List of publications for Philip B. Allen

Favorite Publications of Philip B. Allen


P.B. Allen and M.L. Cohen,
``Pseudopotential Calculation of the Mass Enhancement and
the Superconducting Transition Temperature of Simple Metals",
Phys. Rev.  187, 525-538 (1969).

The main part of my thesis.  Working with Marvin Cohen was a
great pleasure, and Berkeley was particularly interesting in those days.

P. B. Allen,
"Electron-Phonon Effects in the Infrared Properties of Metals"
Phys. Rev. B 3, 305 (1971).

This paper uses Holstein's approach to include (at the level
of Migdal's approximation) the self-energy and vertex corrections
into the Drude theory for normal metals.  The equations were
explicitly given only at T=0.  Dolgov et al have given the
T>0 generalization.

P. B. Allen,
"Neutron Spectroscopy of Superconductors"
Phys. Rev. B 6. 2577 (1972).

This paper gives the relation between the phonon decay rate
(into electron-hole pairs) and the electron-phonon coupling
constant lambda.

J. C. K. Hui and P. B. Allen,
"Effect of Anharmonicity on Superconductivity"
J. Phys. F 4, L42 (1974).

Not the last word on the subject, but one of the few simple
things that can be said.  Anharmonicity from this point of
view does not look very favorable as a way to raise Tc.

P. B. Allen and R. C. Dynes,
"Transition Temperature of Strong-Coupled Superconductors Reanalyzed."
Phys. Rev. B 12, 905 (1975).

Eliashberg theory does not suggest a limit to the magnitude of
Tc from electron-phonon interactions.

P. B. Allen,
"Fermi Surface Harmonics: A General Method for Non-Spherical
Problems.  Application to the Boltzmann and Eliashberg Equations."
Phys. Rev. B 13, 1416 (1976).

P. B. Allen and V. Heine,
"Theory of the Temperature Dependence of Electronic Band Structures."
J. Phys. C 9, 2305 (1976).

P. B. Allen,
"Charge Density Distortions and Lattice Dynamics: A General
Theory and Application to Niobium."
Phys. Rev. B 17, 3725 (1977).

In order to get a complete fit to Nb, both scalar and quadrupolar
electronic charge fluctuations were invoked.  There were too
many free parameters.  Nobu Wakabayashi at the same time used
just the scalar fluctuations and his theory is more appealing
physically, but doesn't fit as well.

P. B. Allen,
"New Method for Solving Boltzmann's Equation for Electrons in
Phys. Rev. B 17, 3725 (1978).

This uses both the Fermi Surface Harmonics (for the "angular"
part of the problem) and a new set of polynomials orthogonal
with weight (-df/dE) which simplify the "radial" part.

P. B. Allen
"Phonons and the Superconducting Transition Temperature."
in "Dynamical Properties of Solids", G. K. Horton and A. A.
Maradudin, eds., (North-Holland, Amsterdam, 1980) pp95-196.

A review article.

P. B. Allen,
"Theory of the Superconducting Transition Temperature, Pair
Susceptibility, and Coherence Length."
In "Modern Trends in the Theory of Condensed Matter", A.
Pekalski and J. Przystawa, eds. (Lecture Notes in Physics No.
115, Springer-Verlag, Berlin, 1980).

A pedagogical article with some new results.  Antisuperconductivity
is introduced.  This is related to what Yang more recently called
"eta pairing."  The meeting in Karpacz where this was presented was
very memorable.

P. B. Allen,
"Theory of Resistivity Saturation."
In "Superconductivity in d- and f-Band Metals", H. Suhl and M.
B. Maple, eds. (Academic Press, NY 1980) pp291-394.

An informal review.  In retrospect, I dismissed unfairly the
"phonon ineffectiveness" idea of Cote and Meisel.  This idea
is implicit in some earlier work of Albert Schmid, and therefore
is certainly not wrong, although I don't think it's the right
explanation of "resistivity saturation."

