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arXiv:cond-mat/0208383 · Physical Science International Journal

Kinetic Energy Driven Stripe Formation and Pairing in Repulsive Electronic Systems

M Bosch, Zohar Nussinov

Published Jan 10, 2016• 1 citation
arXivHTMLPDF

Abstract

We study repulsive Hubbard and t-J type systems on a square lattice (long believed to capture certain quintessential aspects of the high temperature superconductors). These models (alongside the parent compounds of the high temperature superconductors) are antiferromagnetic in the absence of hole doping. As we illustrate, a unifying underlying principle for the dynamics of holes introduced by doping rationalizes the emergence of nonuniform electronic structures- "stripes" and possible pairing tendencies therein. Specifically, our analysis invokes the following (numerically verified) sublattice parity principle: a strong antiferromagnetic background forces injected holes to hop in steps of two such that they always remain on the same sub lattice. When applied to a domain wall in an antiferromagnet, this simple principle naturally gives rise to (bond centered) stripes. We demonstrate that the holes are self-consistently localized on stripes. Extending this picture, we then show that the holes on a stripe favor the formation of pairs on neighboring rungs or sites. Throughout this work much emphasis is placed on the problem of a two leg ladder immersed in a staggered magnetic field. Although we will focus on the square lattice, our considerations may be extended to similar electronic structures appearing in other models on bipartite lattices when these exhibit antiferromagnetic correlations with an underlying sublattice structure.

DOI
10.9734/psij/2016/24117

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We study repulsive Hubbard and t-J type systems on a square lattice (long believed to capture certain quintessential aspects of the high temperature superconductors). These models (alongside the parent compounds of the high temperature superconductors) are antiferromagnetic in the absence of hole doping. As we illustrate, a unifying underlying principle for the dynamics of holes introduced by doping rationalizes the emergence of nonuniform electronic structures- "stripes" and possible pairing tendencies therein. Specifically, our analysis invokes the following (numerically verified) sublattice parity principle: a strong antiferromagnetic background forces injected holes to hop in steps of two such that they always remain on the same sub lattice. When applied to a domain wall in an antiferromagnet, this simple principle naturally gives rise to (bond centered) stripes. We demonstrate that the holes are self-consistently localized on stripes. Extending this picture, we then show that the holes on a stripe favor the formation of pairs on neighboring rungs or sites. Throughout this work much emphasis is placed on the problem of a two leg ladder immersed in a staggered magnetic field. Although we will focus on the square lattice, our considerations may be extended to similar electronic structures appearing in other models on bipartite lattices when these exhibit antiferromagnetic correlations with an underlying sublattice structure.
Antiferromagnetism and superconductivity are often viewed as competing orders in correlated electron systems. Here, we demonstrate that kinetic frustration in hole motion facilitates their coexistence within the square-lattice repulsive Hubbard model. Combining exact analytical solutions on tailored geometries with large-scale numerical simulations, we reveal a robust pairing mechanism: Holes on opposite sublattices behave as if they carry opposite effective charges due to spin singlet formation from kinetic frustration. This emergent property suppresses phase separation and fosters a coherent [Formula: see text]-wave superconducting channel embedded within a long-range antiferromagnetic background. Our findings establish a minimal yet broadly applicable framework for stabilizing strong-coupling superconductivity in doped Mott insulators.
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.
Abstract Doped quantum magnets, especially spin liquids with fractionalized excitations, have long attracted attention as a promising path towards unconventional superconductivity. We investigate the hole-doped Kitaev-Heisenberg ( t – J – K ) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We consider the behavior of the antiferromagnetic Kitaev spin-liquid phase as a function of hopping strength t and doping level. This reveals intriguing pairing tendencies only for tK≲0.65\frac{t}{K}\lesssim 0.65Kt​≲0.65 t K ≲ 0.65 , consistent with prior results on three-leg ladders, and firmly supports the emerging picture that the physics of doped Kitaev spin liquids strongly depends on the kinetic energy of the doped holes. Analysis of one- and two-hole doping uncovers close links between spatial profiles of the plaquette operator and the charge density. We also construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions and intermediate hopping t = 1. Upon doping, the rung-singlet region develops dominant superconducting correlations. Spin-density wave-like behavior is found in the Kitaev limits, and in the stripy phase.
We study kinetic magnetism for the Fermi-Hubbard models in triangular type lattices, including a zigzag ladder, four- and six-legged triangular cylinders and a full two-dimensional triangular lattice. We focus on the regime of strong interactions, U≫tU\gg tU≫t and filling factors around one electron per site. For temperatures well above the hopping strength, the Curie-Weiss form of the magnetic susceptibility suggests effective antiferromagnetic correlations for systems that are hole doped with respect to ν=1ν=1ν=1, and ferromagnetic correlations for systems with electron dopings. We show that these correlations arise from magnetic polaron dressing of charge carrier propagating in a spin incoherent Mott insulator. Effective interactions corresponding to these correlations can strongly exceed the magnetic super-exchange energy. In the case of hole doping, antiferromagnetic polarons originate from kinetic frustration of individual holes in a triangular lattice. In the case of electron doping, Nagaoka type ferromagnetic correlations are induced by propagating doublons. These results provide a theoretical explanation of recent experimental results in moire TMDC materials. To understand many-body states arising from antiferromagentic polarons at low temperatures, we study hole doped systems in finite magnetic fields. At low dopings and intermediate magnetic fields we find a magnetic polaron phase, separated from the fully polarized state by a metamagnetic transition. With decreasing magnetic field the system shows a tendency to phase separate, with hole rich regions forming antiferromagnetic spinbags. We demonstrate that direct observations of magnetic polarons in triangular lattices can be achieved in experiments with ultracold atoms, which allow measurements of three point hole-spin-spin correlations.
It is shown, using asymptotically exact methods, that the two-dimensional repulsive Hubbard model with strongly modulated interactions exhibits ``high-temperature superconductivity.'' Specifically, the explicit modulation, which has the same symmetry as period 4 bond-centered stripes, breaks the system into an alternating array of more and less heavily hole-doped, nearly decoupled two-leg ladders. It is shown that this system exhibits a pairing scale determined by the spin gap of the undoped two-leg ladder, and a phase ordering temperature proportional to a low positive power of the interladder coupling.
Using numerical results from density matrix renormalization group (DMRG) calculations for the t-J model, on systems as large as 10\ifmmode\times\else\texttimes\fi{}7, we examine the structure of the one and two hole ground states in ladder systems and in two dimensional clusters. A simple theoretical framework is used to explain why holes bind in pairs in two-dimensional antiferromagnets. For the case J/t=0.5, which we have studied, the hole pairs reside predominantly on a 2\ifmmode\times\else\texttimes\fi{}2 core plaquette with the probability that the holes are on diagonal sites greater than nearest-neighbor sites. There is a strong singlet bond connecting the spins on the two remaining sites of the plaquette. We find that a general characteristic of dynamic holes in an antiferromagnet is the presence of frustrating antiferromagnetic bonds connecting next-nearest-neighbor sites across the holes. Pairs of holes bind in order to share the frustrating bonds. At low doping, in addition to hole pairs, there are two additional low-energy structures which spontaneously form on certain finite systems. The first is an undoped L\ifmmode\times\else\texttimes\fi{}2 spin-liquid region, or ladder. The second is a hole moving along a one dimensional chain of sites. At higher doping we expect that hole pairing is always favored.