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Gerald D. Mahan

Bio: Gerald D. Mahan is an academic researcher from Pennsylvania State University. The author has contributed to research in topics: Phonon & Seebeck coefficient. The author has an hindex of 64, co-authored 306 publications receiving 24089 citations. Previous affiliations of Gerald D. Mahan include Massachusetts Institute of Technology & University of California, Berkeley.


Papers
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Book
01 Jan 1981
TL;DR: In this article, the authors present a model for the second quantization of a particle and show that it can be used to construct a pair distribution function with respect to a pair of spinless fermions.
Abstract: 1. Introductory Material.- 1.1. Harmonic Oscillators and Phonons.- 1.2. Second Quantization for Particles.- 1.3. Electron - Phonon Interactions.- A. Interaction Hamiltonian.- B. Localized Electron.- C. Deformation Potential.- D. Piezoelectric Interaction.- E. Polar Coupling.- 1.4. Spin Hamiltonians.- A. Homogeneous Spin Systems.- B. Impurity Spin Models.- 1.5. Photons.- A. Gauges.- B. Lagrangian.- C. Hamiltonian.- 1.6. Pair Distribution Function.- Problems.- 2. Green's Functions at Zero Temperature.- 2.1. Interaction Representation.- A. Schrodinger.- B. Heisenberg.- C. Interaction.- 2.2. S Matrix.- 2.3. Green's Functions.- 2.4. Wick's Theorem.- 2.5. Feynman Diagrams.- 2.6. Vacuum Polarization Graphs.- 2.7. Dyson's Equation.- 2.8. Rules for Constructing Diagrams.- 2.9. Time-Loop S Matrix.- A. Six Green's Functions.- B. Dyson's Equation.- 2.10. Photon Green's Functions.- Problems.- 3. Green's Functions at Finite Temperatures.- 3.1. Introduction.- 3.2. Matsubara Green's Functions.- 3.3. Retarded and Advanced Green's Functions.- 3.4. Dyson's Equation.- 3.5. Frequency Summations.- 3.6. Linked Cluster Expansions.- A. Thermodynamic Potential.- B. Green's Functions.- 3.7. Real Time Green's Functions.- Wigner Distribution Function.- 3.8. Kubo Formula for Electrical Conductivity.- A. Transverse Fields, Zero Temperature.- B. Finite Temperatures.- C. Zero Frequency.- D. Photon Self-Energy.- 3.9. Other Kubo Formulas.- A. Pauli Paramagnetic Susceptibility.- B. Thermal Currents and Onsager Relations.- C. Correlation Functions.- Problems.- 4. Exactly Solvable Models.- 4.1. Potential Scattering.- A. Reaction Matrix.- B. T Matrix.- C. Friedel's Theorem.- D. Phase Shifts.- E. Impurity Scattering.- F. Ground State Energy.- 4.2. Localized State in the Continuum.- 4.3. Independent Boson Models.- A. Solution by Canonical Transformation.- B. Feynman Disentangling of Operators.- C. Einstein Model.- D. Optical Absorption and Emission.- E. Sudden Switching.- F. Linked Cluster Expansion.- 4.4. Tomonaga Model.- A. Tomonaga Model.- B. Spin Waves.- C. Luttinger Model.- D. Single-Particle Properties.- E. Interacting System of Spinless Fermions.- F. Electron Exchange.- 4.5. Polaritons.- A. Semiclassical Discussion.- B. Phonon-Photon Coupling.- C. Exciton-Photon Coupling.- Problems.- 5. Electron Gas.- 5.1. Exchange and Correlation.- A. Kinetic Energy.- B. Direct Coulomb.- C. Exchange.- D. Seitz' Theorem.- E. ?(2a).- F. ?(2b).- G. ?(2c).- H. High-Density Limit.- I. Pair Distribution Function.- 5.2. Wigner Lattice and Metallic Hydrogen.- Metallic Hydrogen.- 5.3. Cohesive Energy of Metals.- 5.4. Linear Screening.- 5.5. Model Dielectric Functions.- A. Thomas-Fermi.- B. Lindhard, or RPA.- C. Hubbard.- D. Singwi-Sjolander.- 5.6. Properties of the Electron Gas.- A. Pair Distribution Function.- B. Screening Charge.- C. Correlation Energies.- D. Compressibility.- 5.7. Sum Rules.- 5.8. One-Electron Properties.- A. Renormalization Constant ZF.- B. Effective Mass.- C. Pauli Paramagnetic Susceptibility.- D. Mean Free Path.- Problems.- 6. Electron-Phonon Interaction.- 6.1 Frohlich Hamiltonian.- A. Brillouin-Wigner Perturbation Theory.- B. Rayleigh-Schrodinger Perturbation Theory.- C. Strong Coupling Theory.- D. Linked Cluster Theory.- 6.2 Small Polaron Theory.- A. Large Polarons.- B. Small Polarons.- C. Diagonal Transitions.- D. Nondiagonal Transitions.- E. Dispersive Phonons.- F. Einstein Model.- G. Kubo Formula.- 6.3 Heavily Doped Semiconductors.- A. Screened Interaction.- B. Experimental Verifications.- C. Electron Self-Energies.- 6.4 Metals.- A. Phonons in Metals.- B. Electron Self-Energies.- Problems.- 7. dc Conductivities.- 7.1. Electron Scattering by Impurities.- A. Boltzmann Equation.- B. Kubo Formula: Approximate Solution.- C. Kubo Formula: Rigorous Solution.- D. Ward Identities.- 7.2. Mobility of Frohlich Polarons.- A. Single-Particle Properties.- B. ??1 Term in the Mobility.- 7.3. Electron-Phonon Interactions in Metals.- A. Force-Force Correlation Function.- B. Kubo Formula.- C. Mass Enhancement.- D. Thermoelectric Power.- 7.4. Quantum Boltzmann Equation.- A. Derivation of the Quantum Boltzmann Equation.- B. Gradient Expansion.- C. Electron Scattering by Impurities.- D. T2 Contribution to the Electrical Resistivity.- Problems.- 8. Optical Properties of Solids.- 8.1. Nearly Free-Electron System.- A. General Properties.- B. Force-Force Correlation Functions.- C. Frohlich Polarons.- D. Interband Transitions.- E. Phonons.- 8.2. Wannier Excitons.- A. The Model.- B. Solution by Green's Functions.- C. Core-Level Spectra.- 8.3. X-Ray Spectra in Metals.- A. Physical Model.- B. Edge Singularities.- C. Orthogonality Catastrophe.- D. MND Theory.- E. XPS Spectra.- Problems.- 9. Superconductivity.- 9.1. Cooper Instability.- 9.2. BCS Theory.- 9.3. Electron Tunneling.- A. Tunneling Hamiltonian.- B. Normal Metals.- C. Normal-Superconductor.- D. Two Superconductors.- E. Josephson Tunneling.- 9.4. Infrared Absorption.- 9.5. Acoustic Attenuation.- 9.6. Excitons in Superconductors.- 9.7. Strong Coupling Theory.- Problems.- 10. Liquid Helium.- 10.1. Pairing Theory.- A. Hartree and Exchange.- B. Bogoliubov Theory of 4He.- 10.2. 4He: Ground State Properties.- A. Off-Diagonal Long-Range Order.- B. Correlated Basis Functions.- C. Experiments on nk.- 10.3. 4He: Excitation Spectrum.- A. Bijl-Feynman Theory.- B. Improved Excitation Spectra.- C. Superfluidity.- 10.4. 3He: Normal Liquid.- A. Fermi Liquid Theory.- B. Experiments and Microscopic Theories.- C. Interaction between Quasiparticles: Excitations.- D. Quasiparticle Transport.- 10.5. Superfluid 3He.- A. Triplet Pairing.- B. Equal Spin Pairing.- Problems.- 11. Spin Fluctuations.- 11.1. Kondo Model.- A. High-Temperature Scattering.- B. Low-Temperature State.- C. Kondo Temperature.- 11.2. Anderson Model.- A. Collective States.- B. Green's Functions.- C. Spectroscopies.- Problems.- References.- Author Index.

