... Basis states may be chosen for the OPSP eigenspace in analogy with sinkx and sinky; these eig... more ... Basis states may be chosen for the OPSP eigenspace in analogy with sinkx and sinky; these eigenstates are symmetric under simultaneous interchange of momentum and frequency labels (k---k+Hl,ac)n-(Aw), but are complex conju-gated ... 9. See also VL Berezinskii, Pis'ma Zh. ...
We discuss the form of the infrared conductivity and reflectivity in strong-coupling superconduct... more We discuss the form of the infrared conductivity and reflectivity in strong-coupling superconductors with a finite mean free path. We restrict attention to the local limit, in which the London penetration depth is much larger than the coherence length. We further assume that the fluctua- tions responsible for electronic pairing may be treated within a conventional Eliashberg approxima- tion. The conductivity typically exhibits two onsets: one at 250 and another at 260+~0, with coo a typical fluctuation energy. The strength of the latter onset relative to the one at 250 increases as the ratio of the mean free path to the coherence length increases, and in an extremely clean system (250&)~) becomes the dominant feature in both the conductivity and reflectivity. Infrared reflectivity measurements, which probe the particle-hole excitation spectrum of a solid, have for many years provided an effective means for studying su- perconductivity. In the superconducting state, finite- frequency absorption onsets at a frequency co=25(T), where b, (T) is the temperature-dependent energy gap. For frequencies below 25, the reflectivity is unity. In dir- ty inetals (i.e. , systems with a short mean free path), the reflectivity drops sharply above 2b, in a manner first calculated by Mattis and Bardeen' and by Nam. Reliable measurements of the gap are of particular in- terest for the new high-temperature oxide superconductors where the nature of the pairing mechanism and the strength of the coupling are in question. While a number of experimental groups have now obtained data in sub- stantial agreement, " controversies remain on the inter- pretation of the data and the possible extraction of an en- ergy gap. We briefly summarize the experimental situa- tion below: for the a bplane of Y-Ba2Cu307 (fully oxygenated), infrared response showing a feature at an unusually large energy scale (700 K -8 T, ) is seen in the superconducting state. More recent data confirm this
simulations are used to investigate the competition between superconducting and Peierlscharge-den... more simulations are used to investigate the competition between superconducting and Peierlscharge-density-wave (CDW) correlations in a two-dimensional electron-phonon system. The dependence of these correlations on the band filling (n), phonon frequency too, and electronphonon coupling g is examined. The Peierls-CDW correlations are favored as (n) moves towards half-filling, coo decreases, and g increases. When the Peierls-CDW correlations are weak, the Monte Carlo results for the superconducting correlations are found to be in excellent agreement with the results obtained using the well-known Eliashberg approximation.
Finite-temperature properties of the infinite-U Anderson model for rare-earth alloys are calculat... more Finite-temperature properties of the infinite-U Anderson model for rare-earth alloys are calculated within a unified approach. The impurity-electron density of states and magnetic moment spectrum provide a natural framework for describing both static and dynamic properties. The density of states and moment spectrum exhibit low-energy "Kondo resonances" with approximate single-parameter scaling, which persists for impurity valences in the range 1.0 -0.7. The position of the resonance in the zero-temperature density of states, To, sets the scale for all low-temperature properties. Results are reported for the impurity valence, resistivity, thermopower, thermal conductivity, magnetic sus- ceptibility, specific heat, photoemission and inverse-photoemission spectra, and neutron scattering linewidth. The effect of spin-orbit interactions is incorporated in the theory. The calculation is a di- agrammatic approximation motivated by the simplifying concept of large angular momentum degen- eracy (N). The approximate solution is thermodynamically consistent and satisfies all pertinent sum rules. Static properties (magnetic susceptibility and specific heat) are in good agreement with exact results of the Bethe ansatz. Experimental results on both dilute and concentrated Ce alloys are de- scribed quantitatively with use of a one-parameter (To) theory. SELF-CONSISTENT LARGE-X EXPANSION FOR NORMAL-. . . 