P. B. Allen and J. C. K. Hui,
"Thermodynamics of Solids: Corrections from Electron-Phonon
Z. Phys. B 37, 33-38 (1980).

This paper shows that at high T, the electronic entropy is
actually no bigger than the correction from temperature dependence
of the energy bands, which is an electron-phonon effect.  A
very interesting identity connects this term to the term
coming from temperature-dependent electron-phonon renormalization
of the phonon frequencies.

P. B. Allen and B. Chakraborty,
"Infrared and d.c. Conductivity in Metals with Strong Scattering:
Non-Classical Behavior from a Generalized Boltzmann Equation
Containing Band Mixing Effects."
Phys. Rev. B 23, 4815 (1981).

I think this paper does contain the correct explanation of
resistivity saturation, but unfortunately a numerical implementation
still seems close to prohibitively difficult.  Connected with the
electron-phonon renormalizations which cause the temperature
shift of band structure, there are band-mixing effects which alter
the resistivity.  The parameter of the theory is the ratio of the
scattering rate (2 pi lambda kT) to the band separation, which is
not a small parameter for metals like Nb3Sn (band separation ~1/3 eV.)

F. J. Pinski, P. B. Allen, and W. H. Butler,
"Calculated Electrical and Thermal Resistivities of Nb and Pd."
Phys. Rev. B 23, 5080 (1981).

P. B. Allen and B. Mitrovic,
"Theory of Superconducting Tc."
In "Solid State Physics", F. Seitz, D. Turnbull, and H. Ehrenreich,
eds. (Academic, New York, 1982) pp.1-92.

P. B. Allen and M. Cardona,
"Temperature Dependence of the Direct Gap of Si and Ge."
Phys. Rev. B 27, 4760 (1983).

A. Auerbach and P. B. Allen,
"Universal High-Temperature Saturation in Phonon and Electron
Phys. Rev. B 29, 2884 (1984).

Pauli said to Peierls that when a physicist uses the word
"universal" it just means pure nonsense.  We compare
heat conductivity in insulators with electrical conductivity
in metals, and find analogous saturating behavior.  Even the
"shunt resistor model", which Michael Gurvitch introduced for
electrical resistivity, had been independently proposed by
Slack for the heat resistivity of insulators.  Auerbach and
I argue that the same physics as in the Chakraborty paper listed
above applies to the heat conduction problem in insulators.

F. S. Khan and P. B. Allen,
"Deformation Potentials and Electron-Phonon Scattering: Two
New Theorems."
Phys. Rev. B 29, 2884 (1984).

J. K. Jain and P. B. Allen,
"Plasmons in Layered Films."
Phys. Rev. Letters 54, 2437 (1985).

Jainendra's thesis, before he became famous for inventing
composite Fermions.

F. S. Khan and P. B. Allen,
"Sound Attenuation by Electrons in Metals."
Phys. Rev. B 35, 1002 (1987).

No one ever refers to this paper, but I think it's neat.

P. B. Allen,
"Empirical Electron-Phonon Lambda Values from Resistivity
of Cubic Metallic Elements."
Phys. Rev. B 36, 2920 (1987).

The most reliable lambda values available, I believe.

P. B. Allen,
"Theory of Thermal Relaxation of Electrons in Metals."
Phys. Rev. Lett 59, 1460 (1987).

Ultrafast laser pump-probe experiments can measure the rate
at which hot electrons return to equilibrium.  I put the
nice old papers by Kaganov and others into modern language.
Lambda can be extracted.

P. B. Allen, W. E. Pickett, and H. Krakauer,
"Anisotropic Normal State Transport Properties Predicted and
Analyzed for High Tc Oxide Superconductors."
Phys. Rev. B 37, 7482 (1988).

The referees thought it was crazy to apply LDA to such a
problem, and this paper was hard to get into print.  Our
predictions of anisotropy have been amazingly well verified,
both in resistivity and in the penetration depth of 123.
Also we predicted changes in sign of the Hall coefficient
depending on geometry, before they were observed.

