The in-plane infrared and visible (3 meV–3 eV) reflectivity of Bi2Sr2CaCu2O8+� (Bi-2212) thin films is measured between 300 K and 10 K for different doping levels with unprecedented accuracy. The optical conductivity is derived through an accurate fitting procedure. We study the transfer of spectral weight from finite energy into the superfluid as the system becomes superconducting. In the over-doped regime, the superfluid develops at the expense of states lying below 60 meV, a conventional energy of the order of a few times the superconducting gap. In the underdoped regime, spectral weight is removed from up to 2 eV, far beyond any conventional scale. The intraband spectral weight change between the normal and superconducting state, if analyzed in terms of a change of kinetic energy is � 1 meV. Compared to the condensation energy, this figure addresses the issue of a kinetic energy driven mechanism.

https://www.lps.u-psud.fr/IMG/pdf_santander-cm0504.pdf

The in-plane electrodynamics of the superconductivity in Bi2Sr2CaCu2O8+d: energy scales and spectral weight distribution

We analyse lowering of the kinetic energy in doped antiferromagnets at the transition to the superconducting state. Measurements of optical conductivity indicate that such unconventional behaviour takes place in underdoped Bi-2212. We argue that the definition of the operator representing the kinetic energy is determined by experimental conditions. The thermodynamic average of that operator is related to the integrated spectral weight of the optical conductivity and thus depends on the cut-off frequency limiting that integral. If the upper limit of the integral lies below the charge transfer gap the spectral weight represents the average of the hopping term in the space restricted to the energy range below the gap. We show that the kinetic energy is indeed lowered at the superconducting transition in the t–J model (tJM), which is an effective model defined in the restricted space. That result is in agreement with experimental observations and may be attributed to the formation of spin polarons and the change of roles which are played by the kinetic and the potential energy in the tJM and in some effective model for spin polarons. The total spectral weight represents the kinetic energy in a model defined in a broader space if the upper limit in the integral of the optical conductivity is set above the gap. We demonstrate that the kinetic energy in the Hubbard model is also lowered in the superconducting state. That result does not agree with experimental observations, indicating that the spectral weight is conserved for all temperatures if the upper limit of the integral is set above the charge transfer gap. This discrepancy suggests that a single band model is not capable of describing in some respects the physics of excitations across the gap.

http://iopscience.iop.org/article/10.1088/0953-8984/15/38/025/pdf

Pairing-induced kinetic energy lowering in doped antiferromagnets

Motivated by the possible charge ordering in the recently discovered superconductor ${\mathrm{Na}}_{x}\mathrm{Co}{\mathrm{O}}_{2}\phantom{\rule{0.2em}{0ex}}\mathrm{y}{\mathrm{H}}_{2}\mathrm{O}$, which at filling $x=1∕3$ would correspond to a half-filled honeycomb lattice, we investigate the single-hole dynamics of the $t\text{\ensuremath{-}}J$ model on this lattice. Using exact diagonalization, series expansion, and the self-consistent Born approximation, we calculate the quasiparticle dispersion, bandwidth, and residues and compare our findings to the well-established results for the square lattice. Given the similarities between both lattices, it is not surprising that we find qualitatively similar features for the honeycomb lattice, namely, an almost flat band along the edge of the magnetic Brillouin zone and well-defined hole pockets around the corners. However, we report a considerable disagreement between the three methods used concerning the bandwidth and discuss possible origins of this discrepancy.

Single-hole properties of the t − J model on the honeycomb lattice

The binding of two holes in a coupled-chain model described by the t-t'-J Hamiltonian is studied. Using the Bethe Ansatz analysis, it is shown that two holes form antibound states in a triplet spin state. This result can be extended to the case of more than two holes. The eigenvalue problem when the two holes are in a singlet state is solved exactly and one finds that the two holes can bind for all values of J. In this case, antibound states are found for sufficiently large values of J.

https://iopscience.iop.org/article/10.1088/0953-8984/7/29/014/pdf

Bound and antibound states of holes in a coupled-chain model

In this work, we developed the unit step model as an approximate solution to the single-band Hubbard Hamiltonian to solve variationally strongly correlated interacting elections on a two-dimensional (2D) square lattice. We also showed primarily how to derive possible electronic states available for several 2D N x N square lattices, although, with special emphasis on a 2D 5 x 5 square lattice. The results emerging from our present study was compared with the results of Gutzwiller variational approach (GVA) and correlated variational approach (CVA), at the large limit of the Coulomb interaction strength (U/4t).The approximation to the Hubbard Hamiltonian study is actually necessary because of the strong limitation and difficulty pose by the Hubbard Hamiltonian as we move away from finite - size lattices to larger N - dimensional lattices. Thus this work has provided a means of overcoming the finite - size lattice defects as we pass on to a higher dimension. We have shown in this study, that the repulsive Coulomb interaction which in part leads to the strong electronic correlations, would indicate that the two electron system prefer not to condense into s-wave superconducting singlet state (s = 0), at high positive values of the interaction strength. This study reveals that when the Coulomb interaction is zero, that is, for free electron system (non-interacting), the variational parameters which describe the probability distribution of lattice electron system is the same. The spectra intensity increases with increase in the interaction strength and it decreases to zero when the interaction strength is made negatively large. Keywords : unit step Hamiltonian, Hubbard Hamiltonian, 3D cubic lattice, interaction strength, total energy, lattice separation.

