Welcome to the
HOMEPAGE of TITO WILLIAMS
Name: WILLIAMS, Francis Ian Bickford (Tito)
Birth: April, 1939
Address: SZFKI (Research Institute for Solid State Physics)
Konkoly Thege M. 29-33
PO Box 49
1525 Budapest, Hungary
Tel: (++361)3922222 + 3046
Service de Physique de la Matière Condensée (SPEC)
Centre d’Etudes de Saclay, CEA
91191 Gif-sur-Yvette, France
Secondary: Saltus Grammar School, Bermuda.
Cambridge Higher School Certificate (↔Baccalauréat ) December1954
University: 1955-1958 McGill University, Montréal, Canada.
B.Sc. Honours Mathematics and Physics 1958.
1958-1961 University of Oxford.
D.Phil. November 1961.
Thesis Title:"Electron-Nuclear Double Resonance in Solids"
Thesis supervisor: J.M.Baker in laboratory of B.Bleaney.
Postdoctora:l 1961-1963 University of Liege, Belgium.
Research : Mossbauer Effect
1955-58 Bermuda Scholarship
1958-61 Rhodes Scholarship
1961-63 DSIR (Now EPSRC) Post-doctoral Fellowship
NATO Post-doctoral Fellowship
1963-66 Weir Junior Fellowship, University College, Univ. of Oxford
1963-66 Clarendon Laboratory, University of Oxford, England.
1966-68 Bell Telephone Laboratories, Murray Hill, NJ, USA.
1968-2004 Commissariat à l’Energie Atomique, Saclay, France.
2004- Research Institute for Solid State Physics and Optics (SZFKI), Budapest.
1984 (7m) Brown University, Rhode Island.
1993 (2m) SZFKI, Budapest.
1997-99 (4m) ISSP, Tokyo.
2003 (3m) SZFKI, Budapest.
2003 (2m) Weizmann Institute, Rehovot.
Condensed matter physics:
· ions in insulators
· quantum liquids and solids
· classical and quantum phase transitions
· low dimensional systems
· Electron and nuclear spin resonance (CW, echoes, double resonance)
· Mossbauer spectroscopy
· Low temperatures (including design and construction of mK dilution refrigerators)
· Electrical transport (DC, AC and pulse)
· Frequency swept radio-frequency and microwave spectroscopy with geometrically imposed wavelength (near field)
· Micro- nano-lithography
· Ultra low level low noise electrical measurement
· Electrostatic confinement
· Optics (Laser source Raman, Brillouin and Rayleigh spectroscopy, photon correlation)
· Medium pressure techniques at low temperature.
My scientific interests may be broadly classified into three themes: paramagnetic ions in interaction with insulating crystalline hosts, superfluid and solid heliums as quantum condensed systems and electron liquids and solids as two dimensional systems obeying both classical and quantum statistics (electrons on liquid helium, electrons or holes at semiconductor heterojunctions, vortices in quasi-2D superconductors and recently electrons in graphene).
1958-61 Clarendon Laboratory, University of Oxford, England.
· Electron Paramagnetic Resonance (EPR) at 10GHz and 30GHz
· Electron-Nuclear Magnetic Double Resonance (ENDOR) of transition group ions (3d and 4f) in insulators.
1961-63 Université de Liège, Belgium.
· Mössbauer effect in rare earth metal (Eu)
1963-66 Clarendon Laboratory, University of Oxford
· Electron spin echoes and spin-lattice relaxation of Jahn-Teller coupled ion-lattice distortion.
· Stark effect of non-Kramers doublets of ions in solids.
1966-68 Bell Telephone Laboratories, Murray Hill, NJ, USA.
· Raman and Brillouin scattering with laser sources.
· Jahn-Teller effect.
1968-2004 Service de Physique des Solides et de Résonance Magnétique
(Service de Physique de l'Etat Condensé SPEC), CEA Saclay.
