We analytically calculate the ground state pairing symmetry and excitation spectra of two holes doped into the half-filled t-t'-t''-J_z model in the strong-coupling limit (J_z >> |t|, |t'|, |t''|). For the t'-t''-J_z model, there are regions of d-wave, s-wave, and p-wave symmetry. We find that the t-J_z model maps in lowest order onto the t'-t''-J_z model on the boundary between d and p symmetry, with a flat lower branch of the pair excitation spectrum. In higher order d-wave symmetry is selected; however, we predict that the addition of the appropriate t' and/or t'' should drive the hole-pair symmetry to p-wave. We perturbatively construct an extended quasi-pair for the t-J_z model. We compare with analytic calculations for a 2x2 plaquette and numerical work, and discuss implications for the experimentally relevant parameter regime.We analytically calculate the ground state pairing symmetry and excitation spectra of two holes doped into the half-filled t-t'-t''-J_z model in the strong-coupling limit (J_z >> |t|, |t'|, |t''|). For the t'-t''-J_z model, there are regions of d-wave, s-wave, and p-wave symmetry. We find that the t-J_z model maps in lowest order onto the t'-t''-J_z model on the boundary between d and p symmetry, with a flat lower branch of the pair excitation spectrum. In higher order d-wave symmetry is selected; however, we predict that the addition of the appropriate t' and/or t'' should drive the hole-pair symmetry to p-wave. We perturbatively construct an extended quasi-pair for the t-J_z model. We compare with analytic calculations for a 2x2 plaquette and numerical work, and discuss implications for the experimentally relevant parameter regime.

arXiv:cond-mat/9706073Jun 8, 19970 citations

On the nature of pairing in the two-dimensional t–J model

Thomas Maier

Physica B Condensed MatterFeb 15, 20058 citations

Hole-pair symmetry and excitations in the strong-coupling extended t−Jz model: competition between d -wave and p -wave symmetry

Richard M. Fye, George Balster Martins, Elbio R. Dagotto

We analytically calculate the ground state pairing symmetry and excitation spectra of two holes doped into the half-filled $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}{J}_{z}$ model in the strong-coupling limit $({J}_{z}⪢\ensuremath{\mid}t\ensuremath{\mid},\ensuremath{\mid}{t}^{\ensuremath{'}}\ensuremath{\mid},\ensuremath{\mid}{t}^{\ensuremath{''}}\ensuremath{\mid})$. In leading order, this reduces to the ${t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}{J}_{z}$ model, where there are regions of $d$ -wave, $s$ -wave, and (degenerate) $p$ -wave symmetry. We find that the $t\ensuremath{-}{J}_{z}$ model maps in lowest order onto the ${t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}{J}_{z}$ model on the boundary between $d$ and $p$ symmetry, with a flat lower band in the pair excitation spectrum. In higher order, $d$ -wave symmetry is selected from the lower pair band. However, we observe that the addition of the appropriate ${t}^{\ensuremath{'}}<0$ and/or ${t}^{\ensuremath{''}}>0$, the signs of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ found in the hole-doped cuprates, could drive the hole-pair symmetry to $p$ -wave symmetry, implying the possibility of competition between $p$ -wave and $d$ -wave pair ground states. (An added ${t}^{\ensuremath{'}}>0$ and/or ${t}^{\ensuremath{''}}<0$ generally tend to promote $d$ -wave symmetry.) We perturbatively construct an extended quasipair for the $t\ensuremath{-}{J}_{z}$ model. In leading order, there are contributions from sites at a distance of $\sqrt{2}$ lattice spacings apart; however, contributions from sites two lattice spacings apart, also of the same order, vanish identically. Finally, we compare our approach with analytic calculations for a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette and with existing numerical work, and discuss possible relevance to the physical parameter regime.We analytically calculate the ground state pairing symmetry and excitation spectra of two holes doped into the half-filled $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}{J}_{z}$ model in the strong-coupling limit $({J}_{z}⪢\ensuremath{\mid}t\ensuremath{\mid},\ensuremath{\mid}{t}^{\ensuremath{'}}\ensuremath{\mid},\ensuremath{\mid}{t}^{\ensuremath{''}}\ensuremath{\mid})$. In leading order, this reduces to the ${t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}{J}_{z}$ model, where there are regions of $d$-wave, $s$-wave, and (degenerate) $p$-wave symmetry. We find that the $t\ensuremath{-}{J}_{z}$ model maps in lowest order onto the ${t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}{J}_{z}$ model on the boundary between $d$ and $p$ symmetry, with a flat lower band in the pair excitation spectrum. In higher order, $d$-wave symmetry is selected from the lower pair band. However, we observe that the addition of the appropriate ${t}^{\ensuremath{'}}<0$ and/or ${t}^{\ensuremath{''}}>0$, the signs of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ found in the hole-doped cuprates, could drive the hole-pair symmetry to $p$-wave symmetry, implying the possibility of competition between $p$-wave and $d$-wave pair ground states. (An added ${t}^{\ensuremath{'}}>0$ and/or ${t}^{\ensuremath{''}}<0$ generally tend to promote $d$-wave symmetry.) We perturbatively construct an extended quasipair for the $t\ensuremath{-}{J}_{z}$ model. In leading order, there are contributions from sites at a distance of $\sqrt{2}$ lattice spacings apart; however, contributions from sites two lattice spacings apart, also of the same order, vanish identically. Finally, we compare our approach with analytic calculations for a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette and with existing numerical work, and discuss possible relevance to the physical parameter regime.

