Comment on ``Stripes and the t-J Model''
This is a comment being submitted to Physical Review Letters on a recent letter by Hellberg and Manousakis on stripes in the t-J model.
cond-mat.str-el↗
arXiv subjects
D. J. Scalapino
Publications and source records attributed to D. J. Scalapino.
Competition Between Stripes and Pairing in a t-t'-J Model
As the number of legs n of an n-leg, t-J ladder increases, density matrix renormalization group calculations have shown that the doped state tends to be characterized by a static array of domain walls and that pairing correlations are suppressed. Here we present results for a t-t'-J model in which a diagonal, single particle, next-near-neighbor hopping t' is introduced. We find that this can suppress the formation of stripes and, for t' positive, enhance the d_{x^2-y^2}-like pairing correlations. The effect of t' > 0 is to cause the stripes to evaporate into pairs and for t' < 0 to evaporate into quasi-particles. Results for n=4 and 6-leg ladders are discussed.
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Energetics of Domain Walls in the 2D t-J model
Using the density matrix renormalization group, we calculate the energy of a domain wall in the 2D t-J model as a function of the linear hole density ρ_\ell, as well as the interaction energy between walls, for J/t=0.35. Based on these results, we conclude that the ground state always has domain walls for dopings 0 < x < 0.3. For x < 0.125, the system has (1,0) domain walls with ρ_\ell ~ 0.5, while for 0.125 < x < 0.17, the system has a possibly phase-separated mixture of walls with ρ_\ell ~ 0.5 and ρ_\ell =1. For x > 0.17, there are only walls with ρ_\ell =1. For ρ_\ell = 1, diagonal (1,1) domain walls have very nearly the same energy as (1,0) domain walls.
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Diagonal Ladders: A New Class of Models for Strongly Coupled Electron Systems
We introduce a class of models defined on ladders with a diagonal structure generated by $n_p$ plaquettes. The case $n_p=1$ corresponds to the necklace ladder and has remarkable properties which are studied using DMRG and recurrent variational ansatzes. The AF Heisenberg model on this ladder is equivalent to the alternating spin-1/spin-1/2 AFH chain which is known to have a ferrimagnetic ground state (GS). For doping 1/3 the GS is a fully doped (1,1) stripe with the holes located mostly along the principal diagonal while the minor diagonals are occupied by spin singlets. This state can be seen as a Mott insulator of localized Cooper pairs on the plaquettes. A physical picture of our results is provided by a $t_p-J_p$ model of plaquettes coupled diagonally with a hopping parameter $t_d$. In the limit $t_d \to \infty$ we recover the original $t-J$ model on the necklace ladder while for weak hopping parameter the model is easily solvable. The GS in the strong hopping regime is essentially an "on link" Gutzwiller projection of the weak hopping GS. We generalize the $t_p-J_p-t_d$ model to diagonal ladders with $n_p >1$ and the 2D square lattice. We use in our construction concepts familiar in Statistical Mechanics as medial graphs and Bratelli diagrams.
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The Superconducting Condensation Energy and an Antiferromagnetic Exchange Based Pairing Mechanism
For the traditional low T_c superconductors, the superconducting condensation energy is proportional to the change in energy of the ionic lattice between the normal and superconducting state, providing a clear link between pairing and the electron-ion interaction. Here, for the t-J model, we discuss an analogous relationship between the superconducting condensation energy and the change in the exchange energy between the normal and superconducting states. We point out the possibility of measuring this using neutron scattering and note that such a measurement, while certainly difficult, could provide important evidence for an exchange interaction-based pairing mechanism.
cond-mat.supr-con↗
Comparison of different ladder models
Using density matrix renormalization group calculations, we compare results obtained for the t-J, one-band Hubbard and three-band Hubbard models of a two-leg CuO ladder. Spin and charge gaps, pair binding energies, and effective pair hoppings are calculated for a wide range of parameters. All three models have an insulating state at a filling corresponding to one hole per Cu site. For physically relevant parameters their spin gaps are similar in size but they exhibit quite different charge gaps. We find that the binding energy of a pair of doped holes is of the order of the undoped ladder spin gap for all three models. The main difference between the models is the size of the effective pair hopping, which is significantly larger in the three-band model with parameters appropriate for CuO materials than in the other two models.
