arXiv subjects

Philip B. Allen

Publications and source records attributed to Philip B. Allen.

At least 19 recordsLinked to original sources

arXiv2026

Temperature dependence of the charge density from first principles: application to the (222) forbidden reflection in silicon

Forbidden reflections (FRs) in X-ray diffraction have inherently weak intensity and have long been studied, in particular in semiconductors like silicon. They serve as sensitive probes of symmetry breaking, local strain, impurities, and weak charge redistribution. Despite extensive experimental work, the theory of their temperature dependence has typically relied on simplified models. While atomic Debye-Waller factors work well on allowed reflections, their applicability to the valence charge between atoms, which determines the intensity of FRs such as Si (222), is questionable, and previous agreement between theory and experiment relied on ad-hoc Debye-Waller corrections. We compute the temperature-dependent valence charge density $\rho(\mathbf{r},T)$ of silicon from first principles, using two methods: (i) perturbation theory, and (ii) averaging over thermally distorted supercells in a non-perturbative approach. The perturbative expression for the charge density is far more demanding than that for electronic energies, since it depends on the wavefunctions themselves and requires an explicit sum over unoccupied bands. We use an acoustic sum rule to express the second derivatives of the potential in terms of first derivatives, making the expression tractable within existing frameworks. The (222) FR then follows directly from the Fourier transform of $\rho(\mathbf{r},T)$, with no ad-hoc factors. Both methods give similar results, in reasonable agreement with experiment, with thermal expansion noticeably affecting the temperature dependence. The charge density answers a question the measured intensities could not settle: how the valence charge actually redistributes with temperature. Relative to the rigid model, we find more charge in the bonds and less in the core regions, a redistribution that shows up in the intensity as a somewhat weaker temperature dependence of the (222) FR.

cond-mat.mtrl-sci↗

arXiv2025

Free Electron Theory for Thin Metal Films

Quantum free electrons, i.e. plane waves, with wavevector k, and occupancy constrained by the Pauli exclusion principle, are explained in all solid state physics texts. Although overly simplified, free-electron theory works surprisingly well for many properties of simple metals. For bulk materials, it is assumed that the sample is effectively infinite and that surfaces are irrelevant. Over the past 30 years, experiments that visualize surfaces and enable the study of 2-d materials have revolutionized solid state physics, stimulating new experiment, theory, and applications. Modified free electron models, adapted to films, have enabled modeling of electronic properties of films. This paper analyzes three such models: periodic boundary conditions, hard-wall boundary conditions, and soft-wall (SW) boundary conditions, in order of increasing realism. The SW case is illustrated for an aluminum film consisting of six atomic layers, comparing SW free-electron theory with a scanning tunneling spectroscopy experiment.

cond-mat.mes-hall↗

arXiv2022

Theory of thermal expansion: Quasi-harmonic approximation and corrections from quasiparticle renormalization

"Quasi-harmonic" (QH) theory should not be considered a low-order theory of anharmonic effects in crystals, but should be recognized as an important effect separate from "true" anharmonicity. The original and widely used meaning of QH theory is to put T=0 volume-dependent harmonic phonon energies omega_Q(V) into the non-interacting phonon free energy. This paper uses that meaning, but extends it to include the use of T=0 V-dependent single-particle electron energies epsilon_K(V). It is demonstrated that the "bare" quasiparticle (QP) energies omega_Q(V) and epsilon_K(V) correctly give the first-order term in the V-dependence of the Helmholtz free energy F(V,T). Therefore, they give the leading order result for thermal expansion alpha(T) and for the temperature-dependence of the bulk modulus B(T)-B_0. However, neglected interactions which shift and broaden omega_Q with T, also shift the free energy. In metals, the low T electron-phonon mass enhancement of states near the Fermi level causes a shift in free energy that is similar in size to the electronic QH term. Before T reaches the Debye temperature, the mass renormalization essentially disappears, and remaining electron-phonon shifts of free energy contribute only higher-order terms to thermal expansion. Similarly, anharmonic phonon-phonon interactions shift the free energy, but contribute to thermal expansion only in higher order. Explicit next order formulas are given for thermal expansion, which relate "true" anharmonic and similar free energy corrections to quasiparticle self-energy shifts. The text below, except for Sec. IX, was already published in Modern Physics Letters B, Vol. 34, No. 2 (2020) 2050025. Since then an important error was discovered. The error is corrected in Sec. IX, and will be published as an erratum in Modern Physics Letters B.