P. B. Allen, M. L. Cohen, and D. R. Penn,
"Total Dielectric Function: Algebraic Sign, Electron-Lattice
Response, and Superconductivity."
Phys. Rev. B 38, 2513 (1988).

Ginzburg, Kirzhnits, Maksimov, and Dolgov argued that contrary
to certain gurus, the dielectric function can go negative
even at zero frequency, and this helps explain why Tc isn't
always small in metals.  This paper agrees with that view,
and formulates the theory properly for a real crystal with
local field effects included.

R. H. Brown, P. B. Allen, D. M. Nicholson, and W. H. Butler,
"Resistivity of Strong-Scattering Alloys: Absence of Localization
and Success of Coherent-Potential Approximation Confirmed by
Exact Supercell Calculations in V(1-x)Al(x)."
Phys. Rev. Letters 62, 661 (1989).

I was expecting that we would find a significant difference
between the exact Kubo-Greenwood response and the CPA answer.
But our "exact" numerical results and the CPA results agreed.
Butler's KKR-CPA treatment of this very dirty alloy gives
incredibly good answers.

P. B. Allen and D. Rainer,
"Phonon Suppression of Coherence Peak in Nuclear Spin Relaxation
in Superconductors."
Nature 349, 396 (1991).
W. W. Schulz, P. B. Allen, and N. Trivedi,
"Hall Coefficients of Cubic Metals,"
Phys. Rev. B 45, 10886 (1992).

P. B. Allen and J. L. Feldman,
"Thermal Conductivity of Disordered Harmonic Solids."
Phys. Rev. B 48, 12581 (1993).

The vibrational analog of the Kubo-Greenwood approach.  But how
does a vibrational eigenstate which doesn't propagate (even though
delocalized) carry current?  The answer is that the thermal
gradient necessarily implies that the occupied vibrational
states are non-stationary superpositions of eigenstates, which
are needed in order to localize more vibrational energy at
the hot end than the cold end of the sample.

J. L. Feldman, M. D. Kluge, P. B. Allen, and F. Wooten,
"Thermal Conductivity and Localization in Glasses: Numerical
Study of a Model of Amorphous Silicon."
Phys. Rev. B 48, 12589 (1993).

The theory of the previous paper implemented and successfully
compared with experiment.  I think we explain the plateau.  It
is just the crossover between heat conduction by propagating
sound-like modes at low T, strongly scattered by 2-level systems,
and heat conduction by non-propagating delocalized modes at
higher T.

P. B. Allen, X. Du, L. Mihaly, and L. Forro,
"Thermal Conductivity of Insulating (Y-doped) BSSCO and
Superconducting BSSCO: Failure of the Phonon Gas Model."
Phys. Rev. B 49, 9073-9 (1994).

We tried to publish this under the title "Do Phonons Exist?"
but this proved politically impossible.

R. M. Wentzcovitch, W. W. Schulz, and P. B. Allen,
"VO2: Peierls or Mott-Hubbard? A View from Band Theory."
Phys. Rev. Letters 72, 3389 (1994).

A real shakedown for Renata's nice "strain dynamics" code
which relaxes the size and shape of the unit cell along with
the atom coordinates.  Also a triumph for LDA.

P. B. Allen, H. Berger, O. Chauvet, L. Forro, T. Jarlborg,
A. Junod, B. Revaz, and G. Santi,
"Transport Properties, Thermodynamic Properties, and Electronic
Structure of SrRuO3."
Phys. Rev. B 53, 4393-8 (1996).

SrRuO3 is a metallic ferromagnet, with a uniquely large 4d-
derived moment.  LSD seems right on target, but the metal
seems unconventional by comparison with RuO2.
P. B. Allen,
``Boltzmann Theory and Resistivity of Metals,''
in  Quantum Theory of Real Materials,
edited by J. R. Chelikowsky and S. G. Louie
(Kluwer, Boston, 1996) Chapter 17 pp 219-250.

