Welcome to the

**HOMEPAGE of TITO WILLIAMS**

** **

**CURRICULUM VITAE**

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

Tel: (++331)(0)69087217

**EDUCATION**

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

Academic Awards:

1955-58 Bermuda Scholarship

1958-61 Rhodes Scholarship

1961-63 DSIR (Now EPSRC) Post-doctoral Fellowship

NATO Post-doctoral Fellowship

CIBA Fellowship

1963-66 Weir Junior Fellowship, University College, Univ. of Oxford

**EMPLOYMENT**

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.

**RESEARCH VISITS**

1984 (7m) Brown University, Rhode Island.

1993 (2m) SZFKI, Budapest.

1997-99 (4m) ISSP, Tokyo.

2003 (3m) SZFKI, Budapest.

2003 (2m) Weizmann Institute, Rehovot.

** **

** **

**RESEARCH AREAS**

DOMAINS

Condensed matter physics:

· ions in insulators

· quantum liquids and solids

· classical and quantum phase transitions

· low dimensional systems

EXPERIMENTAL METHODS

· 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.

THREADS

** **

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).

**PROFESSIONAL EXPERIENCE **

** **

** ****Research:**

**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

**Teaching:**

** **

**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 ".

** **

**SCIENTIFIC COORDINATION**

**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).

**SCIENTIFIC RESPONSIBILITIES**

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 **

Organisation:

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)

Programme Commitees:

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.

**RESEARCH PRIZES **

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.

** **

**SELECTED PUBLICATIONS**

** **

*Ions under surface of superfluid
liquid ^{4}He*

**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 ^{4}He,
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 ^{4}He, 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 ^{4}He 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 ^{3}He 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 Bi_{2}Sr_{2}CaCu_{2}O_{8}
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)_{2}PF_{6},
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 (~10^{8} 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<T_{m}
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 <0.2k_{B} 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 (Bi_{2}Sr_{2}CaCu_{2}O_{8+}_{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} PF_{6} .*(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 ^{3}He and ^{4}He**

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 Cu^{2+} 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 Pr^{3+} 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)*