Controlling surface Josephson plasma waves with anisotropy, damping, and heterostructure architecture in layered superconductors

Layered superconductors such as the cuprates behave at terahertz frequencies as strongly anisotropic uniaxial media whose c-axis response is dominated by the Josephson plasma resonance, and they support surface Josephson plasma waves (SJPWs): electromagnetic modes bound to their boundaries. After the 2020 near-field observation of SJPWs in a La1.85Sr0.15CuO4 thin film, the source work posed the open question of how sample anisotropy, quasiparticle damping, and engineered heterostructure architectures control the coupling to these otherwise weakly radiative ('dark') surface modes, to buried-interface modes, and to nonlinear terahertz Josephson responses, and whether such plasma waves can be found in other cuprate families and in iron-based superconductors. The existence and dispersion of surface polaritons at a single uniaxial interface, and of idealized SJPWs in slabs, are settled theory, and several coupling mechanisms (stripe-induced symmetry breaking, metamaterial resonators, microcavity ultrastrong coupling) have since been demonstrated or designed in isolated cases. The surviving open core is a quantitative, experimentally validated account of how anisotropy, damping, and layer architecture jointly determine the existence, dispersion, hybridization, and excitation efficiency of interfacial Josephson plasma modes across superconducting families - including iron-based superconductors, where they remain unobserved - together with the buried-interface superconductivity mapping this control would enable.

Background

In a crystal built of superconducting layers stacked along the c axis, such as the cuprate La2-xSrxCuO4 (LSCO), Cooper pairs tunnel coherently between the layers. The electrodynamics of such a layered superconductor is that of a uniaxial medium: the in-plane and c-axis dielectric functions, $\varepsilon_{ab}(\omega)$ and $\varepsilon_c(\omega)$, differ enormously. Below the superconducting transition temperature $T_c$, $\varepsilon_c(\omega)$ crosses zero at the Josephson plasma frequency $\omega_J$ - a sharp, sub-gap collective oscillation of the interlayer superconducting phase - while $\varepsilon_{ab}(\omega)$ remains metallic, so the anisotropy ratio $\gamma=\varepsilon_{ab}/\varepsilon_c$ reaches large values.

An electromagnetic mode bound to the boundary of such a medium is the surface Josephson plasma wave (SJPW), predicted by Savel'ev, Yampol'skii and Nori in 2005: like an ordinary surface polariton (a light field trapped at an interface by coupling to a material resonance), it propagates along the surface with deep sub-wavelength confinement, and its frequency saturates near $\omega_J$ at large in-plane momenta, below any bulk radiative mode, and it is therefore hard to excite or detect from the far field. For the interface between an isotropic medium of permittivity $\varepsilon_1$ and a uniaxial medium, the mode dispersion is the classical result

$q = \frac{\omega}{c}\sqrt{\frac{\varepsilon_1\varepsilon_c(\omega)\left(\varepsilon_1-\varepsilon_{ab}(\omega)\right)}{\varepsilon_1^2-\varepsilon_{ab}(\omega)\varepsilon_c(\omega)}}$

which reduces to the textbook surface-polariton formula when $\varepsilon_{ab}=\varepsilon_c$; a thin film adds a second (substrate-side) interface and splits the surface branch into hybridized symmetric/antisymmetric pairs. The theory of SJPWs in model geometries - slabs, prism (attenuated-total-reflection) and grating coupling, oblique propagation relative to the anisotropy axis, dissipative media - was worked out by Savel'ev, Yampol'skii, Nori and co-workers between 2005 and 2013, and reviewed by Zhang et al. in 2020. In adjacent non-superconducting systems, anisotropic and hyperbolic - having permittivity-tensor components of opposite sign, so the isofrequency surface opens into cones - surface phonon polaritons at uniaxial crystal interfaces (hexagonal boron nitride, α-MoO3) are now routinely imaged and engineered, so the generic question of surface-polariton existence and dispersion at uniaxial boundaries is not the open issue.

The experiment that defined the present question is that of Lu, Bollinger, He, Sundling, Bozovic and Gozar (npj Quantum Materials 5, 69 (2020)): using cryogenic terahertz scattering-type scanning near-field optical microscopy (s-SNOM - an atomic-force tip that concentrates and scatters evanescent THz near fields, with resolution of order 10 nm, here better than lambda/3000), they showed that a 13-nm LSCO film below $T_c$ scatters sub-gap THz photons more strongly than gold, and interpreted the signal as near-field coupling to SJPWs whose high-momentum asymptote tracks the screened Josephson plasma frequency. The interpretation relied on a spherical-dipole model of the tip; no real-space interference fringes of propagating plasmons were seen (attributed to the sign-changing d-wave superconducting gap and to quasiparticle damping near the 0.8 $T_c$ base temperature); and the authors stated the open problem: analogous plasma waves had not been observed in layered iron-based superconductors, and the coupling to these excitations remained to be explored as a function of sample anisotropy and damping in engineered heterostructures and in other cuprate families - with non-invasive mapping of superfluid profiles confined to buried interfaces and tip-enhanced nonlinear THz Josephson effects as the motivating payoffs.

Problem Statement

Determine, by theory, experiment, or both (a theory-only account being acceptable insofar as it yields experimentally testable predictions), how the dielectric anisotropy $\varepsilon_{ab}(\omega)/\varepsilon_c(\omega)$, the quasiparticle damping entering these dielectric functions, and the interface/heterostructure architecture of layered superconductors (film thickness and substrate; multilayers and superconducting/normal heterostructures; patterned resonators or microcavities; symmetry-breaking modulations such as charge stripes) jointly control (these three factors being the axes along which this control is to be characterised, with the listed architectures illustrative of the architecture axis rather than a checklist of separately required cases):

(i) the existence, dispersion, confinement, and hybridization - including symmetric/antisymmetric film branches and modes localized at buried interfaces - of surface Josephson plasma waves and related interfacial Josephson-plasma modes;

(ii) the efficiency and selectivity with which these otherwise weakly radiative ('dark') modes are excited and detected, whether by near-field tips (requiring quantitative modeling beyond the spherical-dipole approximation, including realistic tip geometry and retardation), by grating or prism coupling, by engineered resonators and cavities, or by symmetry-breaking modulations; and

(iii) the reach of this control across superconducting families - other cuprates beyond La1.85Sr0.15CuO4, and layered iron-based superconductors, in which such surface plasma waves have not been observed - together with the capabilities this control enables, notably non-invasive mapping of superfluid density at buried interfaces and enhancement of nonlinear terahertz Josephson responses at surfaces and interfaces.

These three components serve one overarching objective: a validated electrodynamic account from which one can predict, for a given layered superconductor or heterostructure, whether interfacial Josephson plasma modes exist, what their dispersion and damping are, and how efficiently they can be coupled to. A general account applicable to any given system suffices, provided it yields predictions for the families named in (iii); no family-specific demonstration is separately required. The capabilities noted in (iii) are motivating context rather than mandatory deliverables.

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