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arXiv:1705.08780 · Physical review. B./Physical review. B

Pairing tendencies in a two-orbital Hubbard model in one dimension

N. D. Patel, Alberto Nocera, Gonzalo Álvarez, Adriana Moreo, Elbio R. Dagotto

Published Jul 31, 2017• 30 citations
arXivHTMLPDF

Abstract

The recent discovery of superconductivity under high pressure in the ladder compound ${\mathrm{BaFe}}_{2}{\mathrm{S}}_{3}$ has opened a new field of research in iron-based superconductors with focus on quasi-one-dimensional geometries. In this publication, using the density matrix renormalization group technique, we study a two-orbital Hubbard model defined in one-dimensional chains. Our main result is the presence of hole binding tendencies at intermediate Hubbard $U$ repulsion and robust Hund coupling ${J}_{H}/U=0.25$. Binding does not occur either in weak coupling or at very strong coupling. The pair-pair correlations that are dominant near half-filling, or of similar strength as the charge and spin correlation channels, involve hole-pair operators that are spin singlets, use nearest-neighbor sites, and employ different orbitals for each hole. The Hund coupling strength, presence of robust magnetic moments, and antiferromagnetic correlations among them are important for the binding tendencies found here.

DOI
10.1103/physrevb.96.024520

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The recent discovery of superconductivity under high pressure in the ladder compound BaFe2S3{\mathrm{BaFe}}_{2}{\mathrm{S}}_{3}BaFe2​S3​ has opened a new field of research in iron-based superconductors with focus on quasi-one-dimensional geometries. In this publication, using the density matrix renormalization group technique, we study a two-orbital Hubbard model defined in one-dimensional chains. Our main result is the presence of hole binding tendencies at intermediate Hubbard UUU repulsion and robust Hund coupling JH/U=0.25{J}_{H}/U=0.25JH​/U=0.25. Binding does not occur either in weak coupling or at very strong coupling. The pair-pair correlations that are dominant near half-filling, or of similar strength as the charge and spin correlation channels, involve hole-pair operators that are spin singlets, use nearest-neighbor sites, and employ different orbitals for each hole. The Hund coupling strength, presence of robust magnetic moments, and antiferromagnetic correlations among them are important for the binding tendencies found here.
Using the Density Matrix Renormalization Group and two-leg ladders, we investigate an electronic two-orbital Hubbard model including plaquette-diagonal hopping amplitudes. Our goal is to search for regimes where charges added to the undoped state form pairs, presumably a precursor of a superconducting state. For the electronic density $\ensuremath{\rho}=2$, i.e., the undoped limit, our investigations show a robust $(\ensuremath{\pi},0)$ antiferromagnetic ground state, as in previous investigations. Doping away from $\ensuremath{\rho}=2$ and for large values of the Hund coupling JJJ, a ferromagnetic region is found to be stable. Moreover, when the interorbital on-site Hubbard repulsion is smaller than the Hund coupling, i.e., for ${U}^{\ensuremath{'}}<J$ in the standard notation of multiorbital Hubbard models, our results indicate the coexistence of pairing tendencies and ferromagnetism close to $\ensuremath{\rho}=2$. These results are compatible with previous investigations using one-dimensional systems. Although further research is needed to clarify if the range of couplings used here is of relevance for real materials, such as superconducting heavy fermions or pnictides, our theoretical results address a possible mechanism for pairing that may be active in the presence of short-range ferromagnetic fluctuations.
Abstract We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our ansatz is an optimized linear superposition of Affleck–Kennedy–Lieb–Tasaki valence-bond states, rendering the combination a valence-bond liquid dubbed orbital resonant valence bond. We show that the undoped (one-electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer chains defines our variational state visualized geometrically expressing our chain as a two-leg ladder, with one orbital per leg. As in Anderson’s resonating valence-bond state, our undoped variational state contains preformed singlet pairs that via doping become mobile, leading to superconductivity. Doped real materials with one-dimensional substructures, two near-degenerate orbitals, and intermediate Hubbard U/W strengths—W the carrier’s bandwidth—could realize spin-singlet pairing if on-site anisotropies are small. If these anisotropies are robust, spin-triplet pairing emerges.
