Giant Effective g Factor and Low Effective Mass in \(Pb_{1-x}Sn_{x}Te\): Effect of Strong Spin-Orbit Interaction and Band Inversion

Abstract

The IV-VI compound semiconductors comprising binary and ternary tellurides exhibit an elevated effective g factor \((g_\textrm{eff})\) and reduced effective mass \((m^{*})\) as a consequence of potent spin-orbit (s.o) interaction. In the ternary compound with magnetic impurity, the observations of high \(g_\textrm{eff}\) and corresponding low \(m^{*}\) are not only attributed to s.o interaction, but also s/p-d/f hybridization. However, as compared to the exchange interaction, the s.o interaction is the strongest and most dominating in these diluted magnetic semiconductors. The strength of the s.o coupling is manifested by the presence of an elevated \(g_\textrm{eff}\) and low \(m^{*}\) in the system. In this correspondence, we measure these parameters in \(Pb_{1-x}Sn_{x}Te\), with Sn as the non-magnetic impurity for different carriers at fixed temperature; T = 1.5K. Here, we formulate an effective equation within the framework of multi-band \(\vec {k}\cdot \vec {\pi }\) theory, incorporating the effect of s.o interaction and a magnetic field. We derive expressions for the \(g_\textrm{eff}\) and \(m^{*}\) through Green’s function expansion method by considering the above interactions with Sn impurity and assuming the band inversion model relevant to the \(Pb_{1-x}Sn_{x}Te\) system. Finally, we extensively examine these parameters and their respective anisotropies in \(Pb_{1-x}Sn_{x}Te\) as functions of carrier concentration and impurity levels at \(T=1.5 K\).We introduce a remarkably high effective g factor, specifically \(g_\textrm{eff}=4280\), for n\(-Pb_{1-x}Sn_{x}Te\) and \(g_\textrm{eff}=3680\), for p\(-Pb_{1-x}Sn_{x}Te\). These values exhibit significant anisotropies, accompanied by correspondingly low effective masses, with \(m_{c}^{*}=0.0023m_{0}\) and \(m_{v}^{*}=0.0024m_{0}\) at \(x=0.36\) within the concentration range of \(10^{17}\) to \(10^{18} {\text{cm}}^{{ - 3}}\). The existence of high \(g_\textrm{eff}\) and low \(m^{*}\) in strongly s.o interacting systems like PbTe, and its alloy \(Pb_{1-x}Sn_{x}Te\) qualify them to be used in spin-orbit physics apart from the field of thermoelectronics.