Real-space orbital tiling approach for the design of novel superconductors

TL;DR

The paper addresses the lack of a predictive framework for discovering new superconductors by introducing the Real-space Orbital Superconducting Pathway (ROSP), a real-space orbital tiling model in which Cooper pairs form standing waves along coherent orbital pathways. ROSP unifies superconducting families by frontier orbital tilings rather than structure or electron count, and uses an isolobal analogy to connect materials like LaNiO2 and cuprates. Through a tight-binding toy model, it shows that certain orbital tilings, especially those involving dx2−y2, minimize energy and enable a superconducting state, and it provides a notation system and design heuristics to realize ROSPs in known and new lattice motifs, including anti-cuprate planes. The work also makes concrete material predictions and outlines how computational design tools could generate ROSP-consistent structures, offering a practical route toward discovering new high-Tc superconductors from real-space orbital architecture.

Abstract

Despite substantial advances in the field, we still lack a predictive framework capable of guiding the discovery of new families of superconductors. While momentum-space approaches have advanced the microscopic understanding of superconductivity, they offer limited guidance for materials design based on atomic building blocks. Here, we propose a real-space framework which conceptualizes Cooper pairs as confined standing waves resulting from coherent tilings of atomic orbitals. We call this model the Real-space Orbital Superconducting Pathway (ROSP). Using a tight-binding toy model, we show that the energetics of electron pairing depend on the configuration and overlap of real-space orbitals, which motivates \textit{a priori} design of superconducting families from orbital tiling. We connect the ROSP model to Roald Hoffmann's isolobal analogy to classify families of superconductors based on shared orbital tilings, rather than structure or electron count. As an example, we suggest that superconductivity in La$_{3}$Ni$_{2}$O$_{7}$ and LaNiO$_{2}$, despite differing structures and electron counts, may arise from a common ROSP. We introduce a new notation to classify two-dimensional square-net ROSPs and further propose several new families of superconductors on the anti-cuprate lattice. This framework provides a new model for predicting and designing families of high-T$_c$ superconductors from real-space orbital architecture, even without microscopic knowledge of the attractive pairing interaction.

Figures (11)

• Figure 1: a) Schematic illustration, in momentum space, of BCS Cooper pairing between electrons with opposite spin and momentum on a two-dimensional Fermi surface. b) Schematic of the real-space probability density for the $s$-wave symmetric Cooper pair shown in (a), where darker concentric regions indicate higher probability of finding the paired electrons.
• Figure 2: $|\Psi|^2$ linecuts and heatmaps for trivial cases without electron pairing: a) Snapshot with unfixed phase relations with randomly paired Fermi surface states $\psi_1$ and $\psi_2$. b) Snapshot with unfixed phase relations but with $\psi_1$ and $\psi_2$ Fermi surface states with equal and opposite momenta. c) Snapshot with $\psi_1$ and $\psi_2$ Fermi surface states with equal and opposite momenta, and fixed $\theta_\Delta$ within pairs, but unfixed phases between pairs. These plots demonstrate that there is no standing wave in any case where some of the phases remain random.
• Figure 3: a) Energy of a "single particle" superconducting wavefunction as a function of the fixed phase difference, $\theta_\Delta$, calculated using a tight-binding model of $s$ orbitals. Probability density of finding such a state along atomic sites with $\theta_\Delta$ = b) 0, c) $\pi/2$, d) $\pi$, where brighter coloration corresponds to higher probability
• Figure 4: a) Energy of a "single particle" superconducting wavefunction as a function of phase difference calculated using a tight-binding model of 4$s$, 3$d_{z^2}$, and 3$d_{x^2 - y^2}$ orbitals. Probability density of finding such a state along atomic sites with $\theta_\Delta = 0$ using orbitals b) 4$s$ c) 3$d_{z^2}$, d) 3$d_{x^2 - y^2}$, where brighter coloration corresponds to higher probability.
• Figure 5: (a) MX$_{2}$ structural motif plane present in perovskites and Ruddlesden-Popper materials. (b-f) Schematic ROSPs from tilings of $s$, $p$, and/or $d$ orbitals. Red dashed lines correspond to orbital overlap, with single dash as $\sigma$ and double dash as $\pi$ overlap respectively. Notation is provided to assign each ROSP a unique identifier.