A local moment approach to magnetic impurities in gapless Fermi systems
A local moment approach is developed for single-particle excitations of a symmetric Anderson impurity model (AIM) with a soft-gap hybridization vanishing at the Fermi level: Δ I α |ω| r, with r > 0. Local moments are introduced explicitly from t...
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| Format: | Journal article |
| Language: | English |
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2000
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| _version_ | 1797058988816203776 |
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| author | Logan, D Glossop, M |
| author_facet | Logan, D Glossop, M |
| author_sort | Logan, D |
| collection | OXFORD |
| description | A local moment approach is developed for single-particle excitations of a symmetric Anderson impurity model (AIM) with a soft-gap hybridization vanishing at the Fermi level: Δ I α |ω| r, with r > 0. Local moments are introduced explicitly from the outset, and a two-self-energy description is employed in which single-particle excitations are coupled dynamically to low-energy transverse spin fluctuations. The resultant theory is applicable on all energy scales, and captures both the spin-fluctuation regime of strong coupling (large U), as well as the weak-coupling regime where it is perturbatively exact for those r-domains in which perturbation theory in U is non-singular. While the primary emphasis is on single-particle dynamics, the quantum phase transition between strong-coupling (SC) and local moment (LM) phases can also be addressed directly; for the spin-fluctuation regime in particular a number of asymptotically exact results are thereby obtained, notably for the behaviour of the critical U c(r) separating SC/LM states and the Kondo scale ω m(r) characteristic of the SC phase. Results for both single-particle spectra and SC/LM phase boundaries are found to agree well with recent numerical renormalization group (NRG) studies; and a number of further testable predictions are made. Single-particle spectra are examined systematically for both SC and LM states; in particular, for all 0 ≤ r < 1/2, spectra characteristic of the SC state are predicted to exhibit an r-dependent universal scaling form as the SC/LM phase boundary is approached and the Kondo scale vanishes. Results for the 'normal' r = 0 AIM are moreover recovered smoothly from the limit r → 0, where the resultant description of single-particle dynamics includes recovery of Doniach-Šunjić tails in the wings of the Kondo resonance, as well as characteristic low-energy Fermi liquid behaviour and the exponential diminution with U of the Kondo scale itself. The normal AIM is found to represent a particular case of more generic behaviour characteristic of the r > 0 SC phase which, in agreement with conclusions drawn from recent NRG work, may be viewed as a non-trivial but natural generalization of Fermi liquid physics. © 2000 IOP Publishing Ltd. |
| first_indexed | 2024-03-06T19:57:52Z |
| format | Journal article |
| id | oxford-uuid:26444caa-fd51-4b1d-8af6-b366bff8db03 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:57:52Z |
| publishDate | 2000 |
| record_format | dspace |
| spelling | oxford-uuid:26444caa-fd51-4b1d-8af6-b366bff8db032022-03-26T11:59:57ZA local moment approach to magnetic impurities in gapless Fermi systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:26444caa-fd51-4b1d-8af6-b366bff8db03EnglishSymplectic Elements at Oxford2000Logan, DGlossop, MA local moment approach is developed for single-particle excitations of a symmetric Anderson impurity model (AIM) with a soft-gap hybridization vanishing at the Fermi level: Δ I α |ω| r, with r > 0. Local moments are introduced explicitly from the outset, and a two-self-energy description is employed in which single-particle excitations are coupled dynamically to low-energy transverse spin fluctuations. The resultant theory is applicable on all energy scales, and captures both the spin-fluctuation regime of strong coupling (large U), as well as the weak-coupling regime where it is perturbatively exact for those r-domains in which perturbation theory in U is non-singular. While the primary emphasis is on single-particle dynamics, the quantum phase transition between strong-coupling (SC) and local moment (LM) phases can also be addressed directly; for the spin-fluctuation regime in particular a number of asymptotically exact results are thereby obtained, notably for the behaviour of the critical U c(r) separating SC/LM states and the Kondo scale ω m(r) characteristic of the SC phase. Results for both single-particle spectra and SC/LM phase boundaries are found to agree well with recent numerical renormalization group (NRG) studies; and a number of further testable predictions are made. Single-particle spectra are examined systematically for both SC and LM states; in particular, for all 0 ≤ r < 1/2, spectra characteristic of the SC state are predicted to exhibit an r-dependent universal scaling form as the SC/LM phase boundary is approached and the Kondo scale vanishes. Results for the 'normal' r = 0 AIM are moreover recovered smoothly from the limit r → 0, where the resultant description of single-particle dynamics includes recovery of Doniach-Šunjić tails in the wings of the Kondo resonance, as well as characteristic low-energy Fermi liquid behaviour and the exponential diminution with U of the Kondo scale itself. The normal AIM is found to represent a particular case of more generic behaviour characteristic of the r > 0 SC phase which, in agreement with conclusions drawn from recent NRG work, may be viewed as a non-trivial but natural generalization of Fermi liquid physics. © 2000 IOP Publishing Ltd. |
| spellingShingle | Logan, D Glossop, M A local moment approach to magnetic impurities in gapless Fermi systems |
| title | A local moment approach to magnetic impurities in gapless Fermi systems |
| title_full | A local moment approach to magnetic impurities in gapless Fermi systems |
| title_fullStr | A local moment approach to magnetic impurities in gapless Fermi systems |
| title_full_unstemmed | A local moment approach to magnetic impurities in gapless Fermi systems |
| title_short | A local moment approach to magnetic impurities in gapless Fermi systems |
| title_sort | local moment approach to magnetic impurities in gapless fermi systems |
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