Light-induced switching between singlet and triplet superconducting states

Topological superconductors can host Majorana boundary modes and non-Abelian excitations, but unambiguous realizations remain scarce. Spin-triplet pairing is a promising route, yet clear evidence in candidate materials such as Sr2RuO4 and UTe2 remains inconclusive. Concurrently, ultrafast pump-probe experiments have revealed that light can manipulate superconducting states, exciting Higgs and Leggett modes and even enhancing superconducting signatures in some materials. This motivates the central question: can irradiation of a conventional, inversion-symmetric s-wave superconductor with strong spin-orbit coupling transiently break inversion symmetry to induce odd-parity (triplet) amplitude oscillations and, under strong driving, switch the system into a metastable, opposite-parity superconducting phase? The study proposes and analyzes a mechanism where tailored ultrafast or two-color pulses break dynamical inversion symmetry and, together with spin-orbit coupling, couple singlet and triplet orders, leveraging odd-parity Bardasis-Schrieffer modes lying below the quasiparticle continuum to achieve switching into metastable triplet states after the pulse, when inversion symmetry is restored.

The work builds on extensive literature on topological superconductivity and chiral triplet states, including theoretical classifications and experimental searches in systems like Sr2RuO4 and UTe2. It connects to ultrafast optics in superconductors, where light drives collective modes such as the Higgs and Leggett modes, and to reports of light-induced enhancement or metastable superconductivity in fullerides. Broader efforts have explored light-induced control of competing orders and dynamical symmetry breaking in solids, with selection rules from dynamical symmetries known in high-harmonic generation. Bardasis-Schrieffer modes have been used to probe subdominant pairing interactions in unconventional superconductors and can, under certain conditions, lie below the pair-breaking continuum. Prior theoretical proposals on optical control of chiral superconductors and domain manipulation inform the non-equilibrium control framework adopted here.

The study combines (1) microscopic BCS mean-field quasiparticle dynamics and (2) an effective time-dependent Ginzburg-Landau (TDGL) framework to analyze light-induced coupling between competing superconducting orders and switching to metastable phases.

• Microscopic mean-field modeling: Starting from a BCS-like Hamiltonian with effective attractive local and nearest-neighbor interactions, the superconducting gap is decomposed into irreducible representations (s-, p-, d-wave, etc.). Light couples via the Peierls substitution with vector potential A(t). Spin-orbit coupling (or a small Zeeman term in a single-band rectangular model) reduces spin-rotation symmetry, enabling coupling between singlet and m=0 triplet channels. Quasiparticle equations of motion are solved to track gap dynamics under pulses that either break or preserve dynamical inversion symmetry. Two-color pulses E(t) = E1 cos(ω1 t) + E2 cos(ω2 t) with non-odd-harmonic frequency ratios or ultrafast pulsed envelopes are used to break dynamical inversion symmetry.
• TDGL effective action: A multi-component TDGL Lagrangian includes quadratic, quartic, and gradient terms for competing orders, inertial and damping coefficients, and minimal coupling to light. Symmetry analysis yields selection rules: at linear order in A(t), coupling occurs between orders with Δl = ±1 (e.g., s and p), while quadratic order reproduces conventional Higgs-mode excitation (same parity, Δl = 0 or ±2). Generalized Ginzburg-Landau coefficients (Aij, Bijmn, Dij) are computed diagrammatically from Matsubara Green’s functions to connect the phenomenology to microscopic parameters.
• Models and parameters: (a) Rectangular lattice single-band model (hopping anisotropy t' = 0.2, μ = −0.1; interactions Us = −1.75, Upx = Upy = −2.5 in hopping units). A small Zeeman splitting ΔZeeman = 0.1 is introduced transiently to break SU(2). TDGL coefficients use γ = 1.0, η = 0.1; temperature T = 0.1 (below Tc of s and py channels). x-polarized pulses primarily couple to px order. Gaussian pulses are centered near the Bardasis-Schrieffer (BS) mode frequency ΩBS with widths of a few oscillation periods; detuning slightly below ΩBS reduces overlap with the quasiparticle continuum. (b) Honeycomb lattice Kane-Mele model with strong spin-orbit coupling (t = 1 eV, λ = 0.1 eV, μ = −0.4 eV), effective interactions vs = −1.25 eV and Up = −2.3 eV yielding Tc ~ 10 K and gaps 1–10 meV. Frequencies 1–10 THz, dynamics on picosecond scales, relaxation time longer than Higgs period by ~10. Peak fields ~100 kV/cm. Circularly polarized ultrafast pulses are used to target chiral p ± ip states. A slight phenomenological difference in damping between p+ip and p−ip (η = (1 ± δ)η, δ = 0.5) is introduced to allow settling into one chiral minimum.
• Analysis: Short-time gap dynamics quantify linear-in-field and linear-in-SOC scaling of induced p-wave oscillations under symmetry-breaking drives. Frequency sweeps identify a sub-gap p-wave BS mode. TDGL free-energy landscapes and trajectories under pulsed driving reveal switching thresholds, trade-offs between pulse width (inversion-symmetry breaking) and spectral width (avoiding quasiparticle excitation), and parametric regions of successful switching (fluence vs inverse pulse width). Geometric contributions to the linear coupling matrix element are related to non-Abelian Berry connections and Fermi-surface geometry.