cond-mat.mtrl-sci↗

arXiv2022

Non-local thermal transport modeling using the thermal distributor

Thermal transport in a quasi-ballistic regime is determined not only by the local temperature $T(r)$, or its gradient $\nabla T(r)$, but also by temperature distribution at neighboring points. For an accurate description of non-local effects on thermal transport, we employ the thermal distributor, $Θ(r,r')$, which provides the temperature response of the system at point $r$ to the heat input at point $r'$. We determine the thermal distributors from the linearized Peierls-Boltzmann equation (LPBE) and the relaxation time approximation (RTA) of the Peierls-Boltzmann equation and employ them to describe thermal transport in quasi-ballistic graphene devices.

cond-mat.mes-hall↗

arXiv2022

Nonlocal Phonon Heat Transport Seen in 1-d Pulses

Phonons are the main heat carriers in semiconductor devices. In small devices, heat is not driven by a local temperature gradient, but by local points of heat input and removal. This complicates theoretical modeling. Study of the propagation of vibrational energy from an initial localized pulse provides insight into nonlocal phonon heat transport. We report simulations of pulse propagation in one dimension. The 1d case has tricky anomalies, but provides the simplest pictures of the evolution from initially ballistic toward longer time diffusive propagation. Our results show surprising details, such as diverse results from different definitions of atomistic local energy, and failure to exhibit pure diffusion at long times. Boltzmann phonon gas theory, including external energy insertion, is applied to this inherentlytime-dependent and nonlocal problem. The solution, using relaxation time approximation for impurity scattering, does not closely agree with the simulated results.

cond-mat.other↗

arXiv2021

Phonon Boltzmann equation non-local in space and time: the partial failure of the generalized Fourier law

The purpose of this note is to clarify the solution of the non-local Peierls Boltzmann equation found by Hua and Lindsay (Phys. Rev. B 102, 104310 (2020)). They used methods of Cepellotti and Marzari. The response function "thermal distributor" is discussed. The new, "non-Fourier" term $\vec{B}$ [$\vec{J}_{\rm th}=-κ\vec{\nabla}T +\vec{B}]$ that occurs in non-local situations, gives rise also to a new term in the thermal distributor.

cond-mat.other↗

arXiv2020

Accidental Degeneracy in k-space, Geometrical Phase, and the Perturbation of $π$ by Spin-orbit Interactions

Since closed lines of {\it accidental} electronic degeneracies were demonstrated to be possible, even frequent, by Herring in 1937, no further developments arose for eight decades. The earliest report of such a nodal loop in a real material -- aluminum -- is recounted and elaborated on. Nodal loop semimetals have become a focus of recent activity, with emphasis on other issues. Band degeneracies are, after all, the origin of topological phases in crystalline materials. Spin-orbit interaction lifts accidental band degeneracies, with the resulting spectrum being provided here. The geometric phase $γ(C)=\pmπ$ for circuits $C$ surrounding a line of such degeneracy cannot survive completely unchanged. The change depends on how the spin is fixed during adiabatic evolution. For spin fixed along the internal spin-orbit field, $γ(C)$ decreases to zero as the circuit collapses around the line of lifted degeneracy. For spin fixed along a perpendicular axis, the conical intersection persists and $γ(C)=\pmπ$ is unchanged.

cond-mat.mes-hall↗

arXiv2018

Resistivity of high pressure phosphorus phases

Simple cubic (sc) black phosphorus (denoted BP), stable at P>10GPa, seems an ordinary metal. It has electron-phonon-driven superconductivity with Tc 5-10 K. The A17 phase, stable at atmospheric pressure, has a narrow gap, becomes semimetallic at P=1 GPa, and has a smooth transition to topological metal behavior at P ~ 5 GPa. The A7 phase, stable for 5<P<10 GPa, is metallic, superconducting, and less conventional than the sc phase. Some insights are extracted from analysis of resistivity versus temperature at various pressures. A surprising order-of-magnitude disagreement between theory and experiment is discussed.

