Phase transitions, Dirac and WSM states in Mn_1-xGe_x Bi_2 Te_4

Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), an experimental and theoretical study of changes in the electronic structure (dispersion dependencies) and corresponding modification of the energy band gap at the Dirac point (DP) for topological insulator (TI) Mn_1-xGe_x Bi_2 Te_4 have been carried out with gradual replacement of magnetic Mn atoms by non-magnetic Ge atoms when concentration of the latter was varied from 10% to 75%. It was shown that when Ge concentration increases then the bulk band gap decreases and reaches zero plateau in the concentration range of 45%-60% while non-topological surface states (TSS) are present and exhibit an energy splitting of 100 and 70 meV in different types of measurements. It was also shown that TSS disappear from the measured band dispersions at a Ge concentration of about 40%. DFT calculations of Mn_1-xGe_x Bi_2 Te_4 band structure were carried out to identify the nature of observed band dispersion features and to analyze a possibility of magnetic Weyl semimetal state formation in this system. These calculations were performed for both antiferromagnetic (AFM) and ferromagnetic (FM) ordering types while the spin-orbit coupling (SOC) strength was varied or a strain (compression or tension) along the c-axis was applied. Calculations show that two different series of topological phase transitions (TPTs) may be implemented in this system depending on the magnetic ordering. At AFM ordering transition between TI and trivial insulator phase goes through the Dirac semimetal state, whereas for FM phase such route admits three intermediate states instead of one (TI - Dirac semimetal - Weyl semimetal - Dirac semimetal - trivial insulator).