· Paramagnetic spin-lattice relaxation
· Spin and phonon relaxation in rapid pulsed magnetic field
· Helium and charges in/on helium: transport in solid helium 3 and 4, effective mass of ions under surface of liquid helium
· Brillouin scattering off dislocations in solid helium to investigate quantum delocalised defects (unsuccessful)
· Electrons above liquid helium surface as model two dimensional classical Coulomb system: coupled electron-helium excitations, transverse phonons, specific and latent heats of classical Coulomb (Wigner) crystal, edge magneto-plasmons, structure factor (ongoing))
· Electrons and holes at semiconductor hetero-junctions (GaAs/GaAlAs) as two dimensional quantum Coulomb system: fractional quantum Hall effect/magnetically induced Wigner solid phase transition(pinning-shear elasticity modes, compressibility, edge magneto-plasmons, Coulomb blockade)
· Micrometric and nanometric capillary waves in superfluid helium: excitation, damping, surface tension.
· Disordered quasi-2D vortex lattice dynamics viewed by post threshold current transport in anisotropic high Tc superconductor (BSCCO): current distribution, metastability, free-flux flow resistance, Hall effect threshold.
· Graphene: collective excitations
1984 (7m) Department of Physics, Brown University, Providence, R.I., USA
· Homogeneous nucleation of solid hydrogen in quest for metastable quantum liquid phase.
· Agregation dynamics.
1999 (2m) Institute of Solid State Physics of University of Tokyo, Tokyo, Japan
· Wigner solid dynamics of electrons on fluid and superfluid helium 3 at ultra-low temperature.
2003 (3m) Research Institute for Solid State Physics and Optics, Budapest, H.
· Depinning behaviour of superconducting vortices in layered superconductors
2003 (2m) Weizmann Institute, Rehovot, Israel
· Sub-micron scale electron interferometers and quantum coherence effects.
2004- Research Institute for Solid State Physics and Optics (SZFKI), Budapest, Hungary.
· Disordered quasi-2D vortex lattice dynamics viewed by post threshold current transport in anisotropic high Tc superconductor (BSCCO): current distribution, metastability, free-flux flow resistance, Hall effect threshold.
· Electrons in graphene
1963-66 University College, University of Oxford
· Undergraduate tutorials in Quantum Mechanics, Solid State and Nuclear physics
· Undergraduate lectures in Noise and Stochastic Processes
· Graduate group tutorials in Group Theory
1982 University of Paris Sud, Orsay , France.
· Graduate level course/seminar series: Phase transitions in two-dimensions.
1993 Eötvös University, Budapest, Hungary.
· European Summer School on “Strongly Correlated Electron Systems”. Lectures on “Interacting electrons with two-dimensional dynamics ".
Research Group: At Saclay, at various times: J.Poitrenaud, D.Marty, G.Deville, C.Glattli + thesis students, post-docs and visitors.
Thesis supervision: D.Breen (Oxford), D.Marty, F.Gallet, A.Valdes, C.Glattli, P.Roche, F.Perruchot, A.Beya, F.Portier (University of Paris VI or XI), and co-supervision of E.Paris and C.Dorin (Paris), P.Wright (Oxford), P.Hennigan and J.Doveston (Nottingham).
1973- Group leader “ Two-dimensional Electron Systems”
1992- Section Head “Quantum Condensed Matter Laboratory”
1995-2000 Assistant Director “Service de Physique de l’Etat Condensé”
1994- Research Director (Directeur de Recherches au CEA)
2004- Scientific Advisor au CEA (Conseiller Scientifique)
2004- Scientific Advisor at SZFKI (Research Institute for Solid State Physics and Optics of Hungarian Academy of Sciences)
INTERNATIONAL CONFERENCES AND SCHOOLS
1974 Aussois . "Condensed Phases of Helium" (with A.Landesman)
1983 Les Houches . "Two Dimensional Problems in Condensed Matter Physics" (avec S.Leibler, K.Binder, Müller-Krumbhar et R.Swendson)
1983 (Oxford) "Electron Properties of Two Dimensional Systems" (EP2DS)
1989 (Grenoble) EP2DS
International Advisory Committees:
1987 EP2DS Santa Fe
1991 EP2DS Nara
1993 EP2DS Newport
1995 EP2DS Nottingham
1991 "Strongly Correlated Electron Systems" Crimea
1993 "International Workshop on Electronic Crystals" (ECRYS), Carry le Rouet, France.