/pdf/the-ground-state-analytical-solution-of-two-interacting-30kust2qyc.pdf

The Ground- State Analytical Solution of Two-Interacting Electrons in a Two-Dimensional Square Lattice

We present accurate numerical results for low-lying one- and two-hole states in the {ital t}-{ital J} model on a 4{times}4 lattice. We find six level crossings in the one-hole ground state for 0{lt}{ital t}/{ital J}{lt}{infinity}; accurate {ital t}/{ital J} values of these crossings and the associated ground-state quantum numbers are given. A degeneracy of {bold k}=(0,0) S=1/2, and {ital S}=3/2 one-hole levels at {ital t}/{ital J}=1/2 is noted, which is consistent with a recent analytical result. For small {ital t}/{ital J}, the {ital S}=1/2 one-hole and {ital S}=0 two-hole bandwidths on the 4{times}4 lattice are {ital W}{sub {ital h}}=(1.190 445 7(1)){ital t} and {ital W}{sub hh}=(2.575(4)){ital t}{sup 2}/{ital J}, respectively. The origin of these qualitatively different behaviors is discussed, and a simple relation is found between the small-({ital t}/{ital J}) one-hole bandwidth and a static-hole ground-state matrix element. The linear-{ital t} term in {ital W}{sub {ital h}} is apparently a finite-lattice artifact. As a measure of finite-size effects we determined the rms hole-hole separation in the two-hole ground states; we find evidence of important finite-size effects for {ital t}/{ital J}{approx gt}1, for which the rms hole-hole separation is clearly constrained by the 4{times}4 lattice. Intermediate-({ital t}/{ital J}) hole separations andmore » binding energies for 0.3{approx lt}{ital t}/{ital J}{approx lt}1, however, scale approximately as powers of {ital t}/{ital J}, and can be used to give bulk-limit estimates for {ital t}/{ital J}=3. In particular, we estimate that the bulk-limit ground-state rms hole-hole separation at {ital t}/{ital J}=3 is {approx}1.8{ital a}{sub 0}, corresponding to 7 A in the high-temperature superconductors.« less

Detailed Lanczos study of one- and two-hole band structure and finite-size effects in the t-J model

We present Monte Carlo results for the energies of static holes in the {ital t}-{ital J} model. We consider the cases of zero, one, two, and four holes on square lattices of side {ital L}=4, 6, and 8 and extrapolate these results to give estimates for the bulk limit. We find that the hole energies and finite-size effects are in good agreement with spin-wave theory. Our results are consistent with phase separation in the static limit of the {ital t}-{ital J} model, but indicate that the incorporation of long-range Coulomb repulsion between holes prevents phase separation. We find that hole pairs alone are bound for a certain range of dielectric constant {epsilon}, which is 52{lt}{epsilon}{lt}104 in the static limit of a {ital t}-{ital J}-{epsilon} model with 1/{ital r} Coulomb repulsion, given the currently accepted value of {ital J}. The large observed value of the in-plane dielectric constant of La{sub 2}CuO{sub 4}, {epsilon}=30{plus minus}3, is not far from the lower limit of this theoretical pairing range, so the {ital t}-{ital J}-{epsilon} model may provide a useful approximate description of the mechanism of hole pairing in the high-temperature superconductors. Hole Cooper pairs that act as mediators of high-temperature superconductivity may thus arisemore » from a competition between the large antiferromagnetic coupling {ital J}, which encourages hole clustering, and the {epsilon}-suppressed hole Coulomb repulsion, which restricts hole binding to pairs.« less

Static-hole energies in the t-J model and a t-J- epsilon model of the high-temperature superconductors.

We present Monte Carlo results for the band structure of the lowest-lying [ital S][sub tot]=1/2 one-hole band in the [ital t]-[ital J] model on 4[times]4 and 6[times]6 lattices. In this paper we report measurements for all [bold k] states in the small [ital t]/[ital J] regime 0[le][ital t]/[ital J][le]0.2, and extrapolate to 0[le][ital t]/[ital J][le]0.5. Our results support the conjecture that the linear-[ital t] component of the bandwidth at small [ital t]/[ital J] vanishes as [kappa]/[ital L][sup 2] in the bulk limit, as was anticipated on theoretical grounds; this implies that the propagation of isolated holes is strongly hindered by the staggered magnetization of the ground state. For this initial study we used a very simple trial wave function for importance sampling; it should be possible to obtain comparably accurate Monte Carlo results for band structure at appreciably larger [ital t]/[ital J] with improved importance sampling.

Monte Carlo study of one-hole band structure in the t-J model.

We report numerical results for the two-dimensional Hubbard model in the strong-coupling approximation, including the three-site terms omitted in the [ital t]-[ital J] model, for a 4[times]4 system with periodic boundary conditions. We study the one- and two-hole band structures, the root-mean-square hole-hole separation, and the hole-hole binding energy for both the [ital t]-[ital J] and the strong-coupling models. In the physical parameter region (8[lt][ital U]/[ital t][lt]40) believed appropriate for the high-temperature superconductors, the three-site terms enhance the hole mobility, increasing the one- and two-hole bandwidths and decreasing the binding energy, but changing the hole-hole separation only slightly; quantitative differences between the models range up to 40%. The transition (at large [ital U]/[ital t]) to the ferromagnetic Nagaoka state is sharper in the strong-coupling model; our results do not support a transition through all intermediate [ital S] values in the bulk.

M. D. Kovarik

Papers

Detailed Lanczos study of one- and two-hole band structure and finite-size effects in the t-J model

Static-hole energies in the t-J model and a t-J- epsilon model of the high-temperature superconductors.

Monte Carlo study of one-hole band structure in the t-J model.

Hubbard model in the strong-coupling approximation.