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The Dimer-Hole-RVB State of the 2-Leg t-J Ladder: A Recurrent Variational Ansatz
We present a variational treatment of the ground state of the 2-leg t-J ladder, which combines the dimer and the hard-core boson models into one effective model. This model allows us to study the local structure of the hole pairs as a function of doping. A second order recursion relation is used to generate the variational wave function, which substantially simplifies the computations. We obtain good agreement with numerical density matrix renormalization group results for the ground state energy in the strong coupling regime. We find that the local structure of the pairs depends upon whether the ladder is slightly or strongly dopped.
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Ground State Properties of the Doped 3-Leg t-J Ladder
Results for a doped 3-leg t-J ladder obtained using the density matrix renormalization group are reported. At low hole doping, the holes form a dilute gas with a uniform density. The momentum occupation of the odd band shows a sharp decrease at a large value of k_F similar to the behavior of a lightly doped t-J chain, while the even modes appear gapped. The spin-spin correlations decay as a power law consistent with the absence of a spin gap, but the pair field correlations are negligible. At larger doping we find evidence for a spin gap and as x increases further we find 3-hole diagonal domain walls. In this regime there are pair field correlations and the internal pair orbital has d_x^2-y^2 - like symmetry. However, the pair field correlations appear to fall exponentially at large distances.
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Charge and Spin Structures of a $d_{x^2 - y^2}$ Superconductor in the Proximity of an Antiferromagnetic Mott Insulator
To the Hubbard model on a square lattice we add an interaction, $W$, which depends upon the square of a near-neighbor hopping. We use zero temperature quantum Monte Carlo simulations on lattice sizes up to $16 \times 16$, to show that at half-filling and constant value of the Hubbard repulsion, the interaction $W$ triggers a quantum transition between an antiferromagnetic Mott insulator and a $d_{x^2 -y^2}$ superconductor. With a combination of finite temperature quantum Monte Carlo simulations and the Maximum Entropy method, we study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite temperature Kosterlitz-Thouless transition to the $d_{x^2 -y^2}$ superconducting state. Above and below the Kosterlitz-Thouless transition temperature, $T_{KT}$, we compute the one-electron density of states, $N(ω)$, the spin relaxation rate $1/T_1$, as well as the imaginary and real part of the spin susceptibility $χ(\vec{q},ω)$. The spin dynamics are characterized by the vanishing of $1/T_1$ and divergence of $Re χ(\vec{q} = (π,π), ω= 0)$ in the low temperature limit. As $T_{KT}$ is approached $N(ω)$ develops a pseudo-gap feature and below $T_{KT}$ $Im χ(\vec{q} = (π,π), ω)$ shows a peak at finite frequency.
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DMRG Study of the Striped Phase in the 2D t-J model
Using the density matrix renormalization group (DMRG), we study the 2D t-J model at a hole doping of x=1/8 on clusters as large as 19x8. We find a striped phase which is consistent with recent neutron scattering experiments. We find that bond-centered and site-centered stripes have nearly the same energy, suggesting that in the absence of pinning effects the domain walls can fluctuate.
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Spontaneous Flux and Magnetic Interference Patterns in 0-pi Josephson Junctions
The spontaneous flux generation and magnetic field modulation of the critical current in a 0-pi Josephson junction are calculated for different ratios of the junction length to the Josephson penetration depth, and different ratios of the 0-junction length to the pi-junction length. These calculations apply to a Pb-YBCO c-axis oriented junction with one YBCO twin boundary, as well as other experimental systems. Measurements of such a junction can provide information on the nature of the c-axis Josephson coupling and the symmetry of the order parameter in YBCO. We find spontaneous flux even for very short symmetric 0-pi junctions, but asymmetric junctions have qualitatively different behavior.
