Signatures of broken symmetries in the excitations of a periodic 2DEG coupled to a cylindrical photon cavity

TL;DR

Addresses how broken symmetries in a periodic 2DEG under a perpendicular magnetic field interact with a cylindrical FIR cavity TE$_{011}$ to shape collective excitations. Employs a self-consistent QED-DFT-TP approach with exact diagonalization within each DF iteration, incorporating both para- and diamagnetic electron-photon interactions and a spatially dependent cavity field. A key finding is that increasing the electron-photon coupling $g_\gamma$ and the magnetic field enhances the diamagnetic channel, yielding dominant two-photon diamagnetic transitions near $2.5\omega_c$ and observable chiral differences in the mean photon-number spectra. Broken unit-cell symmetry further activates center-of-mass and monopole breathing modes, with the diamagnetic interaction playing a central role at higher coupling, highlighting the need for full EP coupling and geometry-aware modeling in magnetized 2DEG-cavity systems.

Abstract

In a two-dimensional electron gas (2DEG) in a periodic lateral superlattice subjected to an external homogeneous magnetic field and in a cylindrical far-infrared photon cavity we search for effects of broken symmetries: Static ones, stemming from the unit cell of the system, and the external magnetic field together with the dynamic ones caused by the vector potential of the cavity promoting magnetic types of transitions, and the chirality of the excitation pulse. The Coulomb interaction of the electrons is described within density functional theory, but the electron-photon interactions are handled by a configuration interaction formalism within each step of the density functional approach, both for the static and the dynamic system. In the dynamical calculations we observe weak chiral effects that change character as the strength of the electron-photon interaction and the external magnetic field are increased. From the analysis of the chiral effects we identify an important connection of the para- and diamagnetic electron-photon interactions that promotes the diamagnetic interaction in the present system when the interaction strength is increased. Furthermore, the asymmetric potential in the unit cell of the square array activates collective oscillation modes that are not present in the system when the unit cell has a higher symmetry.

Figures (12)

• Figure 1: The periodic potential $V_\mathrm{per}(\bm{r})$ shown for 4 neighboring unit cells in two different projections in configuration space. The same color scale is used in both panels to indicate the value of the potential.
• Figure 2: The temporal dependence of the excitation of the 2DEG-cavity system $F(t)$ for the cases of a short or long excitation pulse. For the long pulse $\hbar\omega_\mathrm{ext} = 3.5$ meV, and $\hbar\Gamma = 0.5$ meV, but for the short pulse $\hbar\omega_\mathrm{ext} = 1.5$ meV, $\hbar\Gamma = 8.0$ meV. Specially note that for the case of a short pulse the sign of $V_t$ defines the chirality of the pulse. $E_c = \hbar\omega_c$.
• Figure 3: The energy bandstructure for $N_\mathrm{e}=1$, $pq=1$, $E_\gamma =0.7$ meV, and $g_\gamma =0.08$ (left), $N_\mathrm{e}=2$, $pq=1$, $E_\gamma =0.7$ meV, and $g_\gamma =0.04$ (center), and $N_\mathrm{e}=3$, $pq=2$, $E_\gamma =1.0$ meV, and $g_\gamma =0.08$ (right) projected on the $\theta_1$ direction in reciprocal space. The chemical potential is indicated by a horizontal black line. The photon content of the energy bands is color coded according to the color bar at top.
• Figure 4: The mean values for the spatial coordinates of the center of mass for the electron density within a unit cell for the first approximately 60 - 65 ps after the onset of the excitation pulse for different values of the dimensionless electron-photon coupling $g_\gamma$. $pq=2$, $N_\mathrm{e} = 3$, $V_t=0.1\hbar\omega_c$, $\hbar\omega_c=1.429$ meV. The system is excited with the long excitation pulse with $\hbar\omega_\mathrm{ext} = 3.5$ meV, and $\hbar\Gamma = 0.5$ meV.
• Figure 5: The mean values for the spatial coordinates of the center of mass for the electron density within a unit cell for the first 100 ps after the onset of the excitation pulse for different values of the photon energy $E_\gamma$. $g_\gamma = 0.08$, $pq=1$, $N_\mathrm{e} = 1$, $V_t=0.1\hbar\omega_c$, $\hbar\omega_c=0.7145$ meV. The system is excited with the long excitation pulse with $\hbar\omega_\mathrm{ext} = 3.5$ meV, and $\hbar\Gamma = 0.5$ meV.