Unconventional Pairing in Flat-Band Systems Advances Correlated Electron Physics Insights

The emergence of unconventional pairing in flat bands attracts growing interest, particularly in materials exhibiting strong interactions between electrons, such as those found in Moiré structures. J. P. Mendonça, S. Biswas, and M. Dziurawiec, alongside U. Bhattacharya, K. Jachymski, and M. Aidelsburger, investigate this phenomenon using a simplified model, a ladder-like system of interacting fermions. Their work reveals that artificially flattening the electronic band structure promotes non-standard behaviour, violating established principles of electron behaviour and fostering the development of unusual pairing correlations. Importantly, the team demonstrates that this pairing can arise through different mechanisms, creating a competition between distinct pairing channels and highlighting how the geometry of electronic bands fundamentally influences the formation of these interactions, offering insights applicable to diverse systems from ultracold atoms to solid-state materials.

Fermi-Hubbard Ladder Spectral Function and Analysis

Scientists investigate the emergence of unconventional pairing in strongly interacting fermions using a simplified ladder-like system, a model for understanding complex material behaviour. Their work reveals that artificially flattening the electronic band structure promotes non-standard behaviour, violating established principles of electron behaviour and fostering the development of unusual pairing correlations. Importantly, the team demonstrates that this pairing can arise through different mechanisms, creating a competition between distinct pairing channels and highlighting how the geometry of electronic bands fundamentally influences the formation of these interactions, offering insights applicable to diverse systems from ultracold atoms to solid-state materials.

Band Flattening Drives Unconventional Pairing in Fermions

Scientists investigated the emergence of unconventional pairing in strongly repulsive fermions confined to a ladder geometry, a simplified model for exploring complex material behaviour. The study centers on how band flattening, achieved through the introduction of a diagonal hopping term, influences the system’s electronic properties and promotes non-Fermi liquid behaviour. Researchers employed a numerical approach to analyze the system’s response to varying interaction strengths, and the strength of the diagonal hopping, meticulously tracking shifts in singular momenta and the disappearance of a well-defined Fermi surface, key indicators of a transition away from conventional metallic behaviour.

The team analyzed the spectral function, a measure of electron energy and momentum, to characterize the different phases, specifically focusing on the opening of an energy gap at a momentum coinciding with the peak of density fluctuations. Observations revealed that the onset of this gap correlated with the violation of Luttinger’s theorem, a fundamental principle of Fermi liquid theory. Detailed analysis revealed a transition between phases exhibiting distinct spectral features, differentiated by the strength of interactions.

To further differentiate these phases, scientists calculated the singlet-pairing density matrix, a quantity sensitive to the formation of Cooper pairs, excluding local contributions to avoid spurious signals. They focused on two d-wave pairing channels, defined by the spatial arrangement of paired electrons, demonstrating that the diagonal channel exhibits an exponential decay transitioning to algebraic behaviour in a strong non-Fermi liquid regime, indicative of quasi-long-range order. Conversely, the axial channel displays a slow decay at moderate interactions, shifting to a faster decay in both the Fermi-liquid and strong non-Fermi liquid phases, allowing for clear distinction between the phases and their pairing symmetries.

Ladder Material Exhibits Non-Fermi Liquid Behaviour

Scientists demonstrate that flattening of electronic bands in a ladder-like material induces non-Fermi liquid behaviour and unconventional pairing correlations, revealing a competition between different pairing mechanisms. The research team investigated strongly repulsive fermions on a ladder structure, a simplified model for exploring unconventional superconductivity, and discovered that introducing a diagonal hopping term flattens the lower energy band, leading to a breakdown of standard Fermi liquid theory. This violation of Luttinger’s theorem, a fundamental principle governing the behaviour of electrons in metals, is a key indicator of the emergence of novel quantum states.

Experiments revealed that increasing the strength of a ring-exchange interaction further drives the system into a non-Fermi liquid regime, as evidenced by the disappearance of a well-defined Fermi surface in momentum distribution measurements. Specifically, a sharp qualitative change in the momentum distribution occurs with increasing interaction, shifting peaks abruptly to incommensurate momenta and demonstrating a strong violation of the Luttinger theorem. Measurements of the derivative of the momentum distribution with respect to momentum confirm these transitions, showing a clear shift in peak positions and a disappearance of the Fermi surface at higher interaction strengths.

Analysis of the spectral function further supports these findings, revealing a gap opening in distinct non-Fermi liquid regimes, and providing data relevant to experimental techniques such as inelastic neutron scattering, resonant inelastic x-ray scattering, and angle-resolved photoemission spectroscopy. The work establishes how band geometry can enhance fermionic pairing in ladder systems and offers insights applicable to ultracold atoms, quantum dot arrays, and strongly correlated materials.

Geometry Drives Unconventional Electron Pairing

This research demonstrates that manipulating the geometry of electronic bands in materials can induce unconventional pairing between electrons, a phenomenon with implications for understanding correlated electron systems. By studying strongly interacting fermions on a ladder-like structure, scientists have shown that flattening the lower energy band, achieved through diagonal hopping or ring exchange interactions, leads to non-Fermi liquid behaviour. This is evidenced by a violation of the established Luttinger theorem, which normally governs the behaviour of electrons in metals, and the emergence of axial pairing correlations.

The team identified two distinct mechanisms for violating the Luttinger theorem, ranging from a subtle reshaping of the Fermi surface to a more dramatic disruption, and linked these to different pairing symmetries, specifically, dx2−y2 and dxy wave pairings. Analysis of the momentum distribution and spectral function revealed a gap opening coinciding with the onset of this non-Fermi liquid behaviour, providing a clear signature of the transition. While the current study focuses on a simplified model, the findings offer broadly relevant insights applicable to diverse systems including ultracold atoms and strongly interacting solids.

The authors acknowledge that their model is a minimal representation of complex materials and does not capture all possible interactions. Future research directions include exploring the impact of these findings in more realistic material settings and investigating the potential for observing these predicted phases using experimental techniques such as inelastic neutron scattering, resonant inelastic x-ray scattering, and angle-resolved photoemission spectroscopy. These advancements promise a deeper understanding of correlated flat-band systems and the emergence of unconventional superconductivity.