Interaction Energy Eint Research Articles

Properties of the ground state of two-dimensional bipolaron with Rashba spin-orbit coupling

In this paper, based on the Lee-Low-Pines transformation, the ground-state properties of the bipolaron with the Rashba spin-orbit coupling effect in the quantum dot are studied by using the Pekar variational method. The expressions for the ground-state interaction energy Eint and binding energy Eb of the bipolaron are derived. The results show that Eint is composed of four parts: the electron-longitudinal optical (LO) phonon coupling energy Ee-ph, confinement potential of the quantum dot Ecouf, Coulomb energy between two electrons Ecoul and additional term in the Rashba spin splitting energy ER-ph originating from the LO phonon, where Ecouf and Ecoul are positive definite. These indicate that Ecouf and Ecoul are the repulsive potential of the bipolaron. Generally, it is unable to form the electron-electron coupling structure in the quantum dot because two electrons repel each other by means of the screened Coulomb potential and confinement potential of the quantum dot. However, the numerical results show that the ground-state binding energy of the bipolaron Eb is greater than zero under the condition of the electron-phonon strong coupling (coupling strength 6), so the condition of forming the steady bipolaron structure in quantum dots is naturally met (binding energy Eb 0). In addition, the ground-state energy of the bipolaron E is always less than zero, thus the ground-state biplaron in the quantum dot is in the steady bound state. This can be explained by the physical mechanism. Firstly, the electron-LO phonon coupling energy Ee-ph in the ground-state interaction energy of the bipolaron is always negative. Secondly, the electron-LO phonon coupling interaction in the low-dimensional structures of II-VI semiconductors is great enough (generally 6.0) so that the electron-LO phonon coupling energy Ee-ph is dominant in the ground-state energy E and, therefore the screened Coulomb potential and confinement potential of the quantum dot can be overcome and a steady electron-electron structure can be formed. The numerical results also indicate that the binding energy of the bipolaron Eb increases with increasing the confinement strength of quantum dot 0, dielectric constant ratio of medium and electronphonon coupling strength , but it shows the direct opposite cases from linear increase to decrease with increasing the Rashba spin-obit coupling strength R; the ground-state energy of the bipolaron splits into three energy levels due to the Rashba effect: E(), E() and E(), which correspond to spin orientations of two electrons respectively: up, down and antiparallel; the absolute value of ground-state energy |E| increases with increasing and , but it shows the direct opposite cases from linear increase to decrease with increasing the Rashba spin-obit coupling strength R; the electron-phonon coupling energy obviously accounts for a larger proportion than that of the Rashba spin-obit coupling energy in the ground-state energy of the bipolaron, but the electron-phonon coupling and Rashba spin-obit coupling infiltrate each other and influence each other significantly. In short, the electron in narrow-gap II-VI heterojunctions have higher Rashba spin splitting energy and larger application range. For these quantum dot structures, it is impossible and unnecessary to inhibit the formation of bipolarons. It is more accurate that the bipolaron is chosen as the elementary excitation than the single polaron when investigating the electron-phonon interaction and Rashba spin-orbit coupling, and the bipolaron has more practical significances and potential application values.

Study of the properties of strong-coupling magnetopolaron in quantum disks induced by the Rashba spin-orbit interaction

On the basis of Lee-Low-Pines unitary transformation, the properties of strong-coupling magnetopolarons in quantum disks (QDs) induced by the Rashba spin-orbit interaction are studied using the Tokuda improved linearly combined operator method. Results show that the state properties of magnetopolarons are closely linked with the sign of the interaction energy Eint, and the Eint of magnetopolarons changes with the transverse confinement strength 0, the cyclotron frequency of the external magnetic field c, the electron-LO phonon coupling strength , and the thickness L of QDs. The average number N of phonons increases with increasing c, 0 and , but the oscillation decreases with increasing thickness L of QDs. The effective mass m0* of magnetopolarons splits into two (m+*, m-*), induced by the Rashba spin-orbit interaction, and the values of them increase with increasing c, 0 and , but the oscillation decreases with increasing thickness L of QDs. For the ground state of magnetopolarons in QDs, the electron-LO phonon interaction plays a significant role, meanwhile, the Rashba spin-orbit coupling effect cannot be ignored. Only for the lower volocity of the electrons, can the polaron effect and the Rashba spin-orbit interaction effect on the magnetopolaron be obvious.

Strictly two-dimensional self-avoiding walks: Density crossover scaling

The density crossover scaling of thermodynamic and conformational properties of solutions and melts of self-avoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions (d = 2) is investigated by means of molecular dynamics and Monte Carlo simulations of a standard coarse grained bead-spring model. We focus on properties related to the contact exponent set by the intrachain subchain size distribution. With R ∼ N ν being the size of chains of length N and ρ the monomer density, the interaction energy e int between monomers from different chains and the corresponding number n int of interchain contacts per monomer are found to scale as with ν = 3/4 and θ2 = 19/12 for dilute solutions and ν = 1/d and θ2 = 3/4 for N≫ g(ρ) ≈ 1/ρ2. Irrespective of ρ, long chains thus become compact packings of blobs of contour length with d p = d − θ2 = 5/4 being the fractal line dimension. Due to the generalized Porod scattering of the compact chains, the Kratky representation of the intramolecular form factor F(q) reveals a non-monotonous behavior approaching with increasing chain length and density a power-law slope $F(q)q^d /\rho \approx 1/(qR)^{\theta _2 } $ in the intermediate regime of the wavevector q. The specific intermolecular contact probability is argued to imply an enhanced compatibility for polymer blends confined to ultrathin films. We comment briefly on finite persistence length effects.