2001 ECRYS La Colle sur Loup, France.
1973 Prix Eastman-Kodak (Académie des Sciences).
1991 Prix du Commissariat à l’Energie Atomique (CEA).
2000 Prix Spécial de la Société Française de Physique.
Ions under surface of superfluid liquid 4He
Poitrenaud J., Williams F.I.B., Precise Measurement of Effective Mass of Positive and Negative Charge Carriers in Liquid Helium II, Phys. Rev. Lett. 29, 1230-1232 (1972)
Electrons above surface of (superfluid) helium
Marty D., Poitrenaud J., Williams F.I.B., Observation of liquid-to-crystal transition in a two-dimensional electronic system, J. Physique Lett. 41, L311-L314 (1980)
Gallet F., Deville G., Valdes A., Williams F.I.B., Fluctuations and Shear Modulus of a Classical Two-Dimensional Electron Solid: Experiment, Phys. Rev. Lett. 49, 212-215 (1982)
Deville G., Valdes A., Andrei E.Y., Williams F.I.B., Propagation of shear in a two-dimensional electron solid, Phys. Rev. Lett. 53, 588-591 (1984)
Glattli D.C., Andrei E.Y., Williams F.I.B., Thermodynamic measurement on the melting of a 2-Dimensional electron solid, Phys. Rev. Lett. 60, 420-423 (1988)
Glattli D.C., Andrei E.Y., Deville G., Poitrenaud J., Williams F.I.B., Dynamical Hall effect in a two dimensional classical plasma, Phys. Rev. Lett. 54, 1710-1713 (1985)
Williams F.I.B., Structure factor of classical 2-D electron system: a waves and water lilies proposal, NMR and More in Honour of Anatole Abragam GOLDMAN M., PORNEUF M., eds., Editions de Physique, Paris, 1994 p. 359
Surface excitations of superfluid helium (ripplons)
Roche P., Deville G., Keshishev K.O., Appleyard N.J., Williams F.I.B., Low damping of micron wavelength capillary waves on superfluid 4He, Phys. Rev. Lett. 75, 3316-3319 (1995)
Roche P., Roger M., Williams F.I.B., Interpretation of the low damping of subthermal capillary waves (ripplons) on superfluid 4He, Phys. Rev. B 53, 2225-2228 (1996)
Roche P., Deville G., Appleyard N.J., Williams F.I.B., Measurement of the surface tension of superfluid 4He at low temperature by capillary wave resonances, J. Low Temp. Phys.106, 555-573 (1997)
Kirichek O.I., Saitoh M., Kono K., Williams F.I.B., Surface Fluctuations of Normal and Superfluid 3He Probed by Wigner Solid Dynamics, Phys. Rev. Lett. 86, 4064-4067 (2001)
Review: charges at helium surface
Williams F.I.B., Collective aspects of charged particle systems at helium interface, Surf. Sci. 113, 371-388 (1982) in: Proceedings of the Fourth International Conference on Electronic Properties of Two-Dimensional Systems New London, NH, USA August 24-28, 1981
Electrons and holes at solid state interfaces
Andrei E.Y., Glattli D.C., Williams F.I.B., Heiblum M., Low frequency collective excitations in the quantum-hall system, Surf. Sci. 196, 501-506 (1988) WORLOCK J.M., ed., Seventh International Conference on Electronic Properties of Two-Dimensional Systrems (EP2DS-VII) Sante Fe, NM, USA July 27-31, 1987
Andrei E.Y., Deville G., Glattli D.C., Williams F.I.B., Paris E., Etienne B., Observation of a magnetically induced Wigner solid, Phys. Rev. Lett. 60, 2765-2768 (1988)
Williams F.I.B., Wright P.A., Clark R.G., Andrei E.Y., Deville G., Glattli D.C., Probst O., et al.+, Conduction threshold and pinning frequency of magnetically induced Wigner solid, Phys. Rev. Lett. 66, 3285-3288 (1991)
