Fermi-edge singularity in one-dimensional electron systems with long-range Coulomb interactions

Journal Article · Thu Aug 01 04:00:00 EDT 1996 · Physical Review, B: Condensed Matter

DOI:https://doi.org/10.1103/PhysRevB.54.4540· OSTI ID:288892

Otani, H; Ogawa, T ^[1]

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1. Department of Applied Physics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558 (Japan)

Effects of long-range Coulomb interactions on the Fermi-edge singularity in optical spectra are investigated theoretically for one-dimensional spin-1/2 fermion systems with the use of the Tomonaga-Luttinger bosonization technique. Low-energy excitation spectrum near the Fermi level shows that dispersion of the charge-density fluctuation remains gapless but is nonlinear when the electron-electron ({ital e}-{ital e}) Coulomb interaction is of the {ital x}{sup {minus}1} type (i.e., an infinite force range). Temporal behavior of the current-current correlation function is calculated analytically for {ital arbitrary} {ital force} {ital ranges}, {lambda}{sub {ital e}} and {lambda}{sub {ital h}}, of the {ital e}-{ital e} and the electron-hole ({ital e}-{ital h}) Coulomb interactions. (i) When both the {ital e}-{ital e} and the {ital e}-{ital h} interactions have large but finite force ranges ({lambda}{sub {ital e}}{lt}{infinity} and {lambda}{sub {ital h}}{lt}{infinity}), the correlation function yields a {ital power}-{ital law} {ital decay} only for a long-time regime, which is determined by the force ranges as {ital t}{gt}max[{lambda}{sub {ital e}},{lambda}{sub {ital h}}]/{ital v}{sub {ital F}}. Corresponding optical spectrum near the Fermi edge (within an energy range of {h_bar}{ital v}{sub {ital F}}/max[{lambda}{sub {ital e}},{lambda}{sub {ital h}}]) exhibits the power-law divergence or the power-law convergence, which is an ordinary Fermi-edge singularity. (ii) When either the {ital e}-{ital e} or the {ital e}-{ital h} interaction is of the {ital x}{sup {minus}1} type (i.e., {lambda}{sub {ital e}}{r_arrow}{infinity} and/or {lambda}{sub {ital h}}{r_arrow}{infinity}), an exponent of the correlation function is dependent on time to lead the faster decay than that of any power laws. Then the optical spectra show {ital no power law} dependence and {ital always converge (become zero}) at the Fermi edge, which is in striking contrast to the ordinary power-law singularity.

• OSTI ID: 288892
• Journal Information: Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 7 Vol. 54; ISSN 0163-1829; ISSN PRBMDO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOSON EXPANSION
CORRELATION FUNCTIONS
COULOMB FIELD
ELECTRON GAS
ELECTRON-ELECTRON COUPLING
ONE-DIMENSIONAL CALCULATIONS
OPTICAL PROPERTIES
SINGULARITY
SPECTRAL DENSITY