Motivated by high-temperature superconductivity in pressurized La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​, we investigate the pair correlations in the two-orbital Hubbard ladder, which consists of the nearly half-filled and nearly quarter-filled orbitals. By employing the density matrix renormalization group method, we demonstrate that the pair correlation exhibits a power-law decay against the distance while the spin correlation decays exponentially. The decay exponent of the pair correlation of the nearly half-filled orbital is comparable to the exponent of the quasi-long-range superconducting correlation in the doped single-orbital Hubbard ladder, which suggests the importance of the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbital in La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​.
We investigate the pairing tendencies in the hole-doped Haldane spin-1 chain. To allow for doping, we extend the original spin chain Hamiltonian into a fermionic model involving a two-orbital Hubbard chain at intermediate or strong repulsive interaction strengths UUU and for degenerate orbitals. At half filling and large UUU, the ferromagnetic Hund's coupling, JH{J}_{\mathrm{H}}JH​, generates effective spin-1 moments, with antiferromagnetic correlations between sites. Using large-scale density matrix renormalization group calculations, we accurately study the system's behavior under light hole-doping. For U=1.6U=1.6U=1.6 in units of the noninteracting bandwidth and for ${J}_{\mathrm{H}}/U\ensuremath{\gtrsim}0.275$, we find that singlet pairing dominates the long-distance physics, establishing this system as a promising platform for repulsively mediated superconductivity. We provide concrete examples of materials that could realize the physics described here. We also provide evidence that the system approaches a Luther-Emery liquid state at large system sizes, reminiscent of the behavior of doped one-orbital two-leg ladders at weak coupling, which also have superconducting tendencies. The numerically calculated central charge approaches one in the thermodynamic limit, indicating a single gapless mode as is expected for the Luther-Emery state. Exponents characterizing the power-law decays of singlet pair-pair and charge density-density correlations are determined, and found to approximately satisfy the Luther-Emery identity.
The recent detailed study of quasi-one-dimensional iron-based ladders, with the 3d3d3d iron electronic density n=6n=6n=6, has unveiled surprises, such as orbital-selective phases. However, similar studies for n=6n=6n=6 iron chains are still rare. Here a three-orbital electronic Hubbard model was constructed to study the magnetic and electronic properties of the quasi-one-dimensional n=6n=6n=6 iron chain Ce2O2FeSe2{\mathrm{Ce}}_{2}{\mathrm{O}}_{2}\mathrm{Fe}{\mathrm{Se}}_{2}Ce2​O2​FeSe2​, with focus on the effect of doping. Specifically, introducing the Hubbard UUU and Hund JH{J}_{H}JH​ couplings and studying the model via the density matrix renormalization group, we report the ground-state phase diagram varying the electronic density away from n=6n=6n=6. For the realistic Hund coupling JH/U=1/4{J}_{H}/U=1/4JH​/U=1/4, several electronic phases were obtained, including a metal, orbital-selective Mott, and Mott insulating phases. Doping away from the parent phase, the competition of many tendencies leads to a variety of magnetic states, such as ferromagnetism, as well as several antiferromagnetic and magnetic ``block'' phases. In the hole-doping region, two different interesting orbital-selective Mott phases were found: OSMP1 (with one localized orbital and two itinerant orbitals) and OSMP2 (with two localized orbitals and one itinerant orbital). Moreover, charge disproportionation phenomena were found in special doping regions. We argue that our predictions can be tested by simple modifications in the original chemical formula of Ce2O2FeSe2{\mathrm{Ce}}_{2}{\mathrm{O}}_{2}\mathrm{Fe}{\mathrm{Se}}_{2}Ce2​O2​FeSe2​.
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​.