Magnetopolarons in Quantum-Well Wires
- PDF / 246,591 Bytes
- 5 Pages / 420.48 x 639 pts Page_size
- 17 Downloads / 231 Views
MAGNETOPOLARONS IN QUANTUM-WELL WIRES L. WENDLER*, R. HAUPT-, A. CHAPLIK**, 0. HIP6LITO*** and F. OS6RIO.. * Institut fir Theoretische Physik, Technische Universitit Merseburg, Geusaer Strasse,
D/0-4200 Merseburg, Germany ** Institute of Semiconductor Physics, Prospekt Laurentyeva 13, 630090 Novosibirsk,
Russia * * * Departamento de Fisica e Ci~ncia dos Materiais Instituto de Fisica e Quimica de
Sio Carlos, Universidade de Sio Paulo, C.P. 369, 13560-970 - S.%oCarlos - S.P., Brasil * * ** Departamento de Fisica, Instituto de Matemrtica e Fisica, Universidade Federal de Goif.s, C.P. 131, 74000 Goignia, Goigs, Brasil
ABSTRACT The interaction of quasi-one-dimensional electrons and longitudinal-optical (LO) phonons, placed in a perpendicular magnetic field is calculated. Results are presented for the polaron correction to the Landau levels and the polaron cyclotron mass.
In polar semiconductors the Landau levels are modified by polaronic effects. Hence, in these materials the cyclotron resonance frequency wý = eB/m*, with mý the polaron cyclotron mass, is affected by the interaction of the electrons with the optical phonons. Two situations are commonly distinguished in three-dimensional (3D) and quasi-twodimensional (Q2D) systems: the nonresonant magnetopolaron in low magnetic fields and the resonant magnetopolaron in quantizing magnetic fields when the cyclotron energy approximately equals the optical phonon energy. For the 3D and Q2D polaron, considerable work has been devoted to study the magnetic field dependence of the electron-phonon correction to the energy of Landau levels.[1-6] The eigenenergies of a single electron, confined in a zerg thickness x-y plane along the z-direction and confined in a lateral (y-direction) parabolic quantum well in the presence of a quantizing perpendicular (z-direction) magnetic field are given by EN (k,) = hCc(N + 12 1/2) + h,2 k;/27in; N = 0, 1, 2,... where Cf.e = (w' + Q') / is the hybrid frequency with wC = eB/m the cyclotron frequency, m is the effective band mass of the electron and
S= m(C/C1)
2
.
Neglecting the effects of interface phonons [7,8] the Hamiltonian of the electron-phonon interaction Hp, including only 3D bulk longitudinal-optical (LO) phonons is the standard Frbhlich Hamiltonian [9]. The energy levels of an electron are shifted about AEN(k,) by the interaction with the LO phonons: EN(k-)
2 = hoc(N + 1/2) + h k 2/27h + AEN(k,).
Mat. Res. Soc. Symp. Proc. Vol. 283. 01993 Materials Research Society
834
Within the second-order perturbation theory the energy shift of the N-th Landau level is given by 2
AEN(k.)
IMN'N(q-)1
= -
N'=O i
DN'N(
where the matrix element is MNN(q") =< N', k., - q.; 1¢[He.[N,k.;O
>.
The ket
IN, k,;nq >= IN, k, > 0In4. > describes a state composed of an electron in the Landau level N with momentum hk, and n LO phonons with momentum h" and energy hwL. Because we only consider weakly polar semiconductors with a NfQ and at this magnetic field where wC = [(wLIN) 2
-_ Q2]1/2
is valid.
References 1. D.M.Larsen, Phys.Rev.135, A
Data Loading...
