Researchers at the University of Bonn, ENSL, and the University of Salerno have demonstrated how density-assisted hopping can induce superconductivity in a system normally resistant to it. The work reveals that this hopping creates an attractive interaction within the lower energy band of dimerized lattices, overcoming onsite repulsion and potentially leading to superconductivity with a pairing structure beyond the common s-wave form. Characterizing a shift between repulsive and superconducting states, the team identified this transition as a Berezinskii-Kosterlitz-Thouless transition, mapping the phase diagram of a two-leg ladder system with both numerical and analytical methods.

Density-Assisted Hopping Induces Superconductivity in Hubbard Model

Parameters used in the modeling included a filling of n = 0.9375 and a ladder length of L = 80, demonstrating the conditions under which this transition occurs within the dimerized lattice geometry. This finding builds on work exploring the theoretical description of high critical temperature superconductivity, a central challenge in condensed matter physics, and utilizes the two-dimensional Hubbard model as a framework for understanding cuprates.

Density-assisted hopping terms, originating from the down-folding of three-band Hubbard models used to describe cuprate Cu-O planes, are key to this induced superconductivity; these terms were previously studied in the context of two-dimensional hole superconductivity to explain asymmetries between particle and hole doping. The effective attraction opens a spin gap, a step in the emergence of superconductivity, and the transition is robust across a broad range of parameters.

The resulting effective Hamiltonian describes the bonding band, where the interaction becomes attractive under specific conditions, ultimately leading to the observed superconducting phase. This robustness is supported by evidence that the values at which superconductivity appears are similar to those estimated for cuprates, strengthening the connection between the model and real-world materials.

The findings are not limited to ladder geometries; dimerized structures in two and three dimensions also yield effective Hubbard models known to host superconducting phases when interactions are attractive. In bilayer systems, density-assisted hopping between planes would create an effective attractive two-dimensional Hubbard model for the bonding band, a configuration known to support superconductivity.

Attractive Interactions in Dimers Drive Superconducting Phase Transitions

Density-assisted hopping fundamentally alters interactions within dimerized lattices, inducing attraction in the bonding band even when strong repulsive forces are present. This counterintuitive effect, demonstrated through analytical and numerical modeling, establishes a new pathway to superconductivity, potentially extending its reach beyond conventionally understood limits. The work reveals that the density-assisted hopping term acts exclusively within each energy band, creating attraction in the lower band, where electrons are more tightly bound, and repulsion in the upper band.

The transition from a normally repulsive state to a superconducting one in the studied two-leg ladder system is characterized as a Berezinskii-Kosterlitz-Thouless transition, a specific type of quantum phase transition involving the unbinding of topological defects. Researchers at the University of Bonn, ENSL, and the University of Salerno have contributed to this understanding.

The study of the two-leg ladder system utilized the matrix product states ansatz, bosonization and perturbative calculations. The findings suggest that the superconducting phase can persist to interaction strengths beyond the limits of the effective model’s validity, hinting at a potentially robust and versatile route to achieving superconductivity in diverse materials systems.

Hubbard Ladder System Characterized via Matrix Product States

Simulations utilizing matrix product states reveal this precise mechanism governing the emergence of superconductivity despite strong onsite repulsion between electrons. This finding challenges conventional understanding, demonstrating that superconductivity isn’t limited to systems with naturally attractive interactions, and opens new avenues for exploring unconventional superconducting materials. The research details how density-assisted hopping, a quantum mechanical process, fundamentally alters the electronic behavior within dimerized lattice structures like bilayers and ladders.

Analytical calculations show density-assisted hopping creates an attractive interaction specifically within the lower, bonding band of the dimer structure, while simultaneously inducing repulsion in the upper, anti-bonding band. This counterintuitive effect overcomes the inherent repulsive forces between electrons. The resulting superconducting state exhibits a pairing structure more complex than the commonly studied s-wave pairing, suggesting a more exotic and nuanced form of electron correlation.

The amplitude of density-assisted hopping required to induce this superconductivity aligns with estimates derived from studies of cuprate materials, hinting at a shared underlying mechanism. Confirming these analytical predictions, researchers employed the numerically exact matrix product states method, also known as the density matrix renormalization group algorithm, to map the phase diagram of the two-leg ladder system.

This computational approach allowed for a detailed characterization of the transition between the normally repulsive regime and the spin-gapped superconducting phase. In the repulsive regime, the system behaves as a Luttinger liquid, possessing two gapless modes and a central charge of 2, a value derived from conformal field theory.