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Theory of Scanning Tunneling Microscopy Probe of Impurity States in a D-Wave Superconductor
Scanning tunneling microscopy can provide a probe for the detailed study of quasiparticle states in high-Tc superconductors. We propose that it can also be used to acquire specific information about impurity-induced quasiparticle states and the superconducting order-parameter structure. In particular, the local density of states is found to be sensitive to impurity-induced resonances and to the symmetry of the order parameter.
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Monte Carlo study of the pairing interaction in the two-leg Hubbard ladder
Monte Carlo calculations of the irreducible particle-particle interaction on a two-leg Hubbard ladder doped near half-filling are reported. As the temperature is lowered, this interaction develops structure in momentum space similar to the magnetic susceptibility $χ(q)$ and reflects the development of strong short-range antiferromagnetic correlations. Using this interaction, the eigenfunction of the leading singlet pair eigenvalue is found to have $d_{x^2-y^2}$ like symmetry. The single-particle spectral weight is also shown to peak near $(π,0)$ and $(0,π)$ when the ratio of the inter- to intra-chain hopping $t_{\perp}/t\simeq 1.5$, leading to an increased tendency for pairing.
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Enhanced d_{x^2-y^2} pairing correlations in the two-leg Hubbard ladder
The two-leg Hubbard ladder is characterized by the ratio of the inter- to intra-leg hopping t_perp/t, the relative interaction strength U/t and the electron filling. Here, using density matrix renormalization group and Monte Carlo simulations, we examine the dependence of the pairing correlations on these parameters. We find that the pairing correlations are enhanced when the top of the bonding quasiparticle band and the bottom of the antibonding band are near the Fermi level. We present results on the single-particle spectral weight and the antiferromagnetic correlations in order to explain this behavior.
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d_{x^2-y^2} Pair Domain Walls
Using the density matrix renormalization group, we study domain wall structures in the t-J model at a hole doping of x=1/8. We find that the domain walls are composed of d_{x^2-y^2} pairs and that the regions between the domain walls have antiferromagnetic correlations that are pi phase shifted across a domain wall. At x=1/8, the hole filling corresponds to one hole per two domain wall unit cells. When the pairs in a domain wall are pinned by an external field, the d_{x^2-y^2} pairing response is suppressed, but when the pinning is weakened, d_{x^2-y^2} pair-field correlations can develop.
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Weak-coupling calculation of the gap structure of doped n-leg Hubbard ladders
In weak coupling, the spin gap in doped, even, n-leg periodic Hubbard ladders reflects the energy to break a pair into separate quasiparticles. Here we investigate the structure of the gap within a spin-fluctuation exchange approximation. We also calculate the amplitude for removing a singlet pair from two lattice sites separated by a distance (l_x,l_y), which describes the internal structure of a pair.
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d_{x^2-y^2} Symmetry and the Pairing Mechanism
An important question is if the gap in the high temperature cuprates has d_{x^2-y^2} symmetry, what does that tell us about the underlying interaction responsible for pairing. Here we explore this by determining how three different types of electron-phonon interactions affect the d_{x^2-y^2} pairing found within an RPA treatment of the 2D Hubbard model. These results imply that interactions which become more positive as the momentum transfer increases favor d_{x^2-y^2} pairing in a nearly half-filled band.
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Determining the structure of the superconducting gap in Cu_{2}O_{3} 2-leg ladder materials
Superconductivity has been recently observed in Sr_{0.4}Ca_{13.6}Cu_{24}O_{41.84} which contains quasi-one-dimensional Cu_{2}O_{3} 2-leg ladders. If, as suggested by some theories, the superconductivity arises from these 2-leg ladders, it will be important to determine the structure of the superconducting gap. In particular, does the gap in a 2-leg ladder change sign when one goes from the bonding to antibonding fermi surface points? Here we carry out phenomenological calculations of nuclear relaxation rates and inelastic neutron scattering intensity in order to provide estimates of the experimental resolution that will be required to determine the structure of the superconducting gap associated with an array of weakly coupled 2-leg ladders.
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