Perruchot F., Williams F.I.B., Mellor C.J., Gaàl R., Sas B., Henini M., Transverse threshold for sliding conduction in a magnetically induced Wigner solid, Physica B 284-288, 1984-1985 (2000) GANTMAKHER V., HAKONEN P.J., THENEBERG E., PEKOLA J.P., RASMUSSEN F.B., eds., in: Proceedings of the 22nd International Conference on Low Temperature Physics (LT-22) Helsinki, Finland August 4-11, 1999
Pasquier C., Meirav U., Williams F.I.B., Glattli D.C., Jin Y., Etienne B., Quantum limitation on Coulomb blockade observed in a 2-D electron system, Phys. Rev. Lett. 70, 69-72 (1993)
Vortices in quasi-2-D superconductors
Pethes I., Pallinger A., Sas B., Kriza G., Vad K., Pomar A., Portier F., Williams F.I.B., Potential and current distribution in strongly anisotropic Bi2Sr2CaCu2O8 single crystals at current breakdown, Phys. Rev. B 68, 184509 (2003)
Spin density waves
Balicas L., Kriza G., and Williams F.I.B., Sign Reversal of the Quantum Hall Number in (TMTSF)2PF6, Phys. Rev. Lett. 75, 2000 (1995).
Other low temperature interests
Seidel G.M., Maris H.J., Williams F.I.B., Cardon J.G., Supercooling of liquid hydrogen, Phys. Rev. Lett. 56, 2380-2382 (1986)
Marty D., Williams F.I.B., Mobility of Ions in Solid Helium, J. Physique 34, 989-999 (1973)
Pangalos C., Allain Y., Williams F.I.B., Polarization of a paramagnet by a fast high intensity magnetic field pulse: spin and phonon relaxation, phonon spectroscopy, J. Physique 35, 989-992 (1974)
Breen D.P., Krupka D.C., Williams F.I.B., Relaxation in a Jahn-Teller System. I. Copper in Octahedral Water Coordination, Phys. Rev. 179, 241-254 (1969)
Williams F.I.B., Breen D.P., Krupka D.C., Relaxation in a Jahn-Teller System. II, Phys. Rev. 179, 255-271 (1969)
Williams F.I.B., Paraelectric resonance of praseodymium in yttrium ethyl sulphate, Proc. Phys. Soc. 91, 111-123 (1967)
Baker J.M., Williams F.I.B., Electron nuclear double resonance of the divalent europium ion, Proc. Roy. Soc. A 276, 283-294 (1962)
GUIDE TO SELECTED PUBLICATIONS
The physics of systems of low-dimensional degrees of freedom has been a driving force for many of the advances in understanding and exploiting condensed matter. Removing a dimension often strips a problem to its essentials and sometimes even allows a sound theoretical solution which can be compared to a better targeted experiment. One example which has produced fascinatingly new physics is quantum electrons in two dimensions with remarkable and unsuspected quantum Hall effects. Increasing electron correlation results in the quantum fluctuation driven Wigner transition between correlated liquid and crystal. No less interesting is the classical thermal-fluctuation melting transition in 2-D, the marginal dimensionality for crystalline order: understanding it thoroughly, easier in 2-D, helps a more thorough understanding of melting in 3-D. Even lower-dimensional systems unveil further physics: 1-D lines reveal quantisation of conductance in quantum wires, spin and charge-density-wave instabilities, 0-D dots approach atomic systems and show up charging energy phenomena. Clearly low- temperature low-dimensional physics has brought much new insight and will undoubtedly bring many more surprises.
