Phase transitions, Dirac and WSM states in Mn1−xGexBi2Te4

Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), an experimental andtheoretical study of changes in the electronic structure (dispersion dependencies) and corresponding modification of the energyband gap at the Dirac point (DP) for topological insulator (TI) Mn1−xGexBi2Te4 have been carried out with gradual replacementof magnetic Mn atoms by non-magnetic Ge atoms when concentration of the latter was varied from 10% to 75%. It was shownthat when Ge concentration increases then the bulk band gap decreases and reaches zero plateau in the concentration range of45%–60% while non-topological surface states (TSS) are present and exhibit an energy splitting of 100 and 70 meV in differenttypes of measurements. It was also shown that TSS disappear from the measured band dispersions at a Ge concentrationof about 40%. DFT calculations of Mn1−xGexBi2Te4 band structure were carried out to identify the nature of observed banddispersion features and to analyze a possibility of magnetic Weyl semimetal state formation in this system. These calculationswere 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 differentseries of topological phase transitions (TPTs) may be implemented in this system depending on the magnetic ordering. At AFMordering transition between TI and trivial insulator phase goes through the Dirac semimetal state, whereas for FM phase suchroute admits three intermediate states instead of one (TI — Dirac semimetal — Weyl semimetal — Dirac semimetal — trivialinsulator). Weyl points that form in FM system along the ΓZ direction annihilate when either the SOC strength decreases or asufficient tensile strain is applied, which is accompanied by the corresponding TPTs. Model calculations of local magneticordering influence in AFM Mn1−xGexBi2Te4 was carried out by alternating Mn layers and Ge-doped layers and showed that themagnetic Weyl semimetal state in this system is reachable at a Ge concentration of approximately 40% without application ofany external magnetic fields