Modeling of superconducting stripe phases in high-Tc cuprates

F Loder,M Schmid,A P Kampf,T Kopp,S Graser

doi:10.1088/1367-2630/13/11/113037

Abstract

Even before the experimental discovery of spin- and charge-stripe order in La2−x−yNdySrxCuO4 and La2−xBaxCuO4 at x = 1/8, stripe formation was predicted from theoretical considerations. Nevertheless, a consistent description of the complex coexistence of stripe order with superconductivity has remained a challenge. Here we introduce a Hartree–Fock decoupling scheme that unifies previous approaches and allows for a detailed analysis of the competition between antiferromagnetism and superconductivity in real and momentum space. We identify two distinct parameter regimes, where spin-stripe order coexists with either one- or two-dimensional superconductivity; experiments on different striped cuprates are compatible with either the former or the latter regime. We argue that the cuprates at x = 1/8 fall into an intermediate coupling regime with a crossover to long-range phase coherence between individual superconducting stripes.

Highlights

Dynamics of such systems has been explained quite successfully using models of coupled spin ladders [13,14,15], their microscopic origin has remained unresolved within this ansatz, and superconductivity was not incorporated
We have explored how far a mean-field approach of the t–J model and of closely related models can assist our understanding of static spin- and charge-stripe order observed in underdoped cuprates in coexistence with superconductivity
For hole doping x = 1/8 the free energy is minimized by an SDW order with wavelength λ = 8a with concomitant charge density wave (CDW) order with λ = 4a, which agrees with neutron and x-ray scattering experiments for, e.g., La15/8Ba1/8CuO4 or La15/8−yNdySr1/8CuO4

Summary

The t–Jmodel

If a multi-band Hubbard model is mapped onto the t–J model, the superexchange terms lead to a finite and sizable J and to AF order even in the limit of a large intra-orbital U [47] Antiferromagnetism is in this case controlled by. Note that the last term V s ni,−s c†j,s c j,s in (10), which appears identically in HMF , t − Jis absent in the classical BCS theory, because in a homogeneous system it only renormalizes the chemical potential μ used to control the particle number (see section 3) It is, a source of AF order in the nearest-neighbor pairing model HUV. Within the V -model, a finite U -term can be added without a significant influence on the groundstate solution, since the V -term alone is sufficient to drive the AF order parameter close to its maximum

The Bogoliubov–de Gennes equations

Comment on energy minimization

The U -model

The V -model

Temperature dependence

Conclusions