Interest in the dynamics of individual charges in solid and liquid helium led to investigating the effects of interaction. A first experiment on charges confined by the liquid helium surface was designed to measure the effective mass for motion in the superfluid. Interest then turned towards the mirror system of electrons above the helium surface. This system is in many respects more accessible to experiment because of the free electron mass and is undoubtedly the best physically realisable approximation to free two-dimensional dynamics presently known and constitutes an ideal test bed for investigating interacting N-particle systems with 2 degrees of dynamical freedom with an exactly known and scalable Coulomb interaction potential. A series of targeted experiments was undertaken to investigate melting in 2-D in the classical limit where quantum fluctuations do not make a significant contribution. Subsequently, because the surface of liquid helium cannot sustain sufficiently high electron densities to investigate quantum melting, attention was given to electrons (and holes) at high quality solid interfaces (GaAs/GaAlAs heterojunctions) to demonstrate quantum melting in 2-D on going from a quantum liquid state showing fractional quantum Hall effect to a Wigner solid state as the quantum fluctuations are suppressed by application of stronger magnetic field.
Ions confined to 2-D under superfluid liquid helium surface
Effective mass and ion size
The effective mass for ion dynamics in liquid helium was determined by confining the (negative or positive) ions in a precisely known potential well set up by holding the ions against the surface with an electric field and measuring their vibrational frequency in the dissipationless superfluid by resonance with an exciting electric field. A simple model for intrinsic and hydrodynamic mass then leads to ion size. (J.Poitrenaud and Williams, 1972)
Electrons confined to 2-D above (superfluid) liquid helium surface
Classical Coulomb (Wigner) crystallisation
Crystallisation of electrons above liquid helium was observed by monitoring the change in radio-frequency (30MHz) electric susceptibility as a function of temperature. This experiment, begun at much the same time as that of Grimes and Adams, was in the event a confirmation of their observation of a few months before. (J.Poitrenaud, D.Marty and Williams, 1980)
Spatial fluctuations of 2-D electron crystal
The experiment on positional fluctuations of the 2-D electron crystal pointed to a Kosterlitz-Thouless type of phase transition for the melting. The experiment measured the resonance frequency of the electrons in the image lattice of dimples produced in the helium surface by the time averaged pressure obtained by pushing the spatially fluctuating electrons onto the surface with an electric field. (F.Gallet, G.Deville, A.Valdes and Williams, 1982)
2-D Transverse sound and shear modulus
Transverse sound propagation was demonstrated by exciting the electron crystal with the Lorentz force obtained by combining a perpendicular DC magnetic field with a longitudinal finite wavevector rf electric field set up by a meander transmission line. The propagation velocity obtained from the frequency-wavevector relation gives a very direct measure of the shear modulus and its temperature variation and shows unmistakeably the Kosterlitz-Thouless relation between elastic modulus and melting temperature at melting. (Deville, Valdes, E.Andrei and Williams, 1984)
2-D Thermodynamics: heat capacity and melting entropy of electron crystal
The heat capacity of the 2-D classical electron solid (~108 particles) was followed across the melting transition by measuring the electronic temperature rise after application of a heat pulse in a time short compared with energy relaxation to the helium substrate. Thermometry was based on the electron-in-dimple resonance frequency mentioned above and the heat pulse was applied by rf excitation of a magneto-plasmon mode which shares its energy rapidly with the ensemble of vibrational excitations. The disappearance of the dimple lattice as the solid melts required putting a second, higher density, electron solid in contact with the sample under test, introducing the idea of Kapitza resistance across a 1-D boundary. The specific heat for T<Tm was found to be in very good agreement with the phonon contribution calculated from the previous measurements of the shear modulus while the entropy change across the melting transition was shown to be <0.2kB per particle, again compatible with the Kosterlitz-Thouless melting scenario. (C.Glattli, E.Andrei and Williams, 1988)
Quasi 1-D edge magneto-plasmons
The investigation of magneto-plasmons led to the discovery of edge magneto-plasmon modes and the realisation that they are a dynamical manifestation of the Hall effect. When the excitation wavelength is much greater than the distance from the metallic confining electrodes, an exactly-soluble screened-potential approximation is appropriate and was shown to give an excellent quantitative account of the series of edge mode resonances observed. (Glattli, Andrei, Deville, Poitrenaud and Williams, 1985)
Structure factor – Bragg scattering with ripplons (quantised surface ripples)
Principally to be able to detect the presence of a hexatic liquid phase, but also to be able to see the effects of an artificially applied random field on the electron crystal, an experiment was proposed to measure the structure factor of electrons on helium by diffracting sub-micron capillary waves (ripplons) of the superfluid surface off the electrons. The intensity of the uniform (k=0) component of the up and down motion of the electrons, as measured by the displacement current induced in plane parallel confining electrodes, corresponds to zero transfer wave-vector and was shown to give directly the structure factor at the wave-vector of the incoming ripplon. (Williams, 1994).