This is a review of the Bloch-Boltzmann theory of resistivity,
including a derivation of the Bloch-Gruneisen formula and a
critique of its accuracy and range of applicability.  Some
original results on the theory of the Boltzmann transport equation
are given.  The aim was to make the theory accessible especially
to band theorists who are sometimes reluctant to apply their
results to the analysis of electrical transport.

C. Leung, M. Weinert, P. B. Allen, and R. M. Wentzcovitch,
``First Principles Study of Titanium Oxides''
Phys. Rev. B. 54, 7857-7864 (1996).

Like many early transition elements, titanium has many oxidation
states and many thermodynamically stable oxides are formed.
This paper looks at several oxides (TiO, Ti2O3, TiO2) and
shows that LDA theory can account for the odd crystal structure
of TiO and for the relative chemical stability of these compounds.

J. Fabian and P. B. Allen,
``Anharmonic Decay of Vibrational States in Amorphous Silicon,''
Phys. Rev. Letters 77, 3839-3842 (1996).

Part of Jaroslav Fabian's thesis.
Orbach proposed that Dijkhuis and Scholten's experiment can only
be explained on the assumption that vibrational states are mostly
localized which inhibits thermalization.  We show that this would
NOT inhibit thermalization.  We calculate the thermalization rate
of the eigenvibrations of a realistic model.

P. B. Allen,
``Single Particle versus Collective Electronic Excitations,''
in  From Quantum Mechanics to Technology,
edited by Z. Petru, J. Przystawa, and K. Rapcewicz
(Springer, Berlin, 1996) pp. 125-141.

A pedagogical article about how electron-hole pairs and plasmons
are related to each other.  Two paradoxes are discussed and explained.

S. P. Lewis, P. B.Allen, and T. Sasaki,
"Band Structure and Transport Properties of CrO2"
Phys. Rev. B 55, 10253-60 (1997).

This is the first implementation of spin-dependent density-functional theory
for a compound using pseudopotentials and plane-waves.  We were not completely
confident this would succeed, but found rather easy agreement with previous calculations.
CrO2 is a "half-metallic" ferromagnet.  We predicted the frequency of the A1g Raman
mode and also the Drude plasma frequency.  These were both measured in 1999.
Iliev et al. agree perfectly with our A1g phonon prediction, while Singley et al. find
the Drude plasma frequency to be <3 eV.  Our prediction is 2 eV (and isotropic.)

P. B. Allen, V. N. Kostur, N. Takesue, and G. Shirane,
``Neutron Scattering Profile of Q>0 Phonons in BCS Superconductors.''
Phys. Rev. B 56, 5552-5558 (1997).

This theory does a nice job explaining experiments on the borocarbide
superconductors, which have the feature that some of the low energy
phonons have extremely large line-widths representing short lifetimes
for decay into electron-hole pairs.  This decay is suppressed in the
superconducting state, causing a dramatic change in lineshape.  Kee
and Varma (PRL 1997) have a simultaneous theory in which they claim
that nesting is necessary.  This is wrong.  However, it might be the
case that nesting does explain why the normal state decay rates are so large.

J. Fabian and P. B. Allen,
``Thermal Expansion and Gruneisen Parameters of Amorphous Silicon:
A Realistic Model Calculation,''
Phys. Rev. Letters, 79, 1885-88 (1997).

Another part of Jaroslav Fabian's thesis.
Thermal expansion of glasses is a challenging problem, and one of
those few aspects of glasses for which the term "universal" is not
always applied!  The large negative thermal expansion at low T
shows that something interesting is happening, related to the low
frequency vibrations.

P. B. Allen and V. N. Kostur,
``Polaron Defects in a Charge Density Wave: a Model for
Lightly Doped BaBiO3.''
Z. Phy. B 104, 605-612 (1997).

