------------------------------------------------------------
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,
"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
language.
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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