Ashari et al., JLTP 2012
33 Transport in the Wigner Crystal Regime stepwise opening of the gate
34 Time-of-flight Measurements (Pulsed Gate Voltage) Channel 10µm wide. 400µm long Transmitted electrons are detected only above a certain pulse width (25µs in this case, for point contacts : in the nanosecond range)
35 Effect of Coulomb Repulsion on the Transit Time Channel: 3.37µm wide 400µm long V sd = 2V For low electron density: transit time is determined by the potential gradient in the Si substrate For high electron density: Coulomb repulsion between the electrons dominates
36 Helium FET steps in the I-V characteristics (dc) 3 U 13 =0.25V U 13 =0.75V U 13 =1.0V current [pa] 2 1 current [pa] 3,5 3,0 2,5 2,0 1,5 1,0 U 3=0.75V; down U 3=0.75V; up U 3=1.0V; down U 3=1.0V; up U 3=1.5V; down U 3=1.5V; up data from ,5 0 0,0-2,0-1,5-1,0-0,5 0,0 0,5 1,0 U gate [V] I. Doicescu (2005) U gate [V]
37 Onset of Transport Current in an AC Device D. Rees, K. Kono et al., PRL 2011
38 Again detour: colloid system Transport of classical correlated Brownian particles through a channel colloidal particles, in two reservoirs, slightly tilted Video microscope simulation with colloidal particles moving through a 70µm wide channel (M. Koeppl)
39 M. Köppl et al., PRL 97, (2006) Density and Lattice Constants along the Channel
40 Conclusions Electrons on He are model systems for low-dimensional matter: Electrons on films ( infinite 2D system) phase transition classical fluid crystal can be tuned by film thickness (dipolar contribution) phase transition Wigner crystal degenerate Fermi gas quantum melting (has to be studied in more detail) problem: electron loss into metallic substrates: what is the mechanism? (local instability, tunneling?) Electrons in confined geometry He FET: dc measurements are possible electron energy determined by substrate potential & Coulomb repulsion narrow constrictions: correlation phenomena also in classical transport to be studied: structured channels crossover from classical to qm behavior
41 Thanks to the Group Members: J. Klier I. Doicescu A.Valkering T. Günzler G. Mistura D. Schmidt M. Ashari R. Rau F. Shaban T. Lorenz C. Bechinger A. Erbe S. Neser R. Bubeck M. Köppl C. Kreuter Collaborations with K. Kono, D. Rees V.B. Shikin A. Dahm Funding by SFB 513 FG Quantengase EU RTN 2D electrons
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