Effective Lagrangian for a system of nonrelativistic fermions in 2+1 dimensions coupled to an electromagnetic field: Application to anyonic superconductors

Journal Article · Sat Sep 01 04:00:00 EDT 1990 · Physical Review, B: Condensed Matter; (USA)

DOI:https://doi.org/10.1103/PhysRevB.42.4036· OSTI ID:6419154

Panigrahi, P K ^[1]; Ray, R; Sakita, B ^[2]

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1. Department of Physics, University of Illinois at Chicago, Chicago, IL (USA)
2. Department of Physics, City College of the City University of New York, New York, NY (USA)

We study here, in two spatial dimensions, the effective Lagrangian of nonrelativistic charged fermions in an electromagnetic field. The fermionic integration is performed yielding a one-loop effective action that is evaluated using the inhomogeneity (derivative) expansion technique. The effective Lagrangian involves a Chern-Simons (CS) -like term with a coefficient that is a staircase'' function of {ital B}, the magnetic field. We then discuss the application of this effective Lagrangian to a system of anyons, showing that the cancellation of the induced CS term against a CS term included in the beginning to change the fermions to anyons, is favored energetically, together with the expulsion of {ital B} from the system of anyons. The cancellation implies the existence of a massless mode. This, together with the fact that {ital B}=0, implies superconductivity.

• OSTI ID: 6419154
• Journal Information: Physical Review, B: Condensed Matter; (USA), Journal Name: Physical Review, B: Condensed Matter; (USA) Vol. 42:7; ISSN 0163-1829; ISSN PRBMD
• Country of Publication: United States
• Language: English

Related Subjects

656100* -- Condensed Matter Physics-- Superconductivity
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CRYSTAL MODELS
ELECTROMAGNETIC FIELDS
FERMIONS
FUNCTIONS
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
LAGRANGIAN FUNCTION
MATHEMATICAL MODELS
QUASI PARTICLES
SUPERCONDUCTORS