• Dynamical inversion symmetry breaking is essential to excite odd-parity (triplet) order from an even-parity (singlet) superconductor. Two-color pulses with non-odd-harmonic frequency ratios or ultrafast pulse envelopes break the dynamical inversion symmetry; preserving it (e.g., 3:1 frequency ratio) suppresses p-wave response at short times.
• Linear coupling to light: Induced p-wave order parameter oscillations scale linearly with the light field amplitude |A| and linearly with spin-orbit coupling strength, in contrast to Higgs-mode excitations which scale as |A|^2. This follows from a selection rule Δl = ±1 coupling s and p at linear order in A(t).
• Sub-gap odd-parity Bardasis-Schrieffer mode: A p-wave BS amplitude mode appears below the pair-breaking continuum and below the conventional Higgs mode, providing a resonant channel to drive triplet fluctuations efficiently without creating quasiparticles.
• Optical switching to metastable triplet states: Strong driving near ΩBS can switch the system from equilibrium s-wave to a metastable odd-parity superconducting phase. In the rectangular model, an x-polarized Gaussian pulse centered at ~0.75 ΩBS with widths of a few periods and sufficient fluence switches into the p-wave minimum. There is a threshold in pulse width, evidencing the need for strong dynamical inversion-symmetry breaking.
• Chiral topological state in honeycomb model: With strong SOC and appropriate interactions, the free-energy landscape hosts local minima at chiral p ± ip. Ultrafast circularly polarized pulses with widths ~0.1 ps and fluences ~1.0 mJ/cm^2 switch from s-wave to a metastable chiral p + ip state. A slight asymmetry in relaxation rates selects one chirality.
• Geometric control: The linear-in-field coupling matrix element between s and p is dominated at small fields by geometric contributions (non-Abelian Berry connection), distinct from quantum-geometric corrections to superfluid weight.
• Practical parameters: For realistic SOC honeycomb systems, relevant frequencies are 1–10 THz, time scales picoseconds, peak fields ~100 kV/cm, and pulses detuned slightly below ΩBS to reduce overlap with the quasiparticle continuum.

The findings address whether triplet superconductivity can emerge as a metastable phase via light in systems that are singlet in equilibrium. Dynamical inversion symmetry breaking, combined with SOC, directly couples s and p channels at linear order, efficiently exciting odd-parity amplitude oscillations. The presence of a sub-gap p-wave BS mode creates a resonant pathway to amplify triplet fluctuations while avoiding pair-breaking excitations. By shaping pulses to maximize inversion-symmetry breaking yet minimize spectral overlap with the quasiparticle continuum, the order parameter is driven across the free-energy barrier to settle into a metastable competing minimum. The TDGL selection rules and microscopic simulations consistently show linear scaling of the induced triplet response with field and SOC, and suppression when dynamical inversion symmetry is preserved. In the honeycomb model, the metastable p ± ip minima enable chiral topological superconductivity after the pulse, providing a non-equilibrium route to topological phases. The geometric (Berry-connection) control of the coupling suggests material-specific optimization via band-structure engineering. Experimentally, detection of a sub-gap opposite-parity BS mode and the square-root scaling of induced gap oscillations with pump intensity (implying linear coupling) would be key signatures. The approach offers a general probe of subdominant odd-parity instabilities in conventional superconductors and guiding principles for light-induced topological superconductivity.

The work establishes dynamical inversion symmetry breaking with tailored ultrafast or two-color light as a generic mechanism to couple even- and odd-parity superconducting orders linearly in field in centrosymmetric, SOC-strong materials. Identifying and resonantly driving a sub-gap odd-parity Bardasis-Schrieffer mode enables switching from an equilibrium s-wave state into a metastable triplet state, including chiral p ± ip phases on the honeycomb lattice. The method defines practical pulse conditions (frequency near but slightly below ΩBS, short duration to break dynamical inversion symmetry, fluences around mJ/cm^2, fields ~100 kV/cm) and highlights the geometric Berry-connection origin of the linear coupling. Future research directions include: determining general criteria for when subleading stationary points become local minima; incorporating microscopic heating and dissipation pathways beyond TDGL; quantitatively constraining effective low-energy interactions via RG and RPA; and applying the protocol to realistic materials (e.g., 1T' WTe2 and moiré TMDs). Experimental searches for sub-gap opposite-parity BS modes and for gap-oscillation amplitudes scaling linearly with field (square-root in pump intensity) are proposed as key tests.

• TDGL framework neglects explicit quasiparticle excitations and detailed microscopic dissipation; heating effects from strong pulses are not modeled and could affect switching and relaxation.
• Some parameters (e.g., inertial and damping coefficients, slight chirality-dependent damping asymmetry) are phenomenological; selection of δ to choose chirality is not derived microscopically.
• Single-band rectangular model requires a Zeeman field to break SU(2), differing from realistic SOC-based mechanisms; the Zeeman field is adiabatically toggled and assumed to minimally impact free energy.
• Spatial homogeneity is assumed (no gradients), excluding possible spatial textures, domain formation, or vortex dynamics.
• Validity near Tc and within mean-field approximations may limit quantitative predictions at low temperatures or in strongly fluctuating regimes.
• Avoidance of the quasiparticle continuum is enforced by pulse design; if significant spectral weight overlaps the continuum, pair breaking and heating (not captured here) could suppress superconductivity.
• Material-specific interaction strengths and SOC details are simplified; mapping to real compounds requires detailed band-structure and interaction modeling.