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arXiv:cond-mat/9909128 · Physical Review Letters

Metallic Stripe in Two Dimensions: Stability and Spin-Charge Separation

A. L. Chernyshev, A. H. Castro Neto, A. R. Bishop

Published May 22, 2000• 63 citations
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Abstract

The problems of charge stripe formation, spin-charge separation, and stability of the antiphase domain wall (ADW) associated with a stripe are addressed using an analytical approach to the t- J(z) model. We show that a metallic stripe together with its ADW is the ground state of the problem in the low doping regime. The stripe is described as a system of spinons and magnetically confined holons strongly coupled to the two dimensional spin environment with holon-spin-polaron elementary excitations filling a one-dimensional band.

DOI
10.1103/physrevlett.84.4922

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The problems of charge stripe formation, spin-charge separation, and stability of the antiphase domain wall (ADW) associated with a stripe are addressed using an analytical approach to the t- J(z) model. We show that a metallic stripe together with its ADW is the ground state of the problem in the low doping regime. The stripe is described as a system of spinons and magnetically confined holons strongly coupled to the two dimensional spin environment with holon-spin-polaron elementary excitations filling a one-dimensional band.
We attempt to access the regime of strong coupling between charge carriers and transverse dynamics of an isolated conducting ``stripe,'' such as those found in cuprate superconductors. A stripe is modeled as a partially doped domain wall in an antiferromagnet (AF),(\mathrm{AF}),(AF), introduced in the context of two different models: the $t\ensuremath{-}J$ model with strong Ising anisotropy, and the Hubbard model in the Hartree-Fock approximation. The domain walls with a given linear charge density are supported artificially by boundary conditions. In both models we find a regime of parameters where doped holes lose their spin and become holons (charge Q=1,Q=1,Q=1, spin S3=0),{S}_{3}=0),S3​=0), which can move along the stripe without frustrating AF environment. One aspect in which the holons on the AF domain wall differ from those in an ordinary one-dimensional electron gas is their transverse degree of freedom: a mobile holon always resides on a transverse kink (or antikink) of the domain wall. This gives rise to two holon flavors and to a strong coupling between doped charges and transverse fluctuations of a stripe.
To study a possible effect of transverse fluctuations of a stripe in a 2D antiferromagnet on its charge dynamics, we identify elementary excitations of a weakly doped domain wall in the Hubbard model. Hartree-Fock numerics and analysis of fermion zero modes suggest that for U>=3t charged excitations are mobile holons, Q=1, S=0. Each holon resides on a kink in the position of the domain wall. We construct a simple model in which transverse stripe dynamics is induced solely by motion of the holons. In the absence of spin excitations (spinons, Q=0, S=1/2), stripe fluctuations DO NOT suppress a tendency to form a global charge-density order.
Spinless fermions on a lattice with nearest-neighbor repulsion serve as a toy-version Hubbard model and have a symmetry-broken even/odd superlattice at half filling. At infinite repulsion, doped holes form charged stripes that are antiphase walls ( as noted by Mila [Phys. Rev. B 49,49,49, 14 047 (1994)]). Exact-diagonalization data for systems up to 36 sites around 1/4 filling, and also for one or two holes added to a stripe of length up to 12, indicate stability of the stripe-array state against phase separation. In the boson version of the model, the same behavior can be stabilized by addition of a term with four creation/annihilation operators.
We consider a Hubbard-like model of strongly interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls between ordered domains) are a favorable way to dope this system below half filling. The problem of a single stripe can be mapped to fermions in one dimension, which allows understanding of its elementary excitations and calculation of the stripe's effective mass for transverse vibrations. Using Lanczos exact diagonalization, we investigate the excitation gap and dispersion of a hole on a stripe, and the interaction of two holes. We also study the interaction of a few stripes, finding that they repel and the interaction energy decays with stripe separation as if they are hardcore particles moving in one (transverse) direction. To determine the stability of an array of stripes against phase separation into a particle-rich phase and a hole-rich liquid, we evaluate the liquid's equation of state, finding that the stripe-array is not stable for bosons but is possibly stable for fermions.
The dualism between superconductivity and charge/spin modulations (the so-called stripes) dominates the phase diagram of many strongly-correlated systems. A prominent example is given by the Hubbard model, where these phases compete and possibly coexist in a wide regime of electron dopings for both weak and strong couplings. Here, we investigate this antagonism within a variational approach that is based upon Jastrow-Slater wave functions, including backflow correlations, which can be treated within a quantum Monte Carlo procedure. We focus on clusters having a ladder geometry with M M legs (with M M ranging from 2 2 to 10 10 ) and a relatively large number of rungs, thus allowing us a detailed analysis in terms of the stripe length. We find that stripe order with periodicity \lambda=8 λ = 8 in the charge and 2\lambda=16 2 λ = 16 in the spin can be stabilized at doping \delta=1/8 δ = 1 / 8 . Here, there are no sizable superconducting correlations and the ground state has an insulating character. A similar situation, with \lambda=6 λ = 6 , appears at \delta=1/6 δ = 1 / 6 . Instead, for smaller values of dopings, stripes can be still stabilized, but they are weakly metallic at \delta=1/12 δ = 1 / 12 and metallic with strong superconducting correlations at \delta=1/10 δ = 1 / 10 , as well as for intermediate (incommensurate) dopings. Remarkably, we observe that spin modulation plays a major role in stripe formation, since it is crucial to obtain a stable striped state upon optimization. The relevance of our calculations for previous density-matrix renormalization group results and for the two-dimensional case is also discussed.
We present the charge and magnetization density distribution in various stripe phases obtained for two-dimensional models of correlated electrons solved within the Hartree-Fock approximation and a variational local ansatz. Apart from the Hubbard model with local Coulomb interaction U, we investigate its two extensions by adding either static Peierls electron-lattice coupling, or the correlated hopping term in the so-called Hirsch model. It has been found that the stripe ordering is robust and occurs in underdoped $(\ensuremath{\delta}=1/8)$ and overdoped $(\ensuremath{\delta}=1/4)$ systems. At intermediate values of U in underdoped systems $(\ensuremath{\delta}=1/8)$ local correlations stabilize the vertical (01) antiferromagnetic domains, separated by nonmagnetic domain walls filled by one doped hole per two wall atoms. A stripe phase with the same size of magnetic domains and an increased filling of one hole per one wall atom is stable for overdoped $(\ensuremath{\delta}=1/4)$ systems. At larger values of U, both structures are replaced by more extended magnetic domain walls oriented along the (11) direction. These findings agree qualitatively with the experimental results.