Light Pulses Transform Standard Superconductors, Creating Exotic New States of Matter

Researchers have demonstrated a novel method for manipulating superconductivity, inducing higher-order pairing states within conventional s-wave superconductors using light pulses. Hennadii Yerzhakov and Alexander Balatsky, both from Nordita, Stockholm University, and KTH Royal Institute of Technology, present a theoretical framework utilising a time-dependent Ginzburg-Landau model to show how microwave radiation can generate p-wave and d-wave order parameters in centrosymmetric superconductors. This research is significant because it expands the possibilities for controlling superconducting properties locally, potentially offering a new route towards ‘quantum printing’ and advanced superconducting device fabrication. By coupling different superconducting order parameters via the vector potential, the team reveal how to dynamically engineer more complex superconducting states.

Microwave induction of unconventional superconductivity via symmetry-breaking gradient terms

Researchers have demonstrated the induction of p- and d-wave superconducting components within an originally pure s-wave centrosymmetric superconductor using microwave radiation. This breakthrough relies on a generalised time-dependent Ginzburg-Landau model, establishing the possibility of manipulating superconducting states through external electromagnetic fields.
The work introduces gradient terms that couple the s-wave order parameter with other symmetry-allowed components, effectively creating new superconducting pathways. Specifically, the study focuses on Oh point-group symmetry, incorporating both quadratic and, crucially, linear-in-derivatives gradient terms.

These linear terms, enabled by spin-orbit coupling, allow coupling between singlet and triplet order parameters via the vector potential, leading to the generation of p-wave and d-wave superconductivity. This coupling is achieved through a minimal substitution procedure, effectively ‘printing’ new superconducting characteristics onto the material with microwave radiation.

The researchers formulated a model concentrating on systems exhibiting Oh point group symmetry, where the s-wave order parameter is linked to other singlet and triplet order parameters through gradient terms. A key innovation is the formulation of a Lifshitz-type invariant, which, in the presence of spin-orbit coupling, couples s- and p-wave superconducting order parameters.

Under microwave irradiation, this coupling dynamically induces a p-wave component, alongside the generation of additional singlet components. Such dynamically induced singlet-triplet states potentially offer a platform for Floquet-engineered topological superconductivity and the creation of transient topological superconducting states.

This approach presents advantages over conventional methods, circumventing the need for complex heterostructures prone to disorder and imperfections. The manipulation of the superconducting state with light represents a novel facet of quantum printing, where the spatiotemporal structure of the light’s gauge potential modifies the superconducting state. Furthermore, this coupling may also explain the magnetic memory effect observed in 4Hb-TaS2.

Microwave induced symmetry breaking and order parameter coupling via minimal substitution

A generalised time-dependent Ginzburg-Landau model serves as the foundation for this research, investigating the induction of p- and d-wave superconducting components within an originally pure s-wave centrosymmetric system via microwave radiation. The study constructs this model by introducing gradient terms that couple the s-wave superconducting order parameter with other symmetry-allowed components, specializing to point-group symmetry.

These singlet-to-singlet gradient terms are quadratic in spatial derivatives, while linear-in-derivatives terms, permitted by spin-orbit coupling, connect singlet and triplet order parameters. The core innovation lies in the minimal substitution procedure, enabling coupling between different superconducting order parameters through the vector potential and subsequently generating p-wave, d-wave, and other symmetry-allowed components.

This approach diverges from previous work, such as that employing Floquet-Magnus expansion, by not requiring dynamical inversion symmetry breaking as a prerequisite for inducing triplet correlations. The research concentrates on systems exhibiting Oh point group symmetry, coupling the s-wave order parameter to symmetry-allowed singlet and triplet order parameters via these carefully constructed gradient terms.

A key element of the work is the formulation of a Lifshitz-type invariant, first order in spatial derivatives, which couples s- and p-wave superconducting order parameters in the presence of spin-orbit coupling. Under electromagnetic irradiation, this coupling dynamically induces a p-wave component, while additional gradient couplings generate further singlet components.

The equations of motion for this model were then derived to describe the system’s evolution. Analytical and numerical results were obtained to examine the induced superconducting components, providing insights into the potential for Floquet-engineered topological superconductivity and a novel route to p-wave superconductivity without the need for complex heterostructures.

Microwave-induced symmetry breaking and emergence of multi-component superconductivity

Researchers developed a generalised time-dependent Ginzburg-Landau model to explore the induction of p- and d-wave superconducting components within an originally pure s-wave centrosymmetric system using microwave radiation. The model incorporates gradient terms coupling the s-wave order parameter with other symmetry-allowed components, potentially enabling the generation of diverse superconducting states.

Singlet-to-singlet gradient terms are quadratic in spatial derivatives, while linear-in-derivatives terms coupling singlet and triplet order parameters emerge in the presence of spin-orbit coupling. The study details how the superconducting gap transforms under symmetry operations, defining the transformation properties of singlet and triplet pairings.

In the absence of spin-orbit coupling, the symmetry group reduces to G = GD ×T ×U, while the inclusion of spin-orbit coupling further modifies this to G = GD ×T ×U. These transformations dictate how the creation operators and the superconducting gap function behave under various symmetry operations, influencing the mixing of singlet and triplet components at lower temperatures.

Specifically, the research investigates couplings between order parameters via the electromagnetic vector potential, focusing on allowed gradient terms within the Ginzburg-Landau theory. For continuous rotational symmetry, the gap function expands in basis functions, with the s-wave characterised by a single coefficient and the p-wave by nine coefficients.

The model seeks to form invariants that couple the s-wave and p-wave components, containing derivatives that transform according to the D1 representation. In the absence of spin-orbit coupling, such invariants require at least second-order terms in spatial derivatives, limiting their ability to induce a triplet component through microwave irradiation.

However, the presence of spin-orbit coupling fundamentally alters the symmetry landscape. The full group SO × SU reduces to SU, and the irreducible representations become reducible. This allows for the formation of first-order invariants in both spatial derivatives and p-wave components, specifically of the form aijαs∗∂iPjα + c.c., where aijα are coefficients to be determined.

This invariant transforms under a gOS operation, demonstrating the potential to induce the triplet component through microwave irradiation or non-uniformity of the s-wave order parameter. The research suggests this manipulation of the superconducting state could be considered a form of quantum printing.

Microwave induction of unconventional superconductivity and symmetry modification

Researchers have demonstrated the induction of p- and d-wave superconducting components within a centrosymmetric s-wave superconductor using microwave radiation. A generalised time-dependent Ginzburg-Landau model was constructed to explore this possibility, incorporating gradient terms that couple the s-wave order parameter with other symmetry-allowed components.

These terms, quadratic in spatial derivatives for singlet-to-singlet coupling and linear for singlet-to-triplet coupling in the presence of spin-orbit coupling, facilitate the generation of higher-order superconducting states via interaction with the vector potential of the microwave radiation. The simulations reveal that triplet order parameters and lower-symmetry singlet order parameters can be generated through microwave irradiation, with the emergence of the triplet component requiring spin-orbit coupling.

Linearly polarized light induces oscillating p- and d-wave components, while circularly polarized light can establish non-zero average values for these induced states. This manipulation of the superconducting state represents a further development of the quantum printing concept, where light modifies the quantum state of matter.

The authors acknowledge that the observed effects are dependent on specific parameters within the time-dependent Ginzburg-Landau model and the assumption of relatively weak spin-orbit coupling. Future research could focus on exploring the robustness of these findings with varying material properties and microwave parameters. Further investigation into the potential for controlling and stabilising these induced higher-order superconducting states could also advance the development of novel quantum devices and materials.