Metastable Bound States of the Two-Dimensional Bimagnetoexcitons in the Lowest Landau Levels Approximation

Abstract

The possible existence of the bound states of the interacting two-dimensional (2D) magnetoexcitons in the lowest Landau levels (LLLs) approximation was investigated using the Landau gauge description. The magnetoexcitons taking part in the formation of the bound state with resultant wave vector 0 k  have opposite in-plane wave vectors k and k  and look as two electric dipoles with the arms oriented in-plane perpendicularly to the corresponding wave vectors. The bound state of two antiparallel dipoles moving with equal probability in any direction of the plane with equal but antiparallel wave vectors is characterized by the variational wave function of the relative motion () n k  depending on the modulus | | . k The spins of two electrons and the effective spins of two holes forming the bound states were combined separately in the symmetric or in the antisymmetric forms ()     with the same parameter 1   for electrons and holes. In the case of the variational wave function 3 1/2 2 2 2 2 2 0 0 ( ) (8 ) exp[ ] k k l k l     the maximum density of the magnetoexcitons in the momentum space representation is concentrated on the in-plane ring with the radius 0 1/ ( ). r kl   The stable bound states of the bimagnetoexciton molecule do not exist for both spin orientations. Instead of them, a deep metastable bound state with the activation barrier comparable with the ionization potential l I of the magnetoexciton with 0 k  was revealed in the case 1   and 0.5.   In the case 1   and 3.4   only a shallow metastable bound state can appear. 3

Metastable bound states of the quasi–bimagnetoexcitons in the lowest Landau levels approximation

“…The mean distance between the magnetoexcitons in the bound state is 0 , Rl where 0 l is the magnetic length. The calculations with more cumbersome wave function corresponding to the bound state with resulting spin 0 S  formed by 4 two ortho-magnetoexcitons confirmed the earlier obtained results [14,15] and allow to better understand the uniqueness of the triplet-triplet spin configuration studied earlier and its importance in similar biexciton spin structures in the absence of the magnetic field.…”

“…The interaction coefficients depend only on the difference ( pq  ) for the electron-electron ( ee  ) and the hole-hole ( hh  ) interactions, and on the sum ( pq  ) for the electron-hole ( eh  ) interactions. The magnetoexciton creation operator introduced in [12] but with spin labels [15,16] The wave function of the magnetoexciton is…”

“…The electrons and the heavy holes are situated on the LLLs with the cyclotron energies greater than the binding energy of the 2D Wannier-Mott exciton. The spin states of two electrons and the effective spins of two heavy holes were combined to form states characterized by the parameter  with four different values 1, 1 2   corresponding to four different spin structures: triplet-15 triplet, singlet-singlet, ortho-ortho and para-para. Each magnetoexciton with wave vector 0 k  looks as an electric dipole with the length of the arm between the electron and the hole equal to…”

A two–dimensional electron–hole system under the influence of the Chern–Simons gauge field created by quantum point vortices

“…Hamiltonian describing bare 2D electrons and holes in an external perpendicular magnetic field and interacting by the Coulomb forces obtained in [13] looks as follows:…”

“…Coulomb interaction potential in a 2D system can be represented as ( ) were derived in [13], and we just recall them:…”