Quantum coherent states of mass-imbalanced electron-hole system within optical microcavities

TL;DR

The paper addresses how mass imbalance between conduction electrons and valence holes shapes polariton condensation in optical microcavities. It develops a two-band lattice Hamiltonian with interband Coulomb attraction $U$ and light-matter coupling $g$, solved in the unrestricted Hartree-Fock framework and analyzed with random-phase approximation to obtain self-consistent condensate order parameters and dynamical susceptibilities. The main finding is that reducing mass imbalance (smaller $t^h$) drives the system through a sequence from a normal state to excitonic-like polariton, polariton, and finally photonic-like polariton condensates, with distinct momentum- and frequency-resolved signatures in $d_{f k}$, $n_{ ext{ph}}({f k})$, spectral functions, and susceptibilities; the phase diagrams in the $(n,t^h)$ plane reveal how detuning $d$ and Coulomb interaction $U$ shift these boundaries. These results provide a unified, quantitative framework linking microscopic parameters to observable coherent states in mass-imbalanced microcavities and align qualitatively with experimental observations in ZnO/GaN systems, offering guidance for tailoring polariton composition and studying nonequilibrium/topological aspects in the future.

Abstract

The interplay of the excitoniclike polariton, polariton, and photoniclike polariton coherent states in mass-imbalanced electron-hole systems within optical microcavities is theoretically examined. Utilizing the unrestricted Hartree-Fock approximation, we derive a set of self-consistent equations that evaluate the excitonic and photonic order parameters in a two-band electronic model, accounting equally for both electron-hole Coulomb attraction and light-matter coupling. Analyzing the competition among these condensate order parameters reveals a complex phase structure of coherent states in the ground state. As the mass imbalance is reduced, we observe a transition from a normal disordered electron-hole-photon system to excitoniclike, polariton, and ultimately photoniclike polariton condensation states. The distinct features of these robust condensates can be identified in the momentum distribution of the electron-hole pair amplitude and the photonic density, as well as in the wave-number-resolved photoemission spectra of electrons, holes, and photons. Increasing the excitation density further expands the range of condensation states. Additionally, lowering the mass imbalance leads to the emergence of quantum coherent bound states prior to the formation of robust condensates, which are evidenced by the static and dynamical excitonic and photonic susceptibility functions.

Figures (10)

• Figure 1: Sketched band structure and relevant energy scales for the microscopic Hamiltonian in Eq. \ref{['eq1']} addressing the exciton-polariton formation in an optical microcavity.
• Figure 2: The excitonic $\Delta_{ex}$ (solid lines) and the photonic $\Delta_{ph}$ (dashed lines) condensate order parameters as a function of the hole hopping integral $t^h$ for different values excitation density $n$ at Coulomb interaction $U=1$ and detuning $d=2$.
• Figure 3: The chemical potential $\mu$ and the inverse of the photon excitation energy band bottom $1/\omega_{0}$ versus the hole hopping integral $t^h$ for the sets of parameters mentioned in Fig. \ref{['fig1']}.
• Figure 4: Electron-hole pair amplitude $d_{\bf k}$ (left panels) and the photonic density $n_\textrm{ph}({\bf k})$ (right panels) in the first Brillouin zone for three different values of $t^h$ at $U=1$, $d=2$, and $n=0.12$.
• Figure 5: Wave-number resolved photoemission spectra of electrons $A^e({\bf k},\omega)$ (left panels) and holes $A^h({\bf k},\omega)$ (right panels) for the parameters set in Fig. \ref{['fig3']}.