On the energy spectrum of gapless semiconductors with considerably differing masses of electrons and holes

The influence of the interaction of electrons on the spectrum of a gapless semiconductor with m _h ≫ m _e is considered. For k ≫ k₀ = m_ee²/% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Xdmgaaa!37A4!\[\chi\]we obtain % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaH1o% qzdaWgaaWcbaGaaeyzaaqabaGccqGH9aqpcaqGGaWaaSaaaeaacaqG% RbWaaWbaaSqabeaacaqGYaaaaaGcbaGaaGOmaiaab2gadaWgaaWcba% GaaeyzaaqabaaaaOGaey4kaSYaaSaaaeaacaaIZaGaeqiWdaNaaeyz% amaaCaaaleqabaGaaeyzaaaaaOqaaiaaiodacaaIYaGaeq4Xdmgaai% aabUgacqGHsisldaWcaaqaaiaaikdaaeaacqaHapaCaaGaeqyYdC3a% aSbaaSqaaiaaicdaaeqaaOGaaeiiaiaabYgacaqGUbWaaSaaaeaaca% qGRbaabaGaae4AamaaBaaaleaacaqGWaaabeaaaaaakeaacqaH1oqz% daWgaaWcbaGaaeiAaaqabaGccqGH9aqpcaqGGaWaaSaaaeaacaqGRb% WaaWbaaSqabeaacaqGYaaaaaGcbaGaaGOmaiaab2gadaWgaaWcbaGa% aeiAaaqabaaaaOGaey4kaSYaaSaaaeaacaaIZaGaeqiWdaNaaeyzam% aaCaaaleqabaGaaeOmaaaaaOqaaiaaiodacaaIYaGaeq4Xdmgaaiaa% bUgacqGHsisldaWcaaqaaiaaikdaaeaacqaHapaCaaGaeqyYdC3aaS% baaSqaaiaaicdaaeqaaOGaaeiiaiaabYgacaqGUbWaaSaaaeaacaqG% RbaabaGaae4AamaaBaaaleaacaqGWaaabeaaaaaaaaa!7239!\[\begin{gathered}\varepsilon _{\text{e}} = {\text{ }}\frac{{{\text{k}}^{\text{2}} }}{{2{\text{m}}_{\text{e}} }} + \frac{{3\pi {\text{e}}^{\text{e}} }}{{32\chi }}{\text{k}} - \frac{2}{\pi }\omega _0 {\text{ ln}}\frac{{\text{k}}}{{{\text{k}}_{\text{0}} }} \hfill \\\varepsilon _{\text{h}} = {\text{ }}\frac{{{\text{k}}^{\text{2}} }}{{2{\text{m}}_{\text{h}} }} + \frac{{3\pi {\text{e}}^{\text{2}} }}{{32\chi }}{\text{k}} - \frac{2}{\pi }\omega _0 {\text{ ln}}\frac{{\text{k}}}{{{\text{k}}_{\text{0}} }} \hfill \\\end{gathered}\](% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyYdC3aaS% baaSqaaiaaicdaaeqaaOGaeyypa0JaaeyBamaaBaaaleaacaqGLbaa% beaakiaabwgadaahaaWcbeqaaiaabsdaaaGccaGGVaGaaGOmaiabeE% 8aJnaaCaaaleqabaGaaGOmaaaaaaa!41A3!\[\omega _0 = {\text{m}}_{\text{e}} {\text{e}}^{\text{4}} /2\chi ^2\]). In the region k ≪ k₀ the assumption ɛ _e ≫ ɛ _h leads to a contradiction which probably means the failure of the random phase approximation. It is demonstrated that at finite temperatures T ≫ Ω₀ the energy spectra of electrons and holes in the most essential momentum regions remain the same as for T = 0.