Finite-momentum Cooper plasmons in superconducting terahertz microcavities

TL;DR

This work examines the superconducting phase mode in ultrathin films and shows that proximal metal screening within an on-chip THz microcavity yields finite-momentum Cooper plasmons. By combining theory with on-chip THz spectroscopy of a NbN microcavity, two resonances are observed at ~170 GHz and ~650 GHz, whose frequencies and linewidths reveal the participating carrier density and dissipation via the self-energy components $\Re[\Sigma_F]$ and $\Im[\Sigma_B]$. The results establish Cooper plasmons as an emergent collective mode in integrated superconductor-circuit systems and provide design rules to suppress or exploit them in terahertz devices. This approach enables simultaneous access to real and imaginary parts of the self-energy at finite momentum, offering a new lens on superconducting dynamics and potential impacts for high-frequency superconducting circuits.

Abstract

The phase mode of a superconductor's order parameter encodes fundamental information about pairing and dissipation, but is typically inaccessible at low frequencies due to the Anderson-Higgs mechanism. Superconducting samples thinner than the London penetration depth, however, support a gapless phase mode whose dispersion can be reshaped by a proximal screening layer. Here, we theoretically and experimentally show that this screened phase mode in a superconducting thin film integrated into on-chip terahertz circuitry naturally forms a superconducting microcavity that hosts resonant finite-momentum standing waves of supercurrent density, which we term Cooper plasmons. We measure two Cooper plasmons in a superconducting NbN microcavity and demonstrate that their resonance frequencies and linewidths independently report the density of participating carriers and plasmon's dissipation at finite momenta. Our results reveal an emergent collective mode of an integrated superconductor-circuit system and establish design principles for engineering or suppressing Cooper plasmons in superconducting terahertz devices and circuits.

Figures (5)

• Figure 1: Summary of dispersion relations (a) Dispersion relations for the phase mode of the pictured superconducting samples, which take different functional forms due to dimensionality and screening. The dispersions of both the electrodynamically two-dimensional and screened electrodynamically two-dimensional samples are below the light cone. (inset) Landau-Ginzburg potential, with amplitude and phase modes indicated. (b) Electrodynamically three-dimensional superconducting sample, where Cooper pairs interact isotropically with other Cooper pairs (c) Electrodynamically two-dimensional superconductor with both local in-plane and non-local (long-range) out-of-plane interactions. (d) Electrodynamically two-dimensional superconductor with proximal metal screening layer, separated by an oxide. (e) Schematic of a superconducting microcavity capacitively contacted to a gold coplanar stripline (CPS). The superconductor is thinner than the London penetration depth and narrower ($W_{NbN}$) than the wavelength of THz photons. Pictured are two Cooper plasmons (red: lower frequency mode and blue: higher frequency mode), which are resonant current distributions formed of Cooper pairs.
• Figure 2: Normalized microcavity conductivity and collective mode structure below $T_c$ (a) Y$_1/\sigma_0$, proportional to the imaginary part of the microcavity conductivity. For comparison to the experiment presented later, we use a mixture of ohmic and capacitive contact ($\sigma_{ox}/\sigma_{in} \approx 0.4$). (b) Comparison of collective modes. A conventional Carlson-Goldman mode peaks at $T/T_c \sim 0.9$, whereas the amplitude of our interlayer Carlson-Goldman (Cooper) plasmons grows as the temperature drops to zero.
• Figure 3: On-chip THz spectroscopy of NbN with the fast sample interchange architecture. (a) Schematic showing the A switch, the sample board - switch board interface, and the NbN shunt from which the THz transient reflects. The sample board is quartz, the switch board is cyclo-olefin polymer (COP). (b) Cross-section of the sample board along A-A'. (c) Time-domain reflected signal versus temperature with a $T_C$ of 11.1 K, with (d) linecuts at selected temperatures.
• Figure 4: Extracted parameters from fitting experimental data (a) Calculated optical conductance $Y_1Z_0$ with (b) select linecuts. White lines demarcate $T_C$ and the temperature-dependent superconducting gap $2\Delta(T)$. Strong absorptions develop at 150 GHz (m = 0, red mode) and 620 GHz (m = 1, red mode) upon entering the superconducting condensate. The resulting fitted (c) center frequency and (d) full width, half maximum (FWHM). Shaded regions indicate 1-standard deviation from curve-fitting. Fits to the blue mode above 9.9K were terminated, as the Lorentzians there become too broad to fit properly.
• Figure 5: Independent resolution of the real and imaginary parts of the Cooper plasmon's self-energy (a) Real part of the (fermionic) self-energy manifests as a shift in plasma frequency, which can come from carrier density (tunable by a gate in 2D systems) or renormalization of the effective mass by band structure changes or electronic correlations. Inset: band mass renormalization. (b) The imaginary part of the (bosonic) self-energy renormalizes the scattering rate, which manifests as a change to the FWHM. Inset: a sample lifetime renormalization by scattering. Both panels a and b were evaluated at a temperature of 0.1$T_c$. (c) An illustrative superconducting dome, with a pictured quantum critical point.