2037 Sec. II, we attempt to place the present work in context by briefly reviewing previous approaches to the Kondo effect and discussing the basis for the large-degeneracy expansion. In Sec. III, we present an overview of our re- sults, stressing the simplifying features of the physics. Calculational details are discussed at length in Secs. IV and V. In Sec. VI, we compare our results for various properties with the available experiments. Finally, we dis- cuss future directions for this work and summarize our findings in Sec. VII. 300 280 0 O 260 Ct O II. REVIEW Interest in dilute magnetic alloys may be traced back to the earliest days of metals physics, when a low- temperature resistivity minimum was observed in noble metal samples containing small amounts of transition metal impurities' (see Fig. ). Such a resistivity minimum cannot be understood in terms of conventional phonon and nonmagnetic impurity scattering. Experimental interest in transition-metal alloys increased in the late 1950s and early 1960s, but no successful theory was advanced to account for their anomalous behavior. In 1964, Kondo demonstrated that the source of the resistivi- ty minimum was magnetic impurity scattering. While the phonon contribution to the resistivity decreases with temperature, the magnetic contribution increases. In Kondo's perturbative calculation, the resistivity actually diverges logarithmically for T~O. Kondo investigated the so-called antiferromagnetic s-d exchange Hamiltonian, H= g Eknk -2JS.s(0) . k, o (2.1) Here, J is a negative exchange constant, S is the impurity spin and s(0) is the conduction-electron spin density at the impurity. This Hamiltonian is now conventionally known as the "Kondo Hamiltonian. " An alternate model for magnetic alloys was developed in 1961 by Anderson. " The simplest version of the An- derson Hamiltonian may be written ~A ~band +Himp +IImix Hband = g ek n ka k, o H; p --Eden +U"" (2.2) H;"=Vg(ct d +H. c. ) . k, o. The three components of the Hamiltonian describe con- duction electrons, impurity electrons and a hybridization, or mixing interaction, between the two. Creation opera- tors are denoted c|, (conduction) and d (impurity), with n k -c k ck and n = d d . The key features of the model are (a) strong Coulomb correlation between the lo- calized electrons (U) 0) and (b) hybridization between lo- calized and delocalized electrons (V). A measure of the strength of hybirdization is the "hybridization width"
ABSTRACT By introducing a rotationally invariant Stratonovich-Hubbard (S-H) field we studied the ... more ABSTRACT By introducing a rotationally invariant Stratonovich-Hubbard (S-H) field we studied the doped Mott insulator phase of the two-dimension Hubbard model for U/t similar to 4-8. The static spin is decoupled by the S-H field and the static charge interaction is then treated by Hartree-Fock approximation. We sample random spin configurations by Monte Carlo simulation with the Metropolis updating algorithm. The Mott-Hubbard gap and static susceptibilities are studied near the half-filling at low temperature.
We describe an iterative technique for solution of the de Dominicis-Martin parquet equations for ... more We describe an iterative technique for solution of the de Dominicis-Martin parquet equations for lattice electrons and state the relationship of this approach to conserving extensions of Hartree-Fock theory. We propose a physically motivated and computationally feasible pseudopotential approximation, which allows the solution of the parquet equations for the two-dimensional Hubbard model. We present calculations of static and dynamic Hubbard-model correlation functions based on the pseudopotential parquet and a simpler conserving approximation. For a wide parameter range the pseudopotential parquet results are in nearly quantitative agreement with finite-lattice quantum Monte Carlo results.
The fluctuation exchange, or FLEX, approximation for interacting electrons is applied to study in... more The fluctuation exchange, or FLEX, approximation for interacting electrons is applied to study instabilities in the standard three-band model for CuO2 layers in the high-temperature superconductors. Both intra-orbital and near-neigbor Coulomb interactions are retained. The filling dependence of the d x 2 -y 2 transition temperature is studied in both the "hole-doped" and "electrondoped" regimes using parameters derived from constrained-occupancy density-functional theory for La2CuO4. The agreement with experiment on the overdoped hole side of the phase diagram is remarkably good, i.e., transitions emerge in the 40 K range with no free parameters. In addition the importance of the "orbital antiferromagnetic," or flux phase, charge density channel is emphasized for an understanding of the underdoped regime.
The phase boundary between normal and superconducting phases of the negative-U Hubbard model is o... more The phase boundary between normal and superconducting phases of the negative-U Hubbard model is obtained within a self-consistent weak-coupling approach known as the ``pseudopotential parquet'' approximation. The shortcomings of simpler self-consistent approaches, including the Hartree-Fock and fluctuation-exchange approximations, are outlined. For intermediate values of U, pseudopotential parquet predicts (i) a maximum in the superconducting transition temperature Tc at an electron filling of approximately 0.92; and (ii) a sharp decrease in Tc for values of closer to 1. The scale of transition temperatures is consistent with results from quantum simulations.
