Relativistic effects in HgTe and CdTe electronic structure C. D. Hinostroza and P. H. Rivera cristhian.hinostroza2@unmsm.edu.pe priverar@unmsm.edu.pe ABSTRACT Quantum spin Hall phase, or also referred as Topological Insulator state, has been obtai- ned in 2007 in a CdTe/HgTe quantum well. These novel state is possible due to the in- verted band order near the Fermi energy, for the HgTe. These behaviour is originated becau- se there exist a non negligible correlation bet- ween valence electrons of the 5d- and 6s-orbital of Hg, and relativistic effects, speciﬁcally spin- orbit coupling. In this work, we present the electronic struc- ture of Cadmiun Telluride (CdTe) and Mercury Teluride (HgTe), obtained using the local spin density approximation, including the Hubbard correction (LSDA+U), in the density functional theory (DFT), considering non relativistic, rela- tivistic, and relativistic with spin-orbit coupling effects for each alloy. The results show that re- lativistic effects reduce the band gap for both alloys, and inverted band ordering for HgTe is only possibe if spin-orbit copupling is conside- red. THEORY Density functional theory is a method used to solve the many body problem based on the Hohemberg and Kohm theorems. Thus, the ob- servables could be calculates as a functional of the ground state energy electronic density, wich is obtained calculating the density that mini- mizes the energy expresion derived from the Kohn-Sham equation: E = N X i ϵi −EH[ρ] + Exc[ρ] − Z δExc[ρ] δρ(r) ρ(r)dr Where ϵi is related to the kinetic Kohn-Sham energy, EH to the Hartree energy, and Exc is the exchane and correlation nergy, wisch is consi- dered using the LDA approximation, as presen- ted by Perdew and Wang: EXC[n↑, n↓] = Z d3rn(r)ϵhom XC (n↑, n↓) Some systems need to consider a correction in the correlation function due to strong inter- action between electrons. This is achieved ad- ding the Hubbard correction in the LDA energy function. ELDA+U[n(r)] = ELDA[n]+EHub[nσ mm′]−Edc[nσ] Where Edc is the double counting term: Edc[nIσ mm′] = X Iσ U I 2 Tr[nIσ(1 −nIσ)] The relativistic solution is calculated using the Zero order regular aproximation: HZORA = V +p c2 2c2 −V p+ c2 (2c2 −V )2 σ·(∇V ×p) PROCEEDINGS Cadmium and Mercury Telluride are both II- VI type semiconductors. These materials have a Zinc Blende structure with lattice parameter a = 6,46Åand a = 6,48Åfor CdTe and HgTe repec- tively. Both semiconductors below to the F¯43m space group, with group number 216. Wich co- rrespond to two FCC displaced by ( 1 4, 1 4, 1 4) each other. We used the DFT method to get the band structure aplying the LAPW basis as implemen- ted in the package Exciting code. The Ex- change and Correlation energy considered was the LDA as presented by Perdew and Zhang icn- luding the Hubbard correction, and the relativis- tic effects where obtained with the Zero Order Regular Approximation of the Dirac Hamilto- nian. To appreciate the effects of relativistic con- siderations we performed calculations without any relativistic terms, with relativistic terms but without spin-orbit coupling, and within relati- vistic terms considering spin-orbit coupling. RESULTS Non relativistic L Γ X -2 -1 0 1 2 Energy (eV) Cd s L Γ X EF Te p L Γ X -2 -1 0 1 2 Energy (eV) Hg s L Γ X EF Te p Relativistic without s · L L Γ X -2 -1 0 1 2 Energy (eV) Cd s L Γ X EF Te p L Γ X -2 -1 0 1 2 Energy (eV) Hg s L Γ X EF Te p Relativistic considering s · L L Γ X -2 -1 0 1 2 Energy (eV) Cd s L Γ X EF Te p L Γ X -2 -1 0 1 2 Energy (eV) Hg s L Γ X EF Te p CONCLUSIONS From our calculations, we observe that the- re is a dependece between spin-orbit coupling and band ordering, obtained only if electron co- rrelation is considered. Relativistic effects chan- ges the band structure in a non neglible way, reducing the band gap from 3.07 and 2.87 eV to 1.05 and -0.104 eV for CdTe and HgTe res- pectively, also invreasin the velocity of charge carriers at Γ point. There must exist a value x for HgxC