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Journal of Physics Condensed Matter

The ordered phase of electron vortices

Bogdan R. Bułka

Published Feb 19, 1990• 1 citation
Publisher

Abstract

Stability conditions for the ordered state of the magnetic fluxes induced by rotating electrons on a square lattice are analysed in the mean-field approximation for the extended Hubbard model. It is shown that the flux phase can appear if the exchange energy V1 is sufficiently large. The order parameter, magnetic flux Phi enclosed in the unit cell, and critical temperature of the flux phase are monotonically increasing functions of V1. It is also shown that the flux and the antiferromagnetic phase can coexist.

DOI
10.1088/0953-8984/2/7/023

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Stability conditions for the ordered state of the magnetic fluxes induced by rotating electrons on a square lattice are analysed in the mean-field approximation for the extended Hubbard model. It is shown that the flux phase can appear if the exchange energy V1 is sufficiently large. The order parameter, magnetic flux Phi enclosed in the unit cell, and critical temperature of the flux phase are monotonically increasing functions of V1. It is also shown that the flux and the antiferromagnetic phase can coexist.
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This paper describes a group theoretical classification of superconducting states (vortex lattice states) in a unifom magnetic field of the extended Hubbard model with on-site attraction (U<0), or nearest-neighbor attraction (V<0) on a two-dimensional square lattice. Using symmetries of the magnetic translation and the tetragonal rotation of the system, we obtain invariance groups of vortex lattice states. When the magnetic flux φ through a unit cell of the crystal lattice is φ0/p2 (φ0=ch/2e is the flux quantum, p is an integer) we obtained three types of symmorphic tetragonal vortex lattice states, in which the center of point rotations is at a lattice site of the crystal lattice, corresponding to the irreducible representation of the tetragonal symmetry D4. For these three states, locations and winding numbers of vortex lines are determined by the symmetries of their invariance group. From these three symmorphic states we derived three (two) types of non-symmorphic vortex lattice states in which the center of point rotations is at the center of a plaquette (link) of the crystal lattice. We show that d-wave, s-wave and p-wave local order parameters inevitably coexist due to the invariance magnetic translation group L of the vortex lattice state. From the irreducible projective representations (two-dimensional) of L, we show that all energy bands of the quasiparticles are at least doubly degenerate.
We study the two-dimensional one-band Hubbard model on the square lattice through the spin rotation invariant Kotliar-Ruckenstein slave-boson method, with an emphasis on the electron-doped regime. The phase diagram determined within mean field approximation reveals three different magnetically ordered phases separated by first-order transitions, and a wide instability region as indicated by a negative compressibility. We show that this conundrum of the unstable mean field domain is resolved by spatially mixed phases of neighboring stable states. We also find charge density wave type instabilities in the antiferromagnetically ordered (AFM) state at wave vectors commensurate with the doping. The corresponding charge and spin density response functions are calculated from a Gaussian fluctuations formalism about a magnetic saddle point, for which we provide a detailed derivation. Further, we present density and spin excitation spectra in the AFM phase, allowing for a quantitative calculation of the spin wave parameters, the gap in the longitudinal spin excitation spectrum, and the density excitations in the upper Hubbard band.
It is suggested that conventional spin-density-wave states for an interacting many-electron system in a two-dimensional square lattice are energetically unstable to the formation of spin flux. Spin flux corresponds to a rotation of the internal coordinate system of the electron as it traverses a closed loop. The flux is dynamically generated by the electromagnetic interaction in the many-body system. This is illustrated by including the nearest-neighbor Coulomb repulsion between electrons in the Hubbard model. Using a Grassmann field theory, we derive the mean-field equations for spin flux and local-moment ordering. For a wide range of Hubbard model couplings U/t and doping \ensuremath{\delta} we find that the generation of spin flux leads to a lowering of the mean-field local-moment amplitude. This suppression of the local moment offsets the additional quantum zero-point energy associated with spin flux and leads to an overall reduction in the total many-electron energy. When the spin-flux vortex filaments are endowed with a quantum dynamics, chiral symmetry breaking is possible. We show that under certain conditions, this leads to a further reduction of local-moment amplitude and many-electron energy.
We study the extended Hubbard model on a two-dimensional half-filled square lattice using the dynamical cluster approximation. We present results on the phase boundaries between the paramagnetic metallic (normal) state and the insulating antiferromagnetic state, as well as between the antiferromagnetic and charge-order states. We find hysteresis along the antiferromagnet/charge order and normal/charge-order phase boundaries (at larger values of the on-site interaction), indicating first-order phase transitions. We show that nearest-neighbor interactions lower the critical temperature for the antiferromagnetic phase. We also present results for the effect of nearest-neighbor interactions on the antiferromagnetic phase boundary and for the evolution of spectral functions and energetics across the phase transitions.