... The Cu02 Hamiltonian for holes takes the form p(Nd+—N~)= t d g — (d;,p&, +H.c.) (... more ... The Cu02 Hamiltonian for holes takes the form p(Nd+—N~)= t d g — (d;,p&, +H.c.) (il )s — pgn;, +(e — p) gn&, ... Finally, at points in our discussion we refer to results for the one-band Hubbard model pN= —t g (c— ;,c,+H.c.) — pg n;+ U g n;&n;& . I I + Ud g n;tn;), ...
The observed depressions of the superconducting transition temperature caused by 3d magnetic impu... more The observed depressions of the superconducting transition temperature caused by 3d magnetic impurities are compared with the maximum possible value given by theory. Several discrepancies are found, but they might be completely removed by including in the theory the effect of orbital degeneracy.
When superconductivity results from the exchange of electronic excitations (spin or charge fluctu... more When superconductivity results from the exchange of electronic excitations (spin or charge fluctuations), the development of a gap is expected to modify the pairing potential below Tc. One aspect of this feedback phenomenon, pair weakening, is investigated within a modified BCS treatment of d-wave superconductivity in the Hubbard model. It is argued that pair weakening and pair breaking (inelastic scattering)
Page 1. Review of techniques in the large-N expansion for dilute magnetic alloys ... 925 926 927 ... more Page 1. Review of techniques in the large-N expansion for dilute magnetic alloys ... 925 926 927 927 930 933 937 I. OYERVl EW A. introductory remarks In this paper we review a new approach, the large-degeneracy expansion, for investigating models of dilute magnetic alloys. ...
... REVIEW LETTERS Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salp... more ... REVIEW LETTERS Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard Model NE Bickers (a) Institute for Theoretical Physics, University of California at Santa Barbara, Santa Barbara ...
The one-band extended Hubbard model in two dimensions near band-filling 1 2 is solved in the fluc... more The one-band extended Hubbard model in two dimensions near band-filling 1 2 is solved in the fluctuation exchange approximation, including the long-range (1/r) part of the Coulomb interaction, up to 4th neighbor distance. Our results suggest that d x 2 -y 2 pairing in the Hubbard model is robust against the inclusion of long-range Coulomb interactions with moderate 1st neighbor repulsion strength V1. d x 2 -y 2 pairing is suppressed only at large V1 ( > ∼ 0.25U -0.4U ), due to incipient charge density wave instabilities.
... Basis states may be chosen for the OPSP eigenspace in analogy with sinkx and sinky; these eig... more ... Basis states may be chosen for the OPSP eigenspace in analogy with sinkx and sinky; these eigenstates are symmetric under simultaneous interchange of momentum and frequency labels (k---k+Hl,ac)n-(Aw), but are complex conju-gated ... 9. See also VL Berezinskii, Pis'ma Zh. ...
We discuss the form of the infrared conductivity and reflectivity in strong-coupling superconduct... more We discuss the form of the infrared conductivity and reflectivity in strong-coupling superconductors with a finite mean free path. We restrict attention to the local limit, in which the London penetration depth is much larger than the coherence length. We further assume that the fluctua- tions responsible for electronic pairing may be treated within a conventional Eliashberg approxima- tion. The conductivity typically exhibits two onsets: one at 250 and another at 260+~0, with coo a typical fluctuation energy. The strength of the latter onset relative to the one at 250 increases as the ratio of the mean free path to the coherence length increases, and in an extremely clean system (250&)~) becomes the dominant feature in both the conductivity and reflectivity. Infrared reflectivity measurements, which probe the particle-hole excitation spectrum of a solid, have for many years provided an effective means for studying su- perconductivity. In the superconducting state, finite- frequency absorption onsets at a frequency co=25(T), where b, (T) is the temperature-dependent energy gap. For frequencies below 25, the reflectivity is unity. In dir- ty inetals (i.e. , systems with a short mean free path), the reflectivity drops sharply above 2b, in a manner first calculated by Mattis and Bardeen' and by Nam. Reliable measurements of the gap are of particular in- terest for the new high-temperature oxide superconductors where the nature of the pairing mechanism and the strength of the coupling are in question. While a number of experimental groups have now obtained data in sub- stantial agreement, " controversies remain on the inter- pretation of the data and the possible extraction of an en- ergy gap. We briefly summarize the experimental situa- tion below: for the a bplane of Y-Ba2Cu307 (fully oxygenated), infrared response showing a feature at an unusually large energy scale (700 K -8 T, ) is seen in the superconducting state. More recent data confirm this
simulations are used to investigate the competition between superconducting and Peierlscharge-den... more simulations are used to investigate the competition between superconducting and Peierlscharge-density-wave (CDW) correlations in a two-dimensional electron-phonon system. The dependence of these correlations on the band filling (n), phonon frequency too, and electronphonon coupling g is examined. The Peierls-CDW correlations are favored as (n) moves towards half-filling, coo decreases, and g increases. When the Peierls-CDW correlations are weak, the Monte Carlo results for the superconducting correlations are found to be in excellent agreement with the results obtained using the well-known Eliashberg approximation.