The Peierls insulating state is quite deformable; an excess
carrier easily perturbs the charge density wave, forming a
small polaron.  This paper makes a variational calculation and
compares it with an exact calculation for a finite size system
in 3 dimensions.

P. B. Allen and J. Kelner,
``Evolution of a Vibrational Wavepacket on a Disordered Chain,''
Am. J. Phys. 66, 497-506 (1998).

A computer experiment showing how a propagating wavepacket turns
into diffusive energy spreading and then ultimately becomes
Anderson localized, when the 1d medium is weakly disordered.

P. B. Allen and V. Perebeinos,
"Anti-Jahn-Teller Polaron in LaMnO3,"
Phys. Rev. B 60, 10747-53 (1999).

LaMnO3 has a ground state with a cooperative Jahn-Teller distortion
which doubles the unit cell.  The doubly-degenerate Mn3+ Eg orbital
is split by the distortion in a fashion which alternates from cell
to cell, causing the phenomenon of "orbital ordering."  Like the BaBiO3
Peierls insulator, this orbitally-ordered insulator is quite deformable.
An excess hole is easily self-localized in a state which we call an
"anti-Jahn-Teller polaron."  This paper gives a simple model for the
cooperative Jahn-Teller ground state.  The same model, with no additional
adjustment of parameters, describes also the polaron.  The model is solved
in the small U and the large U limits.  The large U limit is simpler and more
relevant to reality.
P. B. Allen and V. Perebeinos,
"Self-Trapped Exciton and Franck-Condon Spectra Predicted in LaMnO3,"
Phys. Rev. Letters 83, 4828-31 (1999).

Here we pursue further the same model discussed in the previous paper.  This
time we look for the lowest (charge-neutral) electronic excitation.  If atoms are
kept frozen in their Jahn-Teller-distorted ground state, then the least energy
excitation is 2D, the Jahn-Teller gap, about 2eV.  In the infinite U limit this excitation
is simply visualized as a 90 degree rotation of the Eg orbital, which is sometimes
called an "orbiton".  But when atoms are allowed to relax to their lowest energy state,
the excitation costs only half as much energy.  Thus the "orbiton" excitation has
the character of a "self-trapped exciton."

In molecular physics it is well known that excited electronic states generally have
different optimal atomic positions than the ground state does.  In such a case, the
optical transition from the ground state goes into any of a series of vibrational
excitations of the electronic excited state, the most intense transition being not to
the lowest vibrational state, but to the one closest geometrically to the ground
electronic state.  The series of optical transitions has a Gaussian envelope.  This
effect was first discussed by Franck (before modern quantum mechanics was
invented.  E. U. Condon put Franck's discussion into modern quantum-mechanical

Our paper makes several predictions about the spectrum of  LaMnO3 based on
this description and derived rigorously from our starting Hamiltonian.  We reinterpret
existing optical spectra, and think that our description does a better job than the
conventional band picture, especially in explaining why the optical spectra are not
disrupted by the loss of magnetic order at the Neel temperature, 140K.
V. Perebeinos and P. B. Allen,
"Franck-Condon-Broadened Angle-Resolved Photoemission Spectra Predicted in LaMnO3"
Phys. Rev. Letters 85, 5178 (2000).

Measuring the energy and momentum of the photoelectron is a nice probe of the spectrum
of the photohole.  In LaMnO3 the ground state of the hole is a small polaron, but the sudden
photohole created in the photoemission process has no lattice relaxation, and is a superposition
of ground-state polaronic hole plus multiple vibrational quanta.  Therefore the spectrum should
have Franck-Condon broadening.  This effect is seen in photoemission from molecules (see
for example a recent experiment on methane vapor, T. D. Thomas et al., J. Chem Phys. 109,
15 July, 1998.)  Sawatzky, Dessau, and maybe others have discussed this effect qualitatively
for photoemission from solids, but I believe that our paper gives the first quantitative prediction
of this effect.

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