cond-mat.supr-con↗

arXiv2018

Temperature in a Peierls-Boltzmann Treatment of Nonlocal Phonon Heat Transport

In nonmagnetic insulators, phonons are the carriers of heat. If heat enters in a region and temperature is measured at a point within phonon mean free paths of the heated region, ballistic propagation causes a nonlocal relation between local temperature and heat insertion. This paper focusses on the solution of the exact Peierls-Boltzmann equation (PBE), the relaxation time approximation (RTA), and the definition of local temperature needed in both cases. The concept of a non-local "thermal susceptibility" (analogous to charge susceptibility) is defined. A formal solution is obtained for heating with a single Fourier component $P(\vec{r},t)=P_0 \exp(i\vec{k}\cdot\vec{r}-iωt)$, where $P$ is the local rate of heating). The results are illustrated by Debye model calculations in RTA for a three-dimensional periodic system where heat is added and removed with $P(\vec{r},t)=P(x)$ from isolated evenly spaced segments with period $L$ in $x$. The ratio $L/\ell_{\rm min}$ is varied from 6 to $\infty$, where $\ell_{\rm min}$ is the minimum mean free path. The Debye phonons are assumed to scatter anharmonically with mean free paths varying as $\ell_{\rm min}(q_D/q)^2$ where $q_D$ is the Debye wavevector. The results illustrate the expected local (diffusive) response for $\ell_{\rm min}\ll L$, and a diffusive to ballistic crossover as $\ell_{\rm min}$ increases toward the scale $L$. The results also illustrate the confusing problem of temperature definition. This confusion is not present in the exact treatment but is fundamental in RTA.

cond-mat.mes-hall↗

arXiv2018

Analysis of nonlocal phonon thermal conductivity simulations showing the ballistic to diffusive crossover

Simulations (e.g. Zhou et al., Phys. Rev. B 79, 115201 (2009)) show nonlocal effects of the ballistic/diffusive crossover. The local temperature has nonlinear spatial variation not contained in the local Fourier law $\vec{j}(\vec{r})=-κ\vec{\nabla}T(\vec{r})$. The heat current $\vec{j}(\vec{r})$ depends not just on the local temperature gradient $\vec{\nabla}T(\vec{r})$, but also on temperatures at points $\vec{r}^{ \ \prime}$ within phonon mean free paths, which can be micrometers long. This paper uses the Peierls-Boltzmann transport theory in non-local form to analyze the spatial variation $ΔT(\vec{r})$. The relaxation-time approximation (RTA) is used because full solution is very challenging. Improved methods of extrapolation to obtain the bulk thermal conductivity $κ$ are proposed. Callaway invented an approximate method of correcting RTA for the $\vec{q}$ (phonon wavevector or crystal momentum) conservation of N (normal as opposed to Umklapp) anharmonic collisions This method is generalized to the non-local case where $κ(\vec{k})$ depends on wavevector of the current $\vec{j}(\vec{k})$ and temperature gradient $i\vec{k}ΔT(\vec{k})$.

cond-mat.mtrl-sci↗

arXiv2017

Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to full first principles theory and Fröhlich polaron

The electron-phonon interaction causes thermal and zero-point motion shifts of electron quasiparticle (QP) energies $ε_k(T)$. Other consequences of interactions, visible in angle-resolved photoemission spectroscopy (ARPES) experiments, are broadening of QP peaks and appearance of sidebands, contained in the electron spectral function $A(k,ω)=-{\Im m}G_R(k,ω) /π$, where $G_R$ is the retarded Green's function. Electronic structure codes (e.g. using density-functional theory) are now available that compute the shifts and start to address broadening and sidebands. Here we consider MgO and LiF, and determine their nonadiabatic Migdal self energy. The spectral function obtained from the Dyson equation makes errors in the weight and energy of the QP peak and the position and weight of the phonon-induced sidebands. Only one phonon satellite appears, with an unphysically large energy difference (larger than the highest phonon energy) with respect to the QP peak. By contrast, the spectral function from a cumulant treatment of the same self energy is physically better, giving a quite accurate QP energy and several satellites approximately spaced by the LO phonon energy. In particular, the positions of the QP peak and first satellite agree closely with those found for the Fröhlich Hamiltonian by Mishchenko $\textit{et al.}$ (2000) using diagrammatic Monte Carlo. We provide a detailed comparison between the first-principles MgO and LiF results and those of the Fröhlich Hamiltonian. Such an analysis applies widely to materials with infra-red active phonons. We also compare the retarded and time-ordered cumulant treatments: they are equivalent for the Fröhlich Hamiltonian, and only slightly differ in first-principles electron-phonon results for wide-band gap materials.