Finite-temperature properties of the infinite-U Anderson model for rare-earth alloys are calculat... more Finite-temperature properties of the infinite-U Anderson model for rare-earth alloys are calculated within a unified approach. The impurity-electron density of states and magnetic moment spectrum provide a natural framework for describing both static and dynamic properties. The density of states and moment spectrum exhibit low-energy "Kondo resonances" with approximate single-parameter scaling, which persists for impurity valences in the range 1.0 -0.7. The position of the resonance in the zero-temperature density of states, To, sets the scale for all low-temperature properties. Results are reported for the impurity valence, resistivity, thermopower, thermal conductivity, magnetic sus- ceptibility, specific heat, photoemission and inverse-photoemission spectra, and neutron scattering linewidth. The effect of spin-orbit interactions is incorporated in the theory. The calculation is a di- agrammatic approximation motivated by the simplifying concept of large angular momentum degen- eracy (N). The approximate solution is thermodynamically consistent and satisfies all pertinent sum rules. Static properties (magnetic susceptibility and specific heat) are in good agreement with exact results of the Bethe ansatz. Experimental results on both dilute and concentrated Ce alloys are de- scribed quantitatively with use of a one-parameter (To) theory. SELF-CONSISTENT LARGE-X EXPANSION FOR NORMAL-. . . 2037 Sec. II, we attempt to place the present work in context by briefly reviewing previous approaches to the Kondo effect and discussing the basis for the large-degeneracy expansion. In Sec. III, we present an overview of our re- sults, stressing the simplifying features of the physics. Calculational details are discussed at length in Secs. IV and V. In Sec. VI, we compare our results for various properties with the available experiments. Finally, we dis- cuss future directions for this work and summarize our findings in Sec. VII. 300 280 0 O 260 Ct O II. REVIEW Interest in dilute magnetic alloys may be traced back to the earliest days of metals physics, when a low- temperature resistivity minimum was observed in noble metal samples containing small amounts of transition metal impurities' (see Fig. ). Such a resistivity minimum cannot be understood in terms of conventional phonon and nonmagnetic impurity scattering. Experimental interest in transition-metal alloys increased in the late 1950s and early 1960s, but no successful theory was advanced to account for their anomalous behavior. In 1964, Kondo demonstrated that the source of the resistivi- ty minimum was magnetic impurity scattering. While the phonon contribution to the resistivity decreases with temperature, the magnetic contribution increases. In Kondo's perturbative calculation, the resistivity actually diverges logarithmically for T~O. Kondo investigated the so-called antiferromagnetic s-d exchange Hamiltonian, H= g Eknk -2JS.s(0) . k, o (2.1) Here, J is a negative exchange constant, S is the impurity spin and s(0) is the conduction-electron spin density at the impurity. This Hamiltonian is now conventionally known as the "Kondo Hamiltonian. " An alternate model for magnetic alloys was developed in 1961 by Anderson. " The simplest version of the An- derson Hamiltonian may be written ~A ~band +Himp +IImix Hband = g ek n ka k, o H; p --Eden +U"" (2.2) H;"=Vg(ct d +H. c. ) . k, o. The three components of the Hamiltonian describe con- duction electrons, impurity electrons and a hybridization, or mixing interaction, between the two. Creation opera- tors are denoted c|, (conduction) and d (impurity), with n k -c k ck and n = d d . The key features of the model are (a) strong Coulomb correlation between the lo- calized electrons (U) 0) and (b) hybridization between lo- calized and delocalized electrons (V). A measure of the strength of hybirdization is the "hybridization width"
ABSTRACT By introducing a rotationally invariant Stratonovich-Hubbard (S-H) field we studied the ... more ABSTRACT By introducing a rotationally invariant Stratonovich-Hubbard (S-H) field we studied the doped Mott insulator phase of the two-dimension Hubbard model for U/t similar to 4-8. The static spin is decoupled by the S-H field and the static charge interaction is then treated by Hartree-Fock approximation. We sample random spin configurations by Monte Carlo simulation with the Metropolis updating algorithm. The Mott-Hubbard gap and static susceptibilities are studied near the half-filling at low temperature.
