Magnetic field spectral crossings of Luttinger holes in quantum wells

Abstract

We develop an analytic approach to two-dimensional (2D) holes in a magnetic field that allows us to gain insight into physics of measuring the parameters of holes, such as cyclotron resonance, Shubnikov-De Haas effect and spin resonance. We derive hole energies, cyclotron masses and the g-factors in the semiclassical regime analytically, as well as analyze numerical results outside the semiclassical range of parameters, qualitatively explaining experimentally observed magnetic field dependence of the cyclotron mass. In the semiclassical regime with large Landau level indices, and for size quantization energy much bigger than the cyclotron energy, the cyclotron mass coinsides with the in-plane effective mass, calculated in the absence of a magnetic field.The hole g-factor in a magnetic field perpendicular to the 2D plane is defined not only by the constant of direct coupling of the angular momentum of the holes to the magnetic field, but also by the Luttinger constants defining the effective masses of holes. We find that the g-factor for quasi 2D holes with heavy mass in the [001] growth direction in GaAs quantum well is g = 4.05 in the semiclasssical regime. Outside the semiclassical range of parameters, holes behave as a species completely different from electrons. Spectra for size-and magnetic-field-quantized holes are non-equidistant, not fan-like, and exhibit multiple crossings, including crossing in the ground level. We calculate the effect of Dresselhaus terms, which transform some of the crossings into anticrossings, and the effects of the anisotropy of the Luttinger Hamiltonian on the 2D hole spectra. Dresselhaus terms of different symmetries are taken into account, and a regularization procedure is developed for the k 3 z Dresselhaus terms. Control of the non-equidistant levels and crossing structure by the magnetic field can be used to control Landau level mixing in hole systems, and thereby control hole-hole interactions in the magnetic field.

Dimensional reduction of the Luttinger Hamiltonian andg-factors of holes in symmetric two-dimensional semiconductor heterostructures

“…This approach used in Ref. 27 for the rectangular well indicated a significant dependence of g-factor on Landau level. However, this method is rather technically involved and computationally expensive.…”

“…We remind that α(k x ) is the coefficient in the gate spin orbit interaction and β(k x ) is the coefficient in the gate Darwin term, both functions have been determined in section V. The α-term in (27) is due to π y = −eBx. Eq.…”

“…The virtual 3D dynamics is even more important for response to the in-plane magnetic field 13,28 . Effects of magnetic field in some dimensionally reduced systems have been considered previously, but only in some limiting cases 13,[24][25][26][27][28][29] . The spin-orbital effects related to the lateral gate potential to the best of our knowledge have been considered before only in a very special limit related to the artificial graphene 30 .…”

Conserved spin quantity in strained hole systems with Rashba and Dresselhaus spin-orbit coupling

“…This problem can be resolved by a regularization procedure as shown in Ref. [30]. Furthermore, contributions due to boundary effects which result from the presence of heterointerfaces are assumed to be small.…”

“…Furthermore, contributions due to boundary effects which result from the presence of heterointerfaces are assumed to be small. Such an interface can allow for additional HH-LH mixing [26,[30][31][32][33]. A possible alternation of spin relaxation due to interface effects will be discussed elsewhere.…”