Quasi 2-D micrometre and sub-micrometre ripplons (quantised capillary waves)
Ripplons in the wave-vector range required for the structure factor experiment had never before been investigated, so the first experimental step was to generate and measure the damping of these surface quasi-2-D excitations. Manipulation of thin films and generation of short wavelength ripplons were ensured by the dielectric polarisation forces in helium imposed by nano-lithographically fabricated interdigital capacitors. Generation and propagation were demonstrated and damping measured. It had been suspected from previous work on coupled electron lattice-ripplon modes that the theoretical predictions of damping were too high, but the experiments showed that they were in fact six orders of magnitude too large for the temperatures and wave-vectors in question! (P.Roche, Deville, K.O.Keshishev, N.J.Appleyard and Williams, 1995)
Scattering mechanisms in ripplon damping and the surface boundary condition
Attempts had already been made to reconcile theory with the widths of electron lattice-ripplon coupled modes which indicated at least two orders of magnitude discrepancy, but it was clear that six orders of magnitude could only result from some fundamental flaw: this was traced to the flow boundary condition being applied to the unperturbed rather than the perturbed surface. Although of seemingly higher order, the alteration in the boundary condition changes a sign in the coupling Hamiltonian with dramatic results on the available phase space for scattering. Once corrected, the ripplon-ripplon scattering mechanism previously thought to be the most important was found to be ten orders of magnitude less effective than previously calculated and in fact ripplon-phonon scattering dominates and accounts very well for the experimental findings. (Roche, M.Roger and Williams, 1996).
Superfluid helium surface tension
The above experiments at very short wavelengths compared to the capillary length also brought a new method to the measurement of the surface tension of the helium superfluid just at the time that this knowledge was becoming critical for helium wetting problems and that high accuracy ab initio calculations had been performed. The result of the Saclay group rather surprisingly confirmed the early static capillary rise measurements rather than the more recent and sophisticated long wavelength normal mode frequency approach which would appear to have suffered from meniscus corrections. The ab initio calculation was also in excellent accord with the measurement. (Roche, Deville, Appleyard and Williams, 1997)
Surface roughness of normal and superfluid helium 3
In collaboration with K.Kono’s group at the ISSP in Tokyo, the damping of “optical” (electron-in-dimple) modes of the Wigner crystal was exploited to measure surface roughness on liquid helium 3 from 150 to 0.3mK. This gave the very unexpected result that although more or less as predicted above 80mK, the roughness became anomalously low as the temperature was reduced, particularly in the superfluid phase. (O.I.Kirichek, M.Saitoh, Kono and Williams,2001)
Confined 2-D geometry: “suspended films” and higher electron densities
The quest for higher electron densities to approach the quantum melting regime inspired the idea of confining the geometry of the helium substrate to raise the wavevector of the surface softening instability and hence the maximum sustainable density This approach uses the superfluid properties of liquid helium to maintain equilibrium between the confined space, which is set above the free surface, and the bulk of liquid and is now called the “suspended film” technique. It was first demonstrated by Marty (1985) in Saclay and is presently in use by many groups, in particular for the Rydberg state qubit experiments of M.Lea and Yu.Muhkarshy in London and Saclay and A.Dahm and J.Goodkind in the USA. (Williams, 1982).