We describe an iterative technique for solution of the de Dominicis-Martin parquet equations for ... more We describe an iterative technique for solution of the de Dominicis-Martin parquet equations for lattice electrons and state the relationship of this approach to conserving extensions of Hartree-Fock theory. We propose a physically motivated and computationally feasible pseudopotential approximation, which allows the solution of the parquet equations for the two-dimensional Hubbard model. We present calculations of static and dynamic Hubbard-model correlation functions based on the pseudopotential parquet and a simpler conserving approximation. For a wide parameter range the pseudopotential parquet results are in nearly quantitative agreement with finite-lattice quantum Monte Carlo results.
The fluctuation exchange, or FLEX, approximation for interacting electrons is applied to study in... more The fluctuation exchange, or FLEX, approximation for interacting electrons is applied to study instabilities in the standard three-band model for CuO2 layers in the high-temperature superconductors. Both intra-orbital and near-neigbor Coulomb interactions are retained. The filling dependence of the d x 2 -y 2 transition temperature is studied in both the "hole-doped" and "electrondoped" regimes using parameters derived from constrained-occupancy density-functional theory for La2CuO4. The agreement with experiment on the overdoped hole side of the phase diagram is remarkably good, i.e., transitions emerge in the 40 K range with no free parameters. In addition the importance of the "orbital antiferromagnetic," or flux phase, charge density channel is emphasized for an understanding of the underdoped regime.
The phase boundary between normal and superconducting phases of the negative-U Hubbard model is o... more The phase boundary between normal and superconducting phases of the negative-U Hubbard model is obtained within a self-consistent weak-coupling approach known as the ``pseudopotential parquet'' approximation. The shortcomings of simpler self-consistent approaches, including the Hartree-Fock and fluctuation-exchange approximations, are outlined. For intermediate values of U, pseudopotential parquet predicts (i) a maximum in the superconducting transition temperature Tc at an electron filling of approximately 0.92; and (ii) a sharp decrease in Tc for values of closer to 1. The scale of transition temperatures is consistent with results from quantum simulations.
... The Cu02 Hamiltonian for holes takes the form p(Nd+—N~)= t d g — (d;,p&, +H.c.) (... more ... The Cu02 Hamiltonian for holes takes the form p(Nd+—N~)= t d g — (d;,p&, +H.c.) (il )s — pgn;, +(e — p) gn&, ... Finally, at points in our discussion we refer to results for the one-band Hubbard model pN= —t g (c— ;,c,+H.c.) — pg n;+ U g n;&n;& . I I + Ud g n;tn;), ...
The observed depressions of the superconducting transition temperature caused by 3d magnetic impu... more The observed depressions of the superconducting transition temperature caused by 3d magnetic impurities are compared with the maximum possible value given by theory. Several discrepancies are found, but they might be completely removed by including in the theory the effect of orbital degeneracy.
When superconductivity results from the exchange of electronic excitations (spin or charge fluctu... more When superconductivity results from the exchange of electronic excitations (spin or charge fluctuations), the development of a gap is expected to modify the pairing potential below Tc. One aspect of this feedback phenomenon, pair weakening, is investigated within a modified BCS treatment of d-wave superconductivity in the Hubbard model. It is argued that pair weakening and pair breaking (inelastic scattering)
Page 1. Review of techniques in the large-N expansion for dilute magnetic alloys ... 925 926 927 ... more Page 1. Review of techniques in the large-N expansion for dilute magnetic alloys ... 925 926 927 927 930 933 937 I. OYERVl EW A. introductory remarks In this paper we review a new approach, the large-degeneracy expansion, for investigating models of dilute magnetic alloys. ...
... REVIEW LETTERS Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salp... more ... REVIEW LETTERS Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard Model NE Bickers (a) Institute for Theoretical Physics, University of California at Santa Barbara, Santa Barbara ...
The one-band extended Hubbard model in two dimensions near band-filling 1 2 is solved in the fluc... more The one-band extended Hubbard model in two dimensions near band-filling 1 2 is solved in the fluctuation exchange approximation, including the long-range (1/r) part of the Coulomb interaction, up to 4th neighbor distance. Our results suggest that d x 2 -y 2 pairing in the Hubbard model is robust against the inclusion of long-range Coulomb interactions with moderate 1st neighbor repulsion strength V1. d x 2 -y 2 pairing is suppressed only at large V1 ( > ∼ 0.25U -0.4U ), due to incipient charge density wave instabilities.
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