Superradiant Quantum Materials

There is currently great interest in the strong coupling between the quantized photon field of a cavity and electronic or other degrees of freedom in materials. A major goal is the creation of novel collective states entangling photons with those degrees of freedom. Here we show that the cooperative effect between strong electron correlations in quantum materials and the long-range interactions induced by the photon field leads to the stabilization of coherent phases of light and matter. By studying a two-band model of interacting electrons coupled to a cavity field, we show that a phase characterized by the simultaneous condensation of excitons and photon superradiance can be realized, hence stabilizing and intertwining two collective phenomena which are rather elusive in the absence of this cooperative effect.

Figure 1

Light-matter phases as a function of the strength of electronic interactions $U$ and the light-matter coupling $g$ at a temperature $T=0.15$. The red (blue) intensity map reflects the evolution of the band populations. In the metal region (red) both orbitals are occupied, whereas in the semiconductor region (blue) the valence band is completely filled.

Figure 2

(a) Phase diagram in the absence of light-matter coupling: metal (red), semiconductor (blue), and excitonic insulator (green). $U_{c1}$ and $U_{c2}$: critical interactions for the EI. The red (blue) intensity map: orbital polarization as in Fig. 1. Dashed line: critical interaction for gap opening in the normal phase. (b) Phase diagram for increasing $g$ (arrow): $g=0$ (green line) $g=0.2$, 0.4, and 0.6 (yellow lines). At finite $g$ the EI (green) transforms into a SXI (yellow). (c) Excitonic and superradiant order parameters as a function of $g$ at $T=0.025$ and three values of $U$.

Figure 3

(a) Spectrum of particle-holes excitations as a function of $U$ at $T=0.025$ at $g=0$. The shaded area represents the particle-hole continuum. Dashed lines: $U_{c1}$ and $U_{c2}$, and $U_{\star }$ as defined in Fig. 2. The dot at $U=U_{c1}$ indicates a $\omega =0$ pole. Full lines: branches of poles crossing zero at $U=U_{c2}$. (b) Density of particle-hole excitations for three values of $U$. Arrows: excitonic resonances.

Figure 4

Photon spectral functions ${\mathcal{A}}_{ph}$ as a function of the light-matter coupling $g$ for $U=0$ (a), $U=0.4$ (b), and $U=2.0$ (c) at $T=0.025$. Dashed lines in panel (a): the upper and lower polaritons. Dashed line in panel (b): dispersion of the low-frequency resonance in the spectral function (see inset). Vertical arrows in panels (b) and (c) indicate the critical couplings for the SXI. Horizontal arrows: excitonic resonances at $g=0$, as defined in Fig. 3.