cond-mat.mtrl-sci↗

arXiv2017

Low temperature-semiconductor band gap thermal shifts: T^4 shifts from ordinary acoustic and T^2 from piezoacoustic coupling

At low temperature T, the experimental gap of silicon decreases as E_g(T)=E_g(0)-AT^4. The main reason is electron-phonon renormalization. The physics behind the T^4-power law is more complex than has been realized. Renormalization by intraband scattering requires a careful non-adiabatic treatment in order to correctly include acoustic phonons and avoid divergences from piezoacoustic phonon interactions. The result is an unexpected low T term E_g(0)+A' T^p with positive coefficient A', and power p=4 for non-piezoelectric materials, and power p=2 for piezoelectric materials. The acoustic phonons in piezoelectric semiconductors generate a piezoelectric field, modifying the electron-phonon coupling. However, at higher T, when thermal acoustic phonons of energy hbar v_s q acquire energies comparable to the electronic intermediate state (higher than the band-edge state by hbar^2 q^2 /2m*), the low q and higher q intraband contributions to T^p rapidly cancel, giving little thermal effect. But there is an additional T-dependence from interband effects of acoustic phonons. This turns out to have power law T^4 for both non-piezoelectric and piezoelectric semiconductors. This term can have either sign, but usually reduces the size of gaps as T increases. It arises after cancellation of the T^2 terms that appear separately in Debye-Waller and Fan parts of the acoustic phonon interband renormalization. The cancellation occurs because of the acoustic sum rule.

cond-mat.mtrl-sci↗

arXiv2016

Phonon thermal conductivity by non-local non-equilibrium molecular dynamics

Non-equilibrium (NE) molecular dynamics (MD), or NEMD, gives a "direct" simulation of thermal conductivity kappa. Heat H(x) is added and subtracted in equal amounts at different places x. After steady state is achieved, the temperature T(x) is found by averaging over finite sections. Usually the aim is to extract a value of dT/dx from a place distant from sources and sinks of heat. This yields an effective kappa(L) for the thermal conductivity, L being the system size. The result is then studied as a function of L, to extract the bulk limit kappa. Here instead, our heat is H(x)~sin(qx), where q=2pi/L. This causes a steady-state temperature T_0 + Delta T sin(2pi x/L). A thermal conductivity kappa(q) is extracted, which is well converged at the chosen q (or L). Bulk conductivity kappa requires taking the q to 0 limit. The method is tested for liquid and crystalline argon. One advantage is reduced computational noise at a given total MD run time. Another advantage is that kappa(q) has a more physical meaning than kappa(L). It can be easily studied using Peierls-Boltzmann transport theory. New formulas for kappa(q) in simplified Debye-type models give new insight about extrapolation to q to 0 or 1/L to 0. In particular, it is shown that kappa(L$ is unlikely to behave as kappa -C/L, and much more likely to behave as kappa-C'/sqrt(L). Convergence problems encountered in computational cells with very large aspect ratios L(parallel)/L(perp) are also analyzed. Some details are contained in the "Supplemental Material" file.

cond-mat.mtrl-sci↗

arXiv2016

Influence of Fröhlich polaron coupling on renormalized electron bands in polar semiconductors. Results for zincblende GaN