2–D electron and hole systems at solid state interfaces
Faced with the impossibility of raising the electron density on free or even confined helium to the levels required for quantum melting and, in the case of thin helium films, the great difficulty of reducing substrate-induced random potentials below the Coulomb interaction strengths, appeal was made to the semiconductor community who had perfected very high quality modulation-doped epitaxial heterojunctions between GaAs and GaAlAs. With a light effective mass and higher densities (up to 3 orders of magnitude) quantum fluctuations become stronger and the dielectrically screened Coulomb interaction weaker. The new compromise is to lower quantum fluctuations by lowering the density, yet not so far that interface defect potentials dominate the Coulomb interaction; therein lies the importance of very high quality samples. Collaborations with M.Heiblum, then at IBM, B.Etienne, at the CNRS and J.Harris and T.Foxon, then at Philips UK and R.Clark, then at Oxford, enabled the Saclay group to enter this new terrain for low dimensional physics.
Quasi 1-D edge magneto-plasmons in the quantum Hall effect regime
Their first low temperature, high field experiment on electrons confined by a heterojunction, employing a purpose built swept frequency, finite wavevector spectrometer, revealed edge magnetoplasmons in the quantum Hall effect regime and showed them to be well defined excitations on the quantum Hall plateaus. This was the clearest and most unequivocal evidence that these excitations, discovered first in the classical electrons on helium system, were also well defined in the quantum Hall system. (Andrei, Glattli, Williams and M.Heiblum, 1987)
Magnetically induced 2-D quantum Wigner solid
The spectrometer had been designed principally to detect the lower magneto-phonon branch which was expected to occur when an elastic shear modulus appears as should be the case for electron solid formation. New modes were indeed detected as increasing magnetic field suppressed quantum fluctuations, accompanied by the disappearance of the fractional quantum Hall effect. These modes result from the transverse restoring force which occurs when a (Wigner) solid forms and pins to the underlying interface defects. The measurements gave the first observation and the first filling factor-temperature phase diagram of this new phase. This new approach to the problem and the application of a new technique - finite wave-vector swept frequency spectroscopy - to a new state of the art material - very high quality heterojunction samples – brought new 2-D physics in the form of the long sought quantum Wigner solid in 2-D. This was a break-through experiment which said what happens beyond the fractional quantum Hall effect and demonstrated a long predicted (Wigner 1937) quantum liquid to solid phase transition of the electrons. (Andrei, Deville, Glattli, Williams, E.Paris and B.Etienne, 1988)
Pinning properties of 2-D quantum Wigner solid
The complement to the previous experiment, and a confirmation of the interpretation, came in showing the quantitative relationship between threshold field for electrical conduction and the pinning mode frequencies. It was also shown that reducing disorder by application of light to the heterojunction reduced the pinning mode frequency and threshold field. At the same time a more detailed and documented phase diagram was established on a universal scaling plot by combining results on a variety of samples of differing densities. (P.A.Wright, R.G.Clark, Andrei, Deville, Glattli, O.Probst, C.Dorin, B.Etienne, J.J.Harris and T.Foxon, 1991)
Hall effect in sliding conduction regime of 2-D Wigner solid
At the same time, a series of careful high impedance transport measurements in the magnetic 2-D Wigner solid phase of both electrons and holes at the GaAs/GaAlAs heterojunction was undertaken to understand the Hall effect in the regime where the solid slides over the host roughness (post threshold conduction). The surprise was the lack of Hall effect until the Lorentz force reaches a threshold force equal to about 1/10 of that required to slide the solid longitudinally. This was seen as a manifestation of the transverse threshold proposed later by T.Giamarchi and P.Ledoussal for the superconducting vortex lattice in a random field. (F.Perruchot, 1995 and Perruchot, Williams, C.J.Mellor, R.Gaal, B.Sas and M.Henini, 2000)
Lower dimensional heterojunction electron structures
Lateral electrostatic confinement of the 2-D heterojunction electrons can be exploited to create 1-D (quantum wire) and 0-D (quantum dot) configurations to which variable conductance tunnel contacts can be established with so called quantum point contacts. By these means an experimental demonstration was given on quantum limitations on Coulomb blockade in a quantum dot connected by two quantum wires to 2-D reservoirs (C.Pasquier, U.Meirav, Williams, Glattli, Y.Jin and Etienne, 1993)
Quasi 2-D vortex system in anisotropic superconductors
The results and interpretation of the previous experiments on the depinning of the 2-D Wigner crystal incited interest in transport and Hall effect in the generically similar quasi 2-D system of interacting vortices in the random potential (pinning) field of the very anisotropic high Tc superconductor BSCCO (Bi2Sr2CaCu2O8+d).
