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Stripe phases—possible ground state of the high- superconductors
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10.1063/1.2199430
/content/aip/journal/ltp/32/4/10.1063/1.2199430
http://aip.metastore.ingenta.com/content/aip/journal/ltp/32/4/10.1063/1.2199430

Figures

Image of FIG. 1.
FIG. 1.

Summary of experimental data illustrating the doping dependence of incommensurability in the cuprates. Results have been obtained by different groups: Nd-LSCO (Refs. 29–32 ); LSCO (Refs. 40–43 and 45–47 ); LCO (Ref. 51 ); Zn-LSCO (Refs. 52 and 53 ); YBCO (Refs. 54 and 55 ). In LSCO, has been defined as a distance from the IC peak position to the AF wave vector either in the orthorhombic or tetragonal notation (see insets), whereas at , both definitions are used due to the coexistence of spin modulations diagonal and parallel to the Cu-O bonds.

Image of FIG. 2.
FIG. 2.

Vertical site-centered (VSC) and diagonal site-centered (DSC) stripe phases as found for at hole doping . The length of arrows is proportional to the magnetization and the hole density is scaled by the diameter of the black circles.

Image of FIG. 3.
FIG. 3.

Vertical bond-centered (VBC) and diagonal bond-centered (DBC) stripe phases as found for at hole doping . The meaning of the arrows and black circles as in Fig. 2 .

Image of FIG. 4.
FIG. 4.

Local hole (top) and magnetization (second row) density; kinetic energy (third row) and (bottom) projected on the bonds in the directions, respectively, of the VSC (left) and DSC (right) stripe phases shown in Fig. 2 (open circles) as well as of the ones obtained in the anisotropic model with (filled circles). For clarity, the latter are shifted by one lattice constant from the origin of the coordinate system.

Image of FIG. 5.
FIG. 5.

The same as in Fig. 4 but for the BC stripe phases shown in Fig. 3 .

Image of FIG. 6.
FIG. 6.

Phase diagrams for stable: () site-centered (SC), and () bond-centered (BC) stripe structures obtained in the anisotropic Hubbard model on a cluster for doping (solid lines) and on a cluster for (dashed lines). Parameters: , .

Image of FIG. 7.
FIG. 7.

Effect of the next-neighbor hopping on the noninteracting 2D DOS at the doping : () hole doping ; () electron doping . The dotted line shows the Fermi energy in the undoped case, and the gray area shows the states occupied by either electrons () or holes ().

Image of FIG. 8.
FIG. 8.

FS obtained in the tight binding model at the doping : () hole doping with and: (black solid line), (gray solid line), and (dashed line); () electron doping with and: (black solid line), (gray solid line), and (dashed line). The long-dashed line in both panels corresponds to the undoped case with . The excessively large value of as compared to LSCO was chosen only for more clarity of the figure.

Image of FIG. 9.
FIG. 9.

Eigenenergy maps of the tight-binding model (12) with as obtained for: () hole doping ; () electron doping .

Image of FIG. 10.
FIG. 10.

Phase boundaries for: () site-centered, and () bond-centered stripes as obtained in the extended Hubbard model with the next-neighbor hopping for doping (solid line) and (dashed line).

Image of FIG. 11.
FIG. 11.

Phase diagrams for the site-centered () and bond-centered () stripes obtained in the extended Hubbard model with the nearest-neighbor Coulomb interaction for doping (solid line) and (dashed line).

Image of FIG. 12.
FIG. 12.

Local hole (top) and magnetization (second row) density; fractional change of the length for the bonds to the right nearest-neighbor along the direction (circles) and double occupancy (squares) (third row), as well as the kinetic energy projected on the bonds in the direction (bottom) of the VSC (left) and DSC (right) stripe phases, as obtained in the Peierls–Hubbard model (14) with , , and (filled symbols). For comparison the results obtained with are shown by open symbols.

Image of FIG. 13.
FIG. 13.

The same as in Fig. 12 but for the bond-centered stripes.

Image of FIG. 14.
FIG. 14.

Phase diagrams for site-centered () and bond-centered () stripe structures as calculated from the Peierls-Hubbard model for doping (solid line) and (dashed line).

Tables

Generic image for table
Table I.

Site-normalized ground-state energy , kinetic energy , and potential energy in the isotropic Hubbard model with and as obtained for different stripe phases: vertical site-centered (VSC), diagonal site-centered (DSC), vertical bond-centered (VBC), and diagonal bond-centered (DBC). In the HF, both types of vertical stripes are degenerate.

Generic image for table
Table II.

The same as in Table I but with the hopping anisotropy .

Generic image for table
Table III.

Local hole and magnetization density of the site-centered stripes shown in Fig. 2 , all labeled by decreasing hole density in the direction. In parentheses the values for the extended hopping model with are given.

Generic image for table
Table IV.

The same as in Table III but for the bond-centered stripes. The VBC stripe is unstable in the extended hopping model with —data in parentheses.

Generic image for table
Table V.

Energies per site: ground-state energy , kinetic energy contributions for the bonds along (10) , (01) , (11) , and directions, as well as the potential energy , all normalized per site, in the extended hopping Hubbard model with and . The VBC stripe is unstable at .

Generic image for table
Table VI.

Energies per site: ground-state energy , kinetic energy , and potential energy components in the extended Hubbard model with the nearest-neighbor Coulomb interaction for and .

Generic image for table
Table VII.

Local hole and magnetization density at nonequivalent atoms of the SC stripe phases, all labeled by decreasing hole density in the direction, in the Peierls-Hubbard model on a cluster with , , and .

Generic image for table
Table VIII.

The same as in Table VII but for the BC stripe phases.

Generic image for table
Table IX.

Ground-state energy per site, kinetic energy , and potential energy components, as obtained in the Peierls-Hubbard model. Parameters: , , and .

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/content/aip/journal/ltp/32/4/10.1063/1.2199430
2006-04-01
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Stripe phases—possible ground state of the high-Tc superconductors
http://aip.metastore.ingenta.com/content/aip/journal/ltp/32/4/10.1063/1.2199430
10.1063/1.2199430
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