\ni We develop a simple method to study the zero-point and thermally renormalized electron energy $\varepsilon_{\mathbf{k}n}(T)$ for $\mathbf{k}n$ the conduction band minimum or valence maximum in polar semiconductors. We use the adiabatic approximation, including an imaginary broadening parameter $iδ$ to supress noise in the density-functional integrations. Fröhlich polaron methods provide analytic expressions for the contribution of the problematic optical phonon mode. We use this to correct the renormalization obtained from the adiabatic approximation. Test calculations are done for zincblende GaN for an 18x18x18 integration grid. The Fröhlich correction is of order -0.02 eV for the zero-point energy shift of the conduction band minimum, and +0.03 eV for the valence band maximum; the correction to renormalization of the 3.28 eV gap is -0.05 eV, a significant fraction of the total zero point renormalization of -0.15 eV.

cond-mat.mtrl-sci↗

arXiv2016

First-principles study of pyroelectricity in GaN and ZnO

First-principles calculations are made for the primary pyroelectric coefficients of wurtzite GaN and ZnO. The pyroelectricity is attributed to the quasiharmonic thermal shifts of internal strains (internal displacements of cations and anions carrying their Born effective charges). The primary (zero-external-strain) pyroelectricity dominates at low temperatures, while the secondary pyroelectricity (the correction from external thermal strains) becomes comparable with the primary pyroelectricity at high temperatures. Contributions from the acoustic and the optical phonon modes to the primary pyroelectric coefficient are only moderately well described by the corresponding Debye function and Einstein function respectively.

cond-mat.mtrl-sci↗

arXiv2015

Special Quasi-ordered Structures: role of short-range order in the semiconductor alloy (GaN)$_{1-x}$(ZnO)$_x$

This paper studies short-range order (SRO) in the semiconductor alloy (GaN)$_{1-x}$(ZnO)$_x$. Monte Carlo simulations performed on a density functional theory (DFT)-based cluster expansion model show that the heterovalent alloys exhibit strong SRO because of the energetic preference for the valence-matched nearest-neighbor Ga-N and Zn-O pairs. To represent the SRO-related structural correlations, we introduce the concept of Special Quasi-ordered Structure (SQoS). Subsequent DFT calculations reveal dramatic influence of SRO on the atomic, electronic and vibrational properties of the (GaN)$_{1-x}$(ZnO)$_x$ alloy. Due to the enhanced statistical presence of the energetically unfavored Zn-N bonds with the strong Zn3$d$-N2$p$ repulsion, the disordered alloys exhibit much larger lattice bowing and band-gap reduction than those of the short-range ordered alloys. Inclusion of lattice vibrations stabilizes the disordered alloy.

cond-mat.mtrl-sci↗

arXiv2015

Electronic and Nuclear Quantum Effects on the Ice XI/Ice Ih Phase Transition

We study the isotope effect on the temperature of the proton order/disorder phase transition between ice XI and ice Ih, using the quasiharmonic approximation combined with \textit{ab initio} density functional theory calculations. We show that this method is accurate enough to obtain a phase transition temperature difference between light ice (H$_2$O) and heavy ice (D$_2$O) of 6 K as compared to the experimental value of 4 K. More importantly, we are able to explain the origin of the isotope effect on the much debated large temperature difference observed in the phase transition. The source of the difference is directly linked to the physics behind the anomalous isotope effect on the volume of hexagonal ice that was recently explained in [Phys. Rev. Lett. 108, 193003 (2012)]. These results indicate that the same physics might be behind the isotope effects in transition temperatures between other ice phases.

cond-mat.mtrl-sci↗

arXiv2015

Electron Self-Energy and Generalized Drude Formula for Infrared Conductivity of Metals

Goetze and Woelfle (GW) wrote the conductivity in terms of a memory function M as (ine2/m)/(omega+M(omega)), where M=i/tau in the Drude limit. The analytic properties of -M are the same as those of the self-energy of a retarded Green's function. In the approximate treatment of GW, -M closely resembles a self-energy, with differences, e.g., the imaginary part is twice too large. The correct relation between -M and the self-energy is known for the electron-phonon case and is conjectured to be similar for other perturbations. When vertex corrections are ignored there is a known relation. A derivation using Matsubara temperature Green's functions is given.

cond-mat.other↗