5,888 citations

Journal ArticleDOI
TL;DR: A review of the literature on thermal transport in nanoscale devices can be found in this article, where the authors highlight the recent developments in experiment, theory and computation that have occurred in the past ten years and summarizes the present status of the field.
Abstract: Rapid progress in the synthesis and processing of materials with structure on nanometer length scales has created a demand for greater scientific understanding of thermal transport in nanoscale devices, individual nanostructures, and nanostructured materials. This review emphasizes developments in experiment, theory, and computation that have occurred in the past ten years and summarizes the present status of the field. Interfaces between materials become increasingly important on small length scales. The thermal conductance of many solid–solid interfaces have been studied experimentally but the range of observed interface properties is much smaller than predicted by simple theory. Classical molecular dynamics simulations are emerging as a powerful tool for calculations of thermal conductance and phonon scattering, and may provide for a lively interplay of experiment and theory in the near term. Fundamental issues remain concerning the correct definitions of temperature in nonequilibrium nanoscale systems. Modern Si microelectronics are now firmly in the nanoscale regime—experiments have demonstrated that the close proximity of interfaces and the extremely small volume of heat dissipation strongly modifies thermal transport, thereby aggravating problems of thermal management. Microelectronic devices are too large to yield to atomic-level simulation in the foreseeable future and, therefore, calculations of thermal transport must rely on solutions of the Boltzmann transport equation; microscopic phonon scattering rates needed for predictive models are, even for Si, poorly known. Low-dimensional nanostructures, such as carbon nanotubes, are predicted to have novel transport properties; the first quantitative experiments of the thermal conductivity of nanotubes have recently been achieved using microfabricated measurement systems. Nanoscale porosity decreases the permittivity of amorphous dielectrics but porosity also strongly decreases the thermal conductivity. The promise of improved thermoelectric materials and problems of thermal management of optoelectronic devices have stimulated extensive studies of semiconductor superlattices; agreement between experiment and theory is generally poor. Advances in measurement methods, e.g., the 3ω method, time-domain thermoreflectance, sources of coherent phonons, microfabricated test structures, and the scanning thermal microscope, are enabling new capabilities for nanoscale thermal metrology.

