Isomeric electronic states in concentric quantum rings

We show that polarized few-electron concentric double quantum rings display localized states that are the quantum analog of classical equilibrium ones. These states have very similar energies but fairly different angular momenta, constituting a new physical realization of the isomeric states found in nuclear and molecular physics. Their fingerprint is a very soft mode in the infrared-absorption spectrum at nearly the dipole excitation energy of a rigidly rotating $N$-electron molecule. The yrast line and the infrared-absorption spectrum are discussed for $N=4$ and 6 electron configurations.

Figure 1

(Color online) Diagrams of the classical starred configurations for one-dimensional CDR with $N=4$ and 6 point-like electrons. Rigid rotation (left column) and scissor modes (right column) are schematically displayed.

Figure 2

Single-particle spin-up states for the CDQR with $N=4$ and $B=7.5\text{T}$, obtained within the LSDA. The solid and dashed horizontal lines correspond, respectively, to the chemical potential and to the energy of the lowest state with $n=2$.

Figure 3

Yrast line for the CDQR with $N=4$ at $B=7.5\text{T}$ (bottom panel), and for the CDQR with $N=6$ at $B=8\text{T}$ (top panel). For the $N=4$ $\left(N=6\right)$ case, all sp states with energies up to the minimum of the $n=4$ $\left(n=2\right)$ sp band have been used, yielding basis of up to $106951$ $\left(133037\right)$ SDs.

Figure 4

(Color online) Two-body density for $N=4$, $L_0=84$, and $B=7.5\text{T}$ (bottom row), and for $N=6$, $L_0=297$, and $B=8\text{T}$ (top row), when one electron (cross) is located in the inner ring (left column) or in the outer ring (right column).

Figure 5

(Color online) Low-energy dipole absorption spectrum, in arbitrary units, for the $N=4$, $L_0=70$ CDQR at $B=7.5\text{T}$ (botom panel), and for the $N=6$, $L_0=275$ CDQR at $B=8\text{T}$ (top panel). The inset in the bottom panel displays the dipole spectrum corresponding to the lowest energy 4000 excitations for each polarization. Solid lines correspond to the $(+)$ circular polarization, and dashed lines to the $(-)$ circular polarization. Peaks are represented by Lorentzians of 0.1 meV full width at half maximum.