However, the introduction of density-assisted hopping alters this behavior, effectively creating an attractive Hubbard model capable of hosting superconducting phases. This mapping to an effectively attractive model is independent of the underlying lattice geometry and also holds in the bilayer system, the researchers report. The formed superconducting pairs within the bonding band are s-wave in nature, but their representation in the original basis is more complex, comprising a superposition of on-site pairs and dimer singlets. This intricate pairing structure suggests that the superconductivity observed is a more exotic state with potentially unique properties.

Berezinskii-Kosterlitz-Thouless Transition Defines Spin-Gapped Regime

Simulations reveal that increasing the ratio of density-assisted hopping to other interactions transforms an initially repulsive interaction within the bonding band into an attractive one, ultimately leading to the emergence of superconductivity. This transition is a defined point where the system’s central charge falls below two, indicating a shift from a gapless to a spin-gapped phase.

Analysis of the inverse correlation length further confirms this transition, demonstrating a gradual opening of the spin gap consistent with a move to the spin-gapped C1S0 phase, normally known as the Luther-Emery phase. The dominance of different correlation functions, density correlations in the gapless phase shifting to pair correlations in the superconducting phase, provides a clear signature of the underlying phase change as the system evolves.

The robustness of this transition extends beyond a narrow parameter range, as the phase diagram reveals superconductivity emerging across a wide regime of density-assisted hopping values. The team found its signatures in a broader parameter regime than the stringent validity of the effective model, demonstrating the transition’s resilience even under varying conditions.

Density-Assisted Hopping Amplitude Mirrors Cuprate Systems

Density-assisted hopping within dimerized lattices induces an attractive interaction in the lower bonding band, a phenomenon mirroring observations in cuprate materials. Analytical work demonstrates this attraction arises even with existing onsite repulsion, potentially leading to unconventional superconductivity with pairing structures beyond the standard s-wave model. This effect, initially theorized to explain asymmetries in hole doping within cuprates, now receives further validation through combined numerical and analytical methods.

The applicability of this mechanism extends beyond solid-state systems, with potential for realization in ultracold-atom experiments, as the model considers dimers formed by two sites experiencing both normal and density-assisted hopping. Researchers examined Hubbard ladders and bilayer Hubbard models as examples of dimer lattices, finding the mapping to an effectively attractive model remains consistent across different lattice geometries, including bilayer systems. Matrix Product States corroborated these analytical findings for the ladder geometry, confirming the robustness of the observed effect.

The team introduced a density-assisted tunneling term where the hopping amplitude depends on the local densities of opposite spins within the dimer. The ratio, c_n, interpolates between scenarios with and without density-assisted hopping, with simulations pinpointing a transition point at n = 0.9375. The researchers report, highlighting the relevance of their findings. This band-selective interaction is a key feature of the proposed mechanism, differentiating it from simpler models of superconductivity.

Bonding and Antibonding Band Separation Impacts Filling Regimes

The separation of bonding and antibonding bands within dimerized lattices significantly alters electron filling patterns, with implications for inducing superconductivity. This counterintuitive effect, observed in both bilayers and ladder structures, fundamentally changes the energy landscape of the system and allows for the potential emergence of superconductivity with pairing structures beyond the commonly observed s-wave pairing. Examining the non-interacting case, where the onsite repulsion, U, is zero, researchers found two distinct bands shifted in energy, the bonding band lower and the antibonding band higher.

Focusing on regimes where these bands are well separated, the study demonstrates that below half-filling, where the total number of electrons is less than one per lattice site, both bands can be partially occupied. However, increased band separation results in only the bonding band remaining partially filled, a key factor in promoting the attractive interactions necessary for superconductivity.

Momentum distribution calculations confirm this behavior, showing that the antibonding band remains nearly empty, with less than 3% of fermions occupying it, while the bonding band accounts for approximately 97% of the particles. When the density-assisted hopping amplitude, t_n⊥, is positive, the bonding band experiences attraction while the antibonding band experiences repulsion. “Remarkably, these terms act exclusively as interactions within each band,” the paper states, highlighting the localized nature of this effect.

Numerical calculations of the momentum distribution support this analytical finding, revealing a jump at the Fermi momentum due to finite size effects, consistent across varying density-assisted hopping ratios. Franco T. Lisandrini, Edmond Orignac, and Roberta Citro, in conversation with the author, performed calculations on systems with L = 80, finding that with simulations pinpointing a transition point at n = 0.9375.

👉 More information
🗞 Superconductivity in the Repulsive Hubbard Model on Different Geometries Induced by Density-Assisted Hopping
✍️ Franco T. Lisandrini, Edmond Orignac, Roberta Citro, Ameneh Sheikhan and Corinna Kollath
🧠 DOI: http://link.aps.org/doi/10.1103/j7pk-khdb

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