2,933 citations

Journal ArticleDOI
TL;DR: A delta-shaped transport distribution is found to maximize the thermoelectric properties, indicating that a narrow distribution of the energy of the electrons participating in the transport process is needed for maximum thermoelectedric efficiency.
Abstract: What electronic structure provides the largest figure of merit for thermoelectric materials? To answer that question, we write the electrical conductivity, thermopower, and thermal conductivity as integrals of a single function, the transport distribution. Then we derive the mathematical function for the transport distribution, which gives the largest figure of merit. A delta-shaped transport distribution is found to maximize the thermoelectric properties. This result indicates that a narrow distribution of the energy of the electrons participating in the transport process is needed for maximum thermoelectric efficiency. Some possible realizations of this idea are discussed.

1,441 citations

Journal ArticleDOI
TL;DR: In this article, a review of thermal transport at the nanoscale is presented, emphasizing developments in experiment, theory, and computation in the past ten years and summarizes the present status of the field.
Abstract: A diverse spectrum of technology drivers such as improved thermal barriers, higher efficiency thermoelectric energy conversion, phase-change memory, heat-assisted magnetic recording, thermal management of nanoscale electronics, and nanoparticles for thermal medical therapies are motivating studies of the applied physics of thermal transport at the nanoscale. This review emphasizes developments in experiment, theory, and computation in the past ten years and summarizes the present status of the field. Interfaces become increasingly important on small length scales. Research during the past decade has extended studies of interfaces between simple metals and inorganic crystals to interfaces with molecular materials and liquids with systematic control of interface chemistry and physics. At separations on the order of ∼1 nm, the science of radiative transport through nanoscale gaps overlaps with thermal conduction by the coupling of electronic and vibrational excitations across weakly bonded or rough interface...

1,307 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that passing an electric current through the junction in one direction caused the water to freeze, and reversing the current caused the ice to quickly melt; thus thermoelectric refrigeration was demonstrated.
Abstract: Thermoelectrics is an old field. In 1823, Thomas Seebeck discovered that a voltage drop appears across a sample that has a temperature gradient. This phenomenon provided the basis for thermocouples used for measuring temperature and for thermoelectric power generators. In 1838, Heinrich Lenz placed a drop of water on the junction of metal wires made of bismuth and antimony. Passing an electric current through the junction in one direction caused the water to freeze, and reversing the current caused the ice to quickly melt; thus thermoelectric refrigeration was demonstrated (figure 1).

755 citations


Cited by
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01 May 1993
TL;DR: Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems.
Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

29,323 citations

Journal ArticleDOI
TL;DR: In this paper, the self-interaction correction (SIC) of any density functional for the ground-state energy is discussed. But the exact density functional is strictly selfinteraction-free (i.e., orbitals demonstrably do not selfinteract), but many approximations to it, including the local spin-density (LSD) approximation for exchange and correlation, are not.
Abstract: The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

16,027 citations

Journal ArticleDOI
TL;DR: In this paper, the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method, is reviewed.
Abstract: This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

6,917 citations

Journal ArticleDOI
TL;DR: In this article, the authors focus on the origin of the D and G peaks and the second order of D peak and show that the G and 2 D Raman peaks change in shape, position and relative intensity with number of graphene layers.

6,496 citations

Journal ArticleDOI
11 Oct 2001-Nature
TL;DR: Th thin-film thermoelectric materials are reported that demonstrate a significant enhancement in ZT at 300 K, compared to state-of-the-art bulk Bi2Te3 alloys, and the combination of performance, power density and speed achieved in these materials will lead to diverse technological applications.
Abstract: Thermoelectric materials are of interest for applications as heat pumps and power generators. The performance of thermoelectric devices is quantified by a figure of merit, ZT, where Z is a measure of a material's thermoelectric properties and T is the absolute temperature. A material with a figure of merit of around unity was first reported over four decades ago, but since then-despite investigation of various approaches-there has been only modest progress in finding materials with enhanced ZT values at room temperature. Here we report thin-film thermoelectric materials that demonstrate a significant enhancement in ZT at 300 K, compared to state-of-the-art bulk Bi2Te3 alloys. This amounts to a maximum observed factor of approximately 2.4 for our p-type Bi2Te3/Sb2Te3 superlattice devices. The enhancement is achieved by controlling the transport of phonons and electrons in the superlattices. Preliminary devices exhibit significant cooling (32 K at around room temperature) and the potential to pump a heat flux of up to 700 W cm-2; the localized cooling and heating occurs some 23,000 times faster than in bulk devices. We anticipate that the combination of performance, power density and speed achieved in these materials will lead to diverse technological applications: for example, in thermochemistry-on-a-chip, DNA microarrays, fibre-optic switches and microelectrothermal systems.

4,921 citations