arXiv:cond-mat/0403733Physical Review BJun 21, 20045 citations

Superconducting pairing symmetries of the Hubbard model on the honeycomb lattice with inhomogeneous hopping strength

Tao Ying, Shuhui Yang

Using finite-temperature determinantal quantum Monte Carlo calculations, we find that the dominant pairing symmetries in the standard Hubbard model on the honeycomb lattice depend on the electron filling. When the electron density $\ensuremath{\rho}$ is larger than around 0.25, the dominant pairing symmetry is the $d+id$ -wave; when the electron density is low enough ($\ensuremath{\rho}\ensuremath{\lesssim}0.25$), the dominant pairing symmetry is the $p+ip$ wave. For two electron densities $\ensuremath{\rho}=0.1$ and $\ensuremath{\rho}=0.4$, where the dominant pairing symmetries are $p+ip$ wave and $d+id$ wave separately, we study the effect of two types of hopping inhomogeneities (the plaquette and the quasi- $1\mathrm{D}$ hopping inhomogeneities) on the pairing symmetries. For $\ensuremath{\rho}=0.1$, the plaquette hopping inhomogeneity drives the dominant $p+ip$ -wave pairing symmetry into the $d+id$ -wave; while the quasi- $1\mathrm{D}$ hopping inhomogeneity almost does not affect the $p+ip$ wave, and arises the $f$ wave, causing the coexistence of $p+ip$ -wave and $f$ -wave pairing. For $\ensuremath{\rho}=0.4$, both the plaquette and the quasi- $1\mathrm{D}$ hopping inhomogeneities destroy the $d+id$ -wave pairing symmetry, without causing other pairing symmetry. Our results suggest that the effect of hopping inhomogeneity on the pairing symmetries is robust and depends on the electron filling. This finding may be useful for the design of artificial graphene superconductors with different kinds of pairing, especially for the realization of the $d+id$ -wave, $p+ip$ -wave, or $f$ -wave superconductors at low filling.Using finite-temperature determinantal quantum Monte Carlo calculations, we find that the dominant pairing symmetries in the standard Hubbard model on the honeycomb lattice depend on the electron filling. When the electron density $\ensuremath{\rho}$ is larger than around 0.25, the dominant pairing symmetry is the $d+id$-wave; when the electron density is low enough ($\ensuremath{\rho}\ensuremath{\lesssim}0.25$), the dominant pairing symmetry is the $p+ip$ wave. For two electron densities $\ensuremath{\rho}=0.1$ and $\ensuremath{\rho}=0.4$, where the dominant pairing symmetries are $p+ip$ wave and $d+id$ wave separately, we study the effect of two types of hopping inhomogeneities (the plaquette and the quasi-$1\mathrm{D}$ hopping inhomogeneities) on the pairing symmetries. For $\ensuremath{\rho}=0.1$, the plaquette hopping inhomogeneity drives the dominant $p+ip$-wave pairing symmetry into the $d+id$-wave; while the quasi-$1\mathrm{D}$ hopping inhomogeneity almost does not affect the $p+ip$ wave, and arises the $f$ wave, causing the coexistence of $p+ip$-wave and $f$-wave pairing. For $\ensuremath{\rho}=0.4$, both the plaquette and the quasi-$1\mathrm{D}$ hopping inhomogeneities destroy the $d+id$-wave pairing symmetry, without causing other pairing symmetry. Our results suggest that the effect of hopping inhomogeneity on the pairing symmetries is robust and depends on the electron filling. This finding may be useful for the design of artificial graphene superconductors with different kinds of pairing, especially for the realization of the $d+id$-wave, $p+ip$-wave, or $f$-wave superconductors at low filling.

