Dielectric function of the semiconductor hole liquid: Full frequency and wave-vector dependence

Abstract

We study the dielectric function of the homogeneous semiconductor hole liquid of p-doped bulk III-V zinc-blende semiconductors within random-phase approximation. The single-particle physics of the hole system is modeled by Luttinger's four-band Hamiltonian in its spherical approximation. Regarding the Coulomb-interacting hole liquid, the full dependence of the zero-temperature dielectric function on wave vector and frequency is explored. The imaginary part of the dielectric function is analytically obtained in terms of complicated but fully elementary expressions, while in the result for the real part nonelementary one-dimensional integrations remain to be performed. The correctness of these two independent calculations is checked via Kramers-Kronig relations. The mass difference between heavy and light holes, along with variations in the background dielectric constant, leads to dramatic alternations in the plasmon excitation pattern, and, generically, two plasmon branches can be identified. These findings are the result of the evaluation of the full dielectric function and are not accessible via a high-frequency expansion. In the static limit a beating of Friedel oscillations between the Fermi wave numbers of heavy and light holes occurs.

Plasmons and screening in a monolayer of MoS2

“…24 In recent years large effort has been made in the discussion of the dielectric function of graphene under various conditions. [25][26][27][28][29][30][31][32] One of the main findings was that the behavior of plasmons in graphene in several aspects is quite different compared to traditional two-dimensional materials such as III-V semiconductor quantum wells [33][34][35][36][37][38] due to the relativistic nature of the charge carriers and the existence of a pseudospin degree of freedom. Although in both systems, ML-MDS and graphene, the atoms are arranged in a honeycomb lattice, with two inequivalent corners of the Brillouin zone denoted as valleys, the energy spectrum in ML-MDS turns out to be quite different compared to that of graphene as in the former electrons and holes cannot be considered as massless particles but rather carry a finite effective mass due to the large band gap being of the order of the hopping parameter.…”

Plasmons in spin-orbit coupled two-dimensional hole gas systems

“…While these bands resemble that of an ordinary electron gas, the eigenstates are clearly more complicated 13 due to their nontrivial spin structure.…”

“…[4][5][6] The latter is not only necessary in understanding screening of extrinsic charged impurities, which in turn is important for transport, but also because of the existence of collective charge excitations known as plasmons. 7,8 Many analytical and numerical studies have been made in the last years regarding the dielectric properties of electron 4,5,[9][10][11] and hole gas systems [12][13][14][15] or promising materials like graphene. [16][17][18][19][20][21][22] As has been shown in recent works, large analytical progress could be made in a two-dimensional electron gas (2DEG) including the effect of an asymmetric confinement, the Rashba SOC, and the contribution due to bulk inversion asymmetry (BIA), the so called Dresselhaus SOC, 5,9,10 or in graphene including several types of spin-orbit interactions (SOIs).…”

“…[20][21][22] Due to the more complicated nature of the valence bands, the calculation of the dielectric function in hole gas systems turns out to be a formidable task even without SOIs. While for the three-dimensional case the free polarizability has been obtained for arbitrary frequencies and wave vectors within the axial model, 13 the solution for the two-dimensional case is not known so far.…”

Electrical and optical conductivities of hole gas in p-doped bulk III–V semiconductors

“…A theoretical study of interacting hole gas in p-doped bulk III-V semiconductors has been done using the self-consistent Hartree-Fock method 9 . The dielectric function and beating pattern of the Friedel oscillations of the bulk hole liquid within the random phase approximation are also studied 10,11 . There have been extensive theoretical 12,13 and experimental [14][15][16][17][18] studies on p-doped III-V ferromagnetic semiconductors 19 such as GaMnAs and InMnAs with the Curie temperature T<170 K. Recently, the magnetotransport coefficients of the Luttinger Hamiltonian have been studied numerically 20 .…”