Quasi 2-D vortex dynamics in strongly anisotropic superconductors
Investigation of the post threshold current “free flux flow” regime of vortex motion by a rapid current-pulse drive, to avoid heating complications, revealed unexpected metastability in the low temperature vortex solid phase. Experiments on lithographically stepped samples were performed to determine the potential and current distribution in this regime as a prelude to Hall effect measurements which showed, like the Wigner solid, a second threshold to transverse force. (I.Pethes, Sas, Kriza, K.Vad, A.Pomar, F.Portier, Williams, 2003)
Quasi 1-D spin density wave system
Charge and spin density waves are quasi 1-D periodic systems which pin to random host potential fluctuations in a very similar way to the 2-D electron crystal.
Quasi 1-D spin density wave quantum Hall effect
Demonstration of the sign reversal in the sequence of quantum Hall effect plateaus in (TMTSF)2 PF6 .(L.Balicas, G.Kriza and Williams, 1995)
Other low temperature but non low-dimensional interests
Supercooling limit of liquid hydrogen
Measurement of homogeneous nucleation times for formation of solid from liquid hydrogen droplets. Solid was distinguished from liquid by its density by optical observation of the height of the plane of flotation in pressurised helium gas subject to a vertical temperature gradient. It was hoped to be able to supercool towards zero temperature to create conditions for Bose-Einstein type condensation, but in the event only 25% supercooling was attained. (G.M.Seidel, H.J.Maris, Williams and J.G.Cardon, 1986)
Ion mobilities in solid 3He and 4He
Time of flight measurements of helium ions between two electrodes by drawing ions from a plasma created by photoelectrons emitted from one electrode by pulsed X-ray bombardment. (D.Marty and Williams, 1973)
Paramagnetic phonon pump and detector: adiabatic magnetisation
The spin-phonon interaction transfers energy between the two systems. By applying a large fast magnetic field pulse, paramagnetic spins in a lattice transfer their energy towards the cold phonons by adiabatic magnetisation. On return of the field the opposite occurs and by measuring the magnetisation one can monitor the relaxation of the phonons. (CPangaloss, Y.Allain and Williams, 1974)
Dynamical Jahn-Teller effect: reorientation rate
The anisotropic spin resonance spectrum distinguishes between three equivalent distortions of the cage surrounding a Cu2+ ion in octahedral coordination. Reorientation thus contributes to the dephasing of spins labelled by the initial rf pulse of an electron spin echo sequence. The echo decay time gives a direct measure of the reorientation rate. The theoretical framework for the Jahn-Teller reorientation rates was given in a companion paper. (D.P.Breen, D.C.Krupka and Williams, 1969; Williams, Krupka and Breen, 1969)
Stark effect of non-Kramers ions in environments lacking inversion symmetry
A non-Kramers (even number of electrons) ion with a degenerate ground state in zero field is not restricted by time inversion symmetry to have a zero linear Stark effect. The paper discusses the form of the matrix representing the Stark effect and presents measurements made by comparing electric dipole resonance intensities with magnetic dipole intensities for the Pr3+ ion in a host lattice site lacking inversion symmetry. (Williams, 1967)
Electron-nuclear spin double resonance: isotopic anomaly of hyperfine structure of europium ion. (J.M.Baker and Williams, 1962)