Physical review. B./Physical review. BSep 16, 202012 citations

d

-wave,

s

-wave, and (degenerate)

p

-wave symmetry. We find that the $t\ensuremath{-}{J}_{z}$ model maps in lowest order onto the ${t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}{J}_{z}$ model on the boundary between

d

and

p

symmetry, with a flat lower band in the pair excitation spectrum. In higher order,

d

-wave symmetry is selected from the lower pair band. However, we observe that the addition of the appropriate ${t}^{\ensuremath{'}}<0$ and/or ${t}^{\ensuremath{''}}>0$, the signs of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ found in the hole-doped cuprates, could drive the hole-pair symmetry to

p

-wave symmetry, implying the possibility of competition between

p

-wave and

d

-wave pair ground states. (An added ${t}^{\ensuremath{'}}>0$ and/or ${t}^{\ensuremath{''}}<0$ generally tend to promote

d

-wave symmetry.) We perturbatively construct an extended quasipair for the $t\ensuremath{-}{J}_{z}$ model. In leading order, there are contributions from sites at a distance of

\sqrt{2}

lattice spacings apart; however, contributions from sites two lattice spacings apart, also of the same order, vanish identically. Finally, we compare our approach with analytic calculations for a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette and with existing numerical work, and discuss possible relevance to the physical parameter regime.

d+id

-wave; when the electron density is low enough ($\ensuremath{\rho}\ensuremath{\lesssim}0.25$), the dominant pairing symmetry is the

p+ip

wave. For two electron densities $\ensuremath{\rho}=0.1$ and $\ensuremath{\rho}=0.4$, where the dominant pairing symmetries are

p+ip

wave and

d+id

wave separately, we study the effect of two types of hopping inhomogeneities (the plaquette and the quasi-

1\mathrm{D}

hopping inhomogeneities) on the pairing symmetries. For $\ensuremath{\rho}=0.1$, the plaquette hopping inhomogeneity drives the dominant

p+ip

-wave pairing symmetry into the

d+id

-wave; while the quasi-

1\mathrm{D}

hopping inhomogeneity almost does not affect the

p+ip

wave, and arises the

f

wave, causing the coexistence of

p+ip

-wave and

f

-wave pairing. For $\ensuremath{\rho}=0.4$, both the plaquette and the quasi-

1\mathrm{D}

hopping inhomogeneities destroy the

d+id

-wave pairing symmetry, without causing other pairing symmetry. Our results suggest that the effect of hopping inhomogeneity on the pairing symmetries is robust and depends on the electron filling. This finding may be useful for the design of artificial graphene superconductors with different kinds of pairing, especially for the realization of the

d+id

-wave,

p+ip

-wave, or

f

-wave superconductors at low filling.