Cavity-altered superconductivity

Abstract

Is it feasible to alter the ground state properties of a material by engineering its electromagnetic environment? Inspired by theoretical predictions, experimental realizations of such cavity-controlled properties without optical excitation are beginning to emerge. Here, we devised and implemented a novel platform to realize cavity-altered materials. Single crystals of hyperbolic van der Waals (vdW) compounds provide a resonant electromagnetic environment with enhanced density of photonic states and prominent mode confinement. We interfaced hexagonal boron nitride (hBN) with the molecular superconductor $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br ($κ$-ET). The frequencies of infrared (IR) hyperbolic modes of hBN match the IR-active carbon-carbon stretching molecular resonance of ($κ$-ET) implicated in superconductivity. Nano-optical data supported by first-principles molecular Langevin dynamics simulations confirm the presence of resonant coupling between the hBN hyperbolic cavity modes and the carbon-carbon stretching mode in ($κ$-ET). Meissner effect measurements via magnetic force microscopy demonstrate a strong suppression of superfluid density near the hBN/($κ$-ET) interface. Non-resonant control heterostructures, including RuCl$_3$/($κ$-ET) and hBN/$\text{Bi}_2\text{Sr}_2\text{CaCu}_2\text{O}_{8+x}$, do not display the superfluid suppression. These observations suggest that hBN/($κ$-ET) realizes a cavity-altered superconducting ground state. Our work highlights the potential of dark cavities devoid of external photons for engineering electronic ground state properties of complex quantum materials.

Figures (4)

• Figure 1: Electromagnetic environment alters the superfluid density at the interface between hBN and $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br ($\kappa$-ET). Schematic at the bottom depicts the Meissner force $F_z$ experienced by the magnetic atomic force microscope tip above the surface of the $\kappa$-ET molecular superconductor. Exfoliated hBN and RuCl$_3$ microcrystals sit on the surface of a bulk $\kappa$-ET crystal (optical images in Supplementary Information Section 4). a,b, Magnetic force microscopy data displayed in the form of the derivative of the Meissner force $\partial_{z} F_{z}$ as a function of tip height on bare $\kappa$-ET (green), hBN/$\kappa$-ET (blue), and RuCl$_3$/$\kappa$-ET (magenta), taken at temperature 2 K. The $\kappa$-ET surface is at $z=0$, and the gray shading highlights the difference between the two curves. The vertical axes in panels a and b are identical. The superfluid density is significantly reduced near the hBN/$\kappa$-ET interface, but not near the RuCl$_3$/$\kappa$-ET interface. Inset: same as a, except that the superconductor has been replaced by $\text{Bi}_2\text{Sr}_2\text{CaCu}_2\text{O}_{8+x}$ (BSCCO). The bare BSCCO curve is plotted using a wider gray line for visual clarity. c, Model real part of the out-of-plane (OOP) permittivity for $\kappa$-ET (green) and the in-plane (IP) permittivities for hBN (blue) and RuCl$_3$ (magenta), based on refs. ET_epsilonhBN_epsilonRuCl3_DC_epsilon. For clarity, the permittivities have been simplified to show only the relevant modes. The C=C stretching mode of $\kappa$-ET (labeled C=C) falls within the hyperbolic region of hBN between the transverse optical (TO) and longitudinal optical (LO) frequencies (gray shading).
• Figure 2: Meissner effect by magnetic force microscopy nano-imaging.a,$\partial_{z} F_{z}$ measured as a function of tip height at temperatures from 2 K to 12 K on bare $\kappa$-ET. The curves flatten as the temperature increases (colorscale). b, c, Constant-height MFM images over an area with hBN/$\kappa$-ET, bare $\kappa$-ET, and RuCl$_3$/$\kappa$-ET regions all within the same field of view, taken at a temperature of 2 K (below $T_{\textrm{c}}$) with a tip height of 300 nm above the $\kappa$-ET surface (b) and at 12 K (above $T_{\textrm{c}}$) with a tip height of 150 nm above $\kappa$-ET (c). The boundaries of the areas covered by hBN and RuCl$_3$ are marked by black dashed lines. The false color map represents the differential Meissner signal $\Delta\partial_{z} F_{z}$. d, Histogram of $\Delta\partial_{z} F_{z}$ values extracted from the image in panel b. Green, magenta, and blue shading highlight typical $\Delta\partial_{z} F_{z}$ values measured over bare $\kappa$-ET, over the RuCl$_3$/$\kappa$-ET interface, and over the hBN/$\kappa$-ET interface respectively.
• Figure 3: Quantifying superfluid density suppression.$\rho_\textrm{eff}/\rho_\textrm{0}$ (defined in the main text) shown as a function of cavity thickness. Measurements on hBN/$\kappa$-ET and RuCl$_3$/$\kappa$-ET are shown in blue and magenta, respectively. Symbols distinguish different devices. The superfluid density is assumed to be uniformly suppressed underneath the hBN and RuCl$_3$ microcrystals. Error bars correspond to the error in local superfluid density due to uncertainty in tip geometry (Supplementary Information Section 5) and exclude spatial variations of the hBN/$\kappa$-ET interface (Supplementary Information Section 8).
• Figure 4: Mode coupling at the hBN/$\kappa$-ET interface. a, Phonon-polariton dispersion for an hBN/$\kappa$-ET interface (32-nm hBN, 100-nm $\kappa$-ET), represented by a false color map of the imaginary part of the Fresnel reflection coefficient $r_p$. Refer to Methods for calculation details. b, s-SNOM experiment schematic on an hBN/$\kappa$-ET heterostructure, showing continuous-wave light backscattered by an atomic force microscope tip. Phonon-polaritons in hBN launched by the tip reflect off the hBN edge, forming interference patterns in the s-SNOM amplitude. The image shown was taken with incident light frequency $\omega = 1477.6$ cm$^{-1}$. The false color scale represents the normalized scattering amplitude S$_4$/S$_3$, where S$_4$ and S$_3$ are the near-field amplitude demodulated at the fourth and third harmonics of the tip-tapping frequency, respectively S4S3. c, (Bottom) Hyperspectral image of S$_4$/S$_3$ at various illumination frequencies, where $x$ is along the phonon-polariton propagation direction. The overlay highlights the kink in the dispersion. Selected profiles are presented in the top panel. Black arrows mark the location of the fifth fringe. The profiles are vertically shifted for clarity. d, Schematic showing the coupling between the C=C stretching resonance and the hyperbolic mode of hBN enabled by the out-of-plane component of the electric field of the HMs discussed in the main text and further analyzed in Supplementary Information Sections 2,3. e, The calculated spectrum of the C=C stretching mode amplitude for BEDT-TTF molecules on hBN (black curve). The gray curve has phonon-phonon scattering suppressed. The red curve is the spectrum in the presence of an oscillating out-of-plane electric field from the HMs of hBN, with field strength $2.6\cdot 10^7$ V/m. Refer to Supplementary Information Section 11 for calculation details.