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Plasma frequency in doped highly mismatched alloys

Highly mismatched alloys (HMAs) have band structures strongly modified due to the introduction of the alloying element. We consider HMAs where the isolated state of the alloying element is near the host conduction band, which causes the conduction band to split into two bands. We determine the bulk plasma frequency when the lower-energy band is partially occupied, as by doping, using a semi-analytical method based on a disorder-averaged Green's function. We include the nontrivial effects of interband transitions to the higher-energy band, which limit the plasma frequency to be less than an effective band gap. We show that the distribution of states in the split bands causes plasmons in HMAs to behave differently than plasmons in standard metals and semiconductors. The effective mass of the lower split band $m^*$ changes with alloy fraction, and we find that the plasmon frequency with small carrier concentration $n$ scales with $\sqrt{n}/m^*$ rather than the $\sqrt{n/m^*}$ that is expected in standard materials. We suggest experiments to observe these phenomena. Considering the typical range of material parameters in this group of alloys and taking a realistic example, we suggest that HMAs can serve as highly tunable low-frequency plasmonic materials.