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arXiv:0711.3075 · Physical Review Letters

Dimensional Tuning of Electronic States under Strong and Frustrated Interactions

Chisa Hotta, Frank Pollmann

Published May 8, 2008• 11 citations
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Abstract

We study a model of strongly interacting spinless fermions on an anisotropic triangular lattice. At half-filling and the limit of strong repulsive nearest-neighbor interactions, the fermions align in stripes and form an insulating state. When a particle is doped, it either follows a one-dimensional free motion along the stripes or fractionalizes perpendicular to the stripes. The two propagations yield a dimensional tuning of the electronic state. We study the stability of this phase and derive an effective model to describe the low-energy excitations. Spectral functions are presented which can be used to experimentally detect signatures of the charge excitations.

DOI
10.1103/physrevlett.100.186404

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We study a model of strongly interacting spinless fermions on an anisotropic triangular lattice. At half-filling and the limit of strong repulsive nearest-neighbor interactions, the fermions align in stripes and form an insulating state. When a particle is doped, it either follows a one-dimensional free motion along the stripes or fractionalizes perpendicular to the stripes. The two propagations yield a dimensional tuning of the electronic state. We study the stability of this phase and derive an effective model to describe the low-energy excitations. Spectral functions are presented which can be used to experimentally detect signatures of the charge excitations.
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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.
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 study ground state properties and particle excitation spectra across a commensurate charge density wave transition in a system of strongly interacting fermions, using series expansion methods and mean-field theory. We consider a 1/3-filled system of spinless fermions on a triangular lattice, with hopping parameter ttt, nearest-neighbor repulsion VVV, and a sublattice dependent chemical potential ${\ensuremath{\mu}}_{s}$. The phase transition is found to be first order for ${\ensuremath{\mu}}_{s}=0$, but becomes continuous with increasing ${\ensuremath{\mu}}_{s}$. The particle and hole excitation spectra exhibit dramatic changes in the vicinity of the phase transitions and in the charge density wave ordered phase. We discuss the relevance of this study to the pinball Fermi liquid phase postulated theoretically in earlier studies as well as to various strongly correlated triangular lattice materials.
Abstract We study competing orders of spinless fermions in the triangular-lattice Hubbard model with nearest-neighbor interaction. We calculate the effective, momentum-resolved two-particle vertex in an unbiased way in terms of the functional renormalization group method and compare two different schemes for the momentum discretization, one based on dividing the Fermi surface into patches and one based on a channel decomposition. We study attractive and repulsive nearest-neighbor interaction and find a competition of pairing and charge instabilities. In the attractive case, a Pomeranchuk instability occurs at Van Hove filling and f-wave and p-wave pairing emerge when the filling is reduced. In the repulsive case, we obtain a charge density wave at Van Hove filling and extended p-wave pairing with reduced filling. The p-wave pairing solution is doubly degenerate and can realize chiral p+ipp+ipp+ip p + i p superconductivity with different Chern numbers in the ground state. We discuss implications for strongly correlated spin-orbit coupled hexagonal electron systems such as moiré heterostructures. Graphic Abstract