Collective excitations and divergent spin currents in non-centrosymmetric superconductors

TL;DR

The paper addresses how Rashba spin-orbit–coupled non-centrosymmetric superconductors respond to ultrafast light, focusing on collective Higgs and Leggett modes and their imprint on nonlinear spin-current signals. It combines an Anderson pseudospin–based analytical framework with time-dependent mean-field theory to derive a closed equation for order-parameter fluctuations, δΔ(ω) = (1 − χ(ω))^{-1} […], and to predict resonant enhancements in spin-current SHG linked to Anderson pseudospin resonances. The results show that both Higgs and Leggett modes appear in the spin-current response, with density fluctuations often dominating, and that interband coupling in TD-MFT can amplify SHG resonances across different singlet–triplet admixtures. These findings point to SHG of the spin current as a practical, low-heating probe of collective modes in light-driven NCS superconductors, with potential implications for ultrafast spectroscopy and spintronics.

Abstract

We study the collective modes in a non-centrosymmetric superconductor with Rashba spin-orbit coupling under laser irradiation. The concept of Anderson Pseudospin Resonance allows to reveal how laser driving gives rise not only to the established resonant enhancement of the third harmonic response, but also to a resonant enhancement in the second harmonic response of the spin current. We propose a theory which explains the phenomenon without including interband transitions. The theory is corroborated by numerical simulations which incorporate interband effects and allow us to clarify the signatures of the collective modes in the long-time dynamics of the superconductor.

Figures (9)

• Figure 1: (a) Free-energy landscape of the system with the order parameters for the two coupled condensates indicated by spheres. Amplitude and phase modes, as well as Leggett modes are indicated by red and green arrows, respectively, while the Leggett mode is represented by an orange wavy line connecting the two condensate order parameters. The system's nonlinear light-matter response is illustrated by the field pulses. (b) The Rashba model dispersion presented in particle-hole space along with the anti-crossing resulting from the superconducting pairing. (c) Illustration of the order parameter values on the different Fermi surfaces.
• Figure 2: Real part of the order parameters $\Delta_{k+}$ and $\Delta_{k-}$ for $\alpha=1.2$, $V_{0}=-16$, $\beta=70$, Debye frequency $\omega_{D}=0.3$ and the following pairings: (a) $e_s=1, e_{tr}=0, e_{m}=0$, (b) $e_{s}=0.7, e_t=0.714, e_{m}=0$, (c) $e_{s}=0, e_t=1, e_{m}=0$.
• Figure 3: Normalized oscillations of the order parameter components as well as the phase mode. The single-cycle laser pulse used to excite the system is shown in the inset. Here, $\alpha=1.2$, $E_{0}=0.2$, $\Omega=1.8$, and $\mu=-1.5$. The interaction corresponds to almost pure singlet pairing with $V_{0}=-16$ and $e_{s}=0.99$, $\beta=100$. The number of $k$-points along each dimension is $800$.
• Figure 4: Fourier transform of the collective modes computed with the time-dependent mean-field formalism with the same parameters as in Fig. \ref{['fig:coll_modes']}. The gold colored curves are results of the analytical formulae, computed on a grid of 300 $k$-points along each axis with $\eta=0.01$.
• Figure 5: (a) 9-cycle pulse of frequency $\Omega=0.1$ and field strength $E_{0}=0.02$ and corresponding spin currents at $\beta=5$ (dashed green line) and $\beta=30$ (solid green line). (b) Comparison of the results of the mean-field dynamics and the analytical formalism ($J_{yx}$) for $e_{s}=0.99$, $e_{m}=0$. For the mean-field case, we present results with ($J^{\mathrm{SCMF}}$) and without ($J^{\mathrm{SCMF}, \; \mathrm{intra}}$) interband coupling. The results of the analytical formulation employ the same parameters, but use a broadening parameter $\eta=0.01$. (c) The Higgs, phase and density contributions [Eq. \ref{['eq:deltaz']}] to the spin current for the same parameters as in (b). The normal state contribution is not accounted for.