Magnetophonon resonance in quantum wires

The magnetophonon resonance (MPR) effect has been used since the mid-1960s to investigate effective mass, optical-phonon energy and electron-phonon interaction in bulk III–V compounds [1–5]. Several authors have also studied MPR effect in two-dimensional (2D) systems, such as GaAs/AlGaAs, GaInAs/InP, and GaInAs/AlInAs heterostructures [6]. The MPR effect manifests itself as an oscillatory behavior of transverse-conductivity σ xx as a function of applied magnetic field B. At high magnetic fields, electrons move perpendicularly to both electric and magnetic fields, and the transverse-current is carried by electron-hopping motion induced by some scattering mechanisms. The MPR effect arises from the resonant absorption or emission of longitudinal-optical (LO) phonons by electrons when the Landau level is sharp and well defined, and scattering by LO phonons makes a significant contribution to limiting electron mobility. As the magnetic field increases, a small part of σ xx resonantly increases each time the integral multiple of the Landau level spacing becomes equal to the LO phonon energy, because the scattering of the electrons takes place with resonant absorption or emission of LO phonons. In bulk materials and 2D systems, the oscillatory part of σ xx is therefore proportional to the Frohlich coupling constant α, and the resonance condition where σ xx becomes maximal is written as $$ \hbar {\omega _{LO}} = P\hbar {\omega _c}(P = 1,2,3, \cdots ),$$ (2.3.1) where ħω LO is the LO phonon energy, P the resonance index, and ħω c = ħeB/m the cyclotron energy. From the measurement of the MPR effect, effective mass in or LO phonon energy ħω LO can be deduced, provided that one of the two is known. In order to observe the MPR effect, the temperature must be high enough to have a sufficient phonon population, but not too high, since the thermal broadening of the Landau levels reduces the oscillation amplitude. Optimal temperatures are known to be usually in the range 100–250 K for III-V materials.