Cuprate Twistronics for Quantum Hardware

TL;DR

This review surveys over three decades of cuprate twistronics, connecting experimental advances in atomically thin cuprate films and cryogenic stacking with theoretical insights on Andreev processes, topological superconductivity, and disorder in twisted $d$-wave systems. It outlines how intrinsic Josephson junctions and cryogenic stacking enable controlled twist angles and clean interfaces, and presents a coherent framework for emergent phenomena near 45°, including second-harmonic Josephson coupling and potential Majorana physics. The authors connect these fundamental findings to quantum hardware prospects, detailing qubit concepts such as flowermon and d-mon architectures that leverage anisotropic order parameters for enhanced protection against decoherence. The outlook identifies fabrication, stability, and interface-control challenges while highlighting technological paths—such as CST, glovebox handling, and UHV exfoliation—that could unlock scalable cuprate-based quantum circuits and new routes to harness strongly correlated states in engineered interfaces.

Abstract

Recent advances in the manipulation of complex oxide layers, particularly the fabrication of atomically thin cuprate superconducting films via molecular beam epitaxy, have revealed new ways in which nanoscale engineering can govern superconductivity and its interwoven electronic orders. In parallel, the creation of twisted cuprate heterostructures through cryogenic stacking techniques marks a pivotal step forward, exploiting cuprate superconductors to deepen our understanding of exotic quantum states and propel next-generation quantum technologies. This review explores over three decades of research in the emerging field of cuprate twistronics, examining both experimental breakthroughs and theoretical progress. It also highlights the methodologies poised to surmount the outstanding challenges in leveraging these complex quantum materials, underscoring their potential to expand the frontiers of quantum science and technology.

Figures (8)

• Figure 1: Overview of the three major fields intersecting in cuprate twistronics. Quantum hardware, particularly superconducting nanocircuits, faces the challenges of having novel functionalities and improved coherence, which may be addressed by integrating new materials like cuprates. High-temperature cuprate superconductors (BSCCO, YBCO, LSCO) exhibit inherent complexity and are highly sensitive, requiring advanced nanoscale control techniques. Advances such as Molecular Beam Epitaxy, mechanical exfoliation, and cryogenic stacking have opened possibilities for integrating these materials into quantum technologies.
• Figure 2: a) Optical image of mechanically exfoliated Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ (BSCCO) flakes on a standard SiO$_2$/Si substrate. The color variations correspond to differences in thickness, ranging from $\sim$10 nm to $\sim$200 nm. The inset highlights the material's crystal structure, which is representative of the cuprates structure. The layered arrangement is visible, resembling a stack of superconducting/insulating layers, thus forming intrinsic Josephson junctions ($I_c$ is the critical current and $\varphi$ is the phase difference). b) A schematic of typical mesa structure used for probing the electronic properties of the intrinsic stack in cuprates.
• Figure 3: Schematic of the cryogenic stacking technique (CST) for fabricating c-axis BSCCO Josephson junctions (JJs). A Polydimethylsiloxane (PDMS) stamp is positioned on a mechanically exfoliated BSCCO flake. At -90$\,^\circ$C, the PDMS is dragged to separate the flake into two parts: a "bottom" flake that remains on the substrate and a "top" flake that adheres to the stamp. The top flake is then quickly aligned and placed back onto the bottom flake to form the JJ. Gradually increasing the temperature to -30$\,^\circ$C allows the PDMS stamp to be removed from the stacked flakes. Finally, thermal evaporation, combined with a stencil mask technique, is used to create electrical contacts on the JJ.
• Figure 4: a) Typical optical image of a twisted van der Waals cuprate structure created using the cryogenic stacking technique. The schematic illustrates the junction geometry achieved through the cleaving and restacking of a single flake. b) Expected angular dependence of the critical current, normalized to its value at $\vartheta = 0^\circ$, for s-wave, d-wave (first and second order), and p-wave symmetries.
• Figure 5: The top panel illustrates the schematic representation of Andreev reflection (a) and the formation of Andreev bound states (b) resulting from multiple Andreev reflections. When an electron from the normal metal with energy below the superconducting gap hits the interface, it is reflected as a hole while a Cooper pair is transmitted into the superconductor. The bottom panel depicts the case of a superconductor with a $d$-wave order parameter (OP). Here, an injected electron from the normal metal undergoes both normal reflection (as an electron) and Andreev reflection (as a hole). The transmitted holelike and electronlike quasiparticles experience different effective pair potentials. Depending on the orientation of OP relative to the interface normal ($\alpha$), the effective pair potential can always have the same sign (c), always opposite signs (e), or a mixed behavior depending on the incident electron’s angle $\vartheta$ (d).