------------------------------------------------------------

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

Metals."

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

Interactions."

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

Transport."

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,

"VO_{2}: 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 SrRuO_{3}."

Phys. Rev. B **53**, 4393-8 (1996).

SrRuO_{3} is a metallic ferromagnet,
with a uniquely large 4d-

derived moment. LSD seems
right on target, but the metal

seems unconventional by comparison
with RuO_{2}.

------------------------------------------------------------

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, Ti_{2}O_{3}, TiO_{2}) 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 CrO_{2}"

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.

CrO_{2} is a "half-metallic"
ferromagnet. We predicted the frequency of the A_{1g} Raman

mode and also the Drude plasma frequency.
These were both measured in 1999.

Iliev et al. agree perfectly with
our A_{1g} 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 BaBiO_{3}.''

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 LaMnO_{3},"

Phys. Rev. B **60**, 10747-53
(1999).

LaMnO_{3} has a ground state
with a cooperative Jahn-Teller distortion

which doubles the unit cell.
The doubly-degenerate Mn^{3+} E_{g} orbital

is split by the distortion in a
fashion which alternates from cell

to cell, causing the phenomenon
of "orbital ordering." Like the BaBiO_{3}

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 LaMnO_{3},"

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 E_{g
}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

language.

Our paper makes several predictions about the spectrum of LaMnO_{3
}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 LaMnO_{3
}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.

*Return to Philip
B. Allen's home page.*