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arXiv:cond-mat/9903251 · Physical review. B, Condensed matter

Superconductivity versus tunneling in a doped antiferromagnetic ladder

J. P. Rodriguez

Published Jul 1, 1999• 0 citations
arXivHTMLPDF

Abstract

The low-energy charge excitations of a doped antiferromagnetic ladder are modeled by a system of interacting spinless fermions that live on the same ladder. A relatively large spin gap is assumed to ``freeze out'' all spin fluctuations. We find that the formation of rung hole pairs coincides with the opening of a single-particle gap for charge excitations along chains and with the absence of coherent tunneling in between chains. We also find that such hole pairs condense into either a crystalline or superconducting state as a function of the binding energy.

DOI
10.1103/physrevb.60.1303

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The low-energy charge excitations of a doped antiferromagnetic ladder are modeled by a system of interacting spinless fermions that live on the same ladder. A relatively large spin gap is assumed to ``freeze out'' all spin fluctuations. We find that the formation of rung hole pairs coincides with the opening of a single-particle gap for charge excitations along chains and with the absence of coherent tunneling in between chains. We also find that such hole pairs condense into either a crystalline or superconducting state as a function of the binding energy.
A two-chain ladder model is considered that is described by the strong-coupling t - t ´- J - J ´ Hamiltonian. For the case of two holes moving in a background of antiferromagnetically interacting spins, exact, analytical results are derived for the ground-state energy and low-lying excitation spectrum. The ground state is a bound state of two holes with total spin S = 0. The charge excitation is gapless and the spin excitation has a gap. The corresponding wave functions are also exactly determined. The bound hole pair is found to have symmetry of the d-wave type. In the limit of strong rung coupling, the model maps onto an effective hard-core-boson model which exhibits dominant superconducting pairing correlations.
Abstract Conventional superconductivity emerges from pairing of charge carriers—electrons or holes—mediated by phonons 1 . In many unconventional superconductors, the pairing mechanism is conjectured to be mediated by magnetic correlations 2 , as captured by models of mobile charges in doped antiferromagnets 3 . However, a precise understanding of the underlying mechanism in real materials is still lacking and has been driving experimental and theoretical research for the past 40 years. Early theoretical studies predicted magnetic-mediated pairing of dopants in ladder systems 4–8 , in which idealized theoretical toy models explained how pairing can emerge despite repulsive interactions 9 . Here we experimentally observe this long-standing theoretical prediction, reporting hole pairing due to magnetic correlations in a quantum gas of ultracold atoms. By engineering doped antiferromagnetic ladders with mixed-dimensional couplings 10 , we suppress Pauli blocking of holes at short length scales. This results in a marked increase in binding energy and decrease in pair size, enabling us to observe pairs of holes predominantly occupying the same rung of the ladder. We find a hole–hole binding energy of the order of the superexchange energy and, upon increased doping, we observe spatial structures in the pair distribution, indicating repulsion between bound hole pairs. By engineering a configuration in which binding is strongly enhanced, we delineate a strategy to increase the critical temperature for superconductivity.
We discuss an electronic model consisting of two chains or planes, each described by a t-J model, coupled by t'-J' interactions between them. For J'\ensuremath{\sim}J or larger we show the presence of a spin-gap and hole-pair formation upon doping. The model exhibits superconducting pairing correlations away from half filling. We support our claims by numerical studies of the spin gap, the binding energy of holes, and the pairing correlations on finite clusters. The hole-pairing operator is a spin singlet with one member of the pair in each chain or plane. Our model belongs to the universality class of the U0 Hubbard model with \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\gg}t. We argue that this model may be physically realized by doping the orthorhombic compound (VO)2{)}_{2})2​P2{\mathrm{P}}_{2}P2​O7{\mathrm{O}}_{7}O7​.
The spin and charge excitations of the t-J ladder are studied by exact diagonalization techniques for several electron densities. The various modes are classified according to their spin (singlet or triplet excitations) and their parity under a reflection with respect to the symmetry axis along the chains and a finite-size scaling of the related gaps is performed. At low doping, formation of hole pairs leads to a spin gap for all J/t ratios. This phase is characterized by (at least) one vanishing energy mode only in the charge bonding channel when Kx{\mathit{K}}_{\mathit{x}}Kx​\ensuremath{\rightarrow}0 consistent with the existence of superconducting pairing correlations. At larger doping the spin gap disappears. Although the antibonding modes remain gapped, low-energy Kx{\mathit{K}}_{\mathit{x}}Kx​\ensuremath{\sim}0 and Kx{\mathit{K}}_{\mathit{x}}Kx​\ensuremath{\sim}2kF{\mathit{k}}_{\mathit{F}}kF​ spin and charge bonding modes are found consistent with a single-band Luttinger scenario. At sufficient low electron density and above a critical value of J/t we also expect another phase of electron pairs with gapped spin excitations.
A proper theoretical description of doped antiferromagnets is until now an unresolved issue. In this work we study chain and ladder systems, and in particularly we focus on the physically most interesting two leg ladder. Our starting point is the Spin Fermion model in which an antiferromagnetic background of localized spins interacts with mobile holes via a rotation invariant Kondo-like term. The interesting region of the phase diagram is that close to the Mott-insulator transition where the doping delta is zero. At zero doping in fact the system is an insulator and the spins organize themselves in a spin liquid, a rotational invariant state characterized by a finite correlation length and an energy gap (a spin gap) above the ground state. Such a state is also the ground state of a field theory, the non linear sigma model (NLsigmaM) which is recognized as the low energy effective theory for antiferromagnetic spin ladder. The first question we answer is how such a spin state evolves as one moves off from the Mott phase by increasing the doping. Integrating out the fermions in our model we obtain an effective theory for the spins which we are able to evaluate in the continuum limit. The effective theory is again a NLsigmaM with coupling constants which depend on the concentration of dopant holes. In contrast to existing mean field calculation our theory predicts a lowering of the spin gap with doping and a consequent increase in the correlation length. Indeed a lowering of the spin gap due to doping is also observed in numerical simulation and on NMR experiments on $Sr14-xCaxCu24O41 with which we obtain very good agreement. Secondly we concentrated on the behavior of the fermions. The general paradigm of interacting fermions in one dimension is that of the Luttinger Liquid characterized by bosonic excitations and spin charge separation. By generalizing our approach we are able to access the one particle fermion propagator as a quantity averaged over the NLsigmaM which controls the spin background. We see that in the limit of zero doping the quasiparticle weight Z is non-zero in a neighborhood of the Fermi energy. This in turn implies that the Luttinger liquid parameter Krho goes to one as the doping delta goes to zero as was first argued by Schulz. Our stronger result allows us to assert that in the very low doping regime the fermions constitute a Fermi liquid.
A simple interlayer pair tunneling is solved exactly. We find that in the normal state spin-1/2 particle and hole excitations are gapped. But the state is an unusual metal, characterized by novel fermionic spin zero and charge +2e and -2e excitations that exist about their own Fermi surfaces. The model is consistent with a number of properties of the underdoped cuprates. At finite temperature the Fermi surface appears partially gapped, and at high temperatures the spin gap disappears completely. Superconductivity is induced by an additional intralyer interaction which opens a gap in the charge-fermion spectrum. The symmetry of this charge gap (and hence that of the order parameter) is igenerally different from the symmetry of one-electron or - hole gap. The former can be a d wave, while the latter is more complex.