Yu-Hang Li of Nankai University, Congjun Wu of Westlake University, and Wang Yang have identified a surprising mechanism for topological superconductivity in twisted bilayer cuprates. Their work reveals a three-component superconducting state, described by the order parameter s + $d_{1} e^{iφ_1}$ + $d_{2} e^{iφ_2}$ , that breaks both time-reversal and $C_{4}$ rotational symmetries when $φ_{1} - φ_{2}$ is not equal to 0 or π. The researchers demonstrate that this symmetry breaking can realize a topologically nontrivial phase, and their results show that s-wave pairing does not preclude chiral topological superconductivity, suggesting twisted cuprates are a more robust platform than previously appreciated.

Twisted Bilayer Cuprates: A Platform for Topological Superconductivity

Researchers found that the Josephson critical current remains sizable at a 45° twist, suggesting a pathway to optimizing device performance. This finding builds on investigations into how manipulating the stacking and rotation of these materials can generate exotic quantum states.

The superconducting state within these twisted bilayers is described by an order parameter of s + $d_{1} e^{iφ_1}$ + $d_{2} e^{iφ_2}$ , where s = $s_{1}$ + $s_{2}$ is the layer-symmetric s-wave pairing and $d_{i}$ is the pairing in layer i. Ginzburg-Landau analysis and self-consistent mean-field calculations confirm this state is stable across a wide range of parameters. This symmetry breaking is not merely a theoretical prediction; researchers identified nematic Kerr anisotropy as a key signature that distinguishes this three-component state from other possible superconducting arrangements, such as s + id and $d_{1}$ + $e^{i φ} d_{2}$ .

The results demonstrate that s-wave pairing does not preclude chiral topological superconductivity, establishing twisted bilayer cuprates as a potentially more robust platform for realizing these exotic states than previously thought. The team’s calculations demonstrate the viability of this state. The researchers further note that “nematic Kerr responses exhibiting $C_{4}$ -symmetry breaking provide experimental tests for this frustrated three-component pairing, distinguishing it from both d + id and s + id pairings.”

Multicomponent Superconductivity with s-wave Admixture in Twisted Bilayers

The interplay between different superconducting components within twisted bilayer cuprates allows for a topologically nontrivial state even with a substantial s-wave contribution, challenging previous assumptions about material limitations. Ginzburg-Landau analysis and self-consistent mean-field calculations show that a frustrated three-component pairing state s + $e^{iφ_1} d_{1}$ + $e^{iφ_2} d_{2}$ is stabilized over a broad parameter regime. Solving the linearized gap equation near the superconducting transition reveals that interlayer tunneling significantly enhances the s-wave transition temperature, while mildly suppressing the channel, establishing an extended regime of competing s- pairings.

Spontaneous Symmetry Breaking in the Pairing State (φ_1-φ_2 ≠ 0,π)

The stability of a three-component superconducting state in twisted bilayer cuprates hinges on a specific phase relationship, where the difference between $φ_{1}$ and $φ_{2}$ deviates from zero or pi. This deviation induces a spontaneous breaking of time-reversal and $C_{4}$ rotational symmetries, potentially unlocking a topologically nontrivial phase of matter. It provides a pathway to experimentally distinguish this complex pairing state from simpler superconducting arrangements like d + id and s + id pairings.

Nematic Kerr anisotropy is a key diagnostic for this frustrated three-component pairing, offering a means to confirm its presence. The team’s modeling demonstrates that this state remains topologically nontrivial over a finite range of parameters, suggesting a degree of flexibility in material design.

Unlike a $d_{1}$ + $e^{i φ} d_{2}$ state, which exhibits suppressed coupling near a 45-degree twist angle, the s + $d_{1} e^{iφ_1}$ + $d_{2} e^{iφ_2}$ state maintains a finite critical current at this angle. This retention of a sizable current “is in agreement with the robust experimental response in this angular regime,” according to the research. The underlying mechanism for this symmetry breaking is linked to the invariance of the pairing state under combined anti-unitary operations.

These operations, involving both layer interchange and complex conjugation, impose a phase constraint, $φ_{1}$ + $φ_{2}$ = π, but allow for $φ_{1} - φ_{2}$ to differ from zero or pi, driving the symmetry breaking. The researchers found that symmetry operations can transform the pairing configuration, resulting in four degenerate ground state solutions. This degeneracy, while complex, doesn’t undermine the overall stability of the topological state.

In summary, the work demonstrates that twisted bilayer cuprates can host a stable, topologically nontrivial s + $d_{1} e^{iφ_1}$ + $d_{2} e^{iφ_2}$ state, characterized by frustrated phase locking and spontaneous symmetry breaking. This state can be identified through nematic Kerr anisotropy alongside a sizable Josephson critical current near 45 degrees, offering a multi-faceted approach to confirming its existence and properties.

Ginzburg-Landau Analysis of Frustrated Pairing States

Ginzburg-Landau analysis reveals a stabilized superconducting state within twisted bilayer cuprates across a wide range of parameters, extending beyond previously understood limits. Self-consistent mean-field calculations pinpoint a frustrated three-component pairing configuration, s + $e^{iφ_1} d_{1}$ + $e^{iφ_2} d_{2}$ , where s represents layer-symmetric s-wave pairing and $d_{i}$ denotes pairing within each layer. This complex interplay between pairing components establishes an extended regime where s- pairings compete, supporting the conditions for this unique state.

Topological Nontriviality Rescued by s-wave Pairing

This sizable Josephson critical current near the 45° twist is particularly noteworthy, as it challenges previous assumptions about the fragility of topological superconductivity in the presence of s-wave pairing. By simultaneously breaking time-reversal and $C_{4}$ lattice rotational symmetries for $φ_{1} - φ_{2}$ ≠ 0,π, this state transcends the s + id paradigm, realizing a chiral superconducting state with nematic and potentially topological characteristics.

Increasing the strength of interlayer tunneling within twisted bilayer cuprates directly boosts the s-wave component of superconductivity, a finding that expands the parameter space for realizing exotic quantum states in these materials.

👉 More information
🗞 Topological multicomponent superconductivity with sizable s -wave admixture in twisted bilayer cuprates
✍️ Yu-Hang Li, Congjun Wu and Wang Yang
🧠 DOI: http://link.aps.org/doi/10.1103/6cyn-zbpm

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