Topological tight binding models on some non-trivial lattices: Union of geometry, flat bands and topology.

We introduce a topological tight binding model based on certain rules that we have formulated to study systems with certain non-trivial bulks (abbreviated as SAB). These rules allows us to study bulks that have twists and branching. We discuss certain cases in the SAB model with different number of bands, exhibiting several interesting physical properties. For every bulk there can be two sets of configurations: the orientable and the non-orientable configuration. The later exhibits several non-trivial physical properties like exact flat bands (exactly at particle hole symmetry level), zero energy states localised in the bulk, topological edge states etc. We then discuss a three band non-orientable SAB model which is easy to visualise and hence can be realized in experiments first. We also investigate the effects of disorder (both chiral symmetry preserving and breaking) in the non-orientable configurations hosting flat bands. We find for chiral symmetry preserving disorders, some of them (non-degenerate flat band) are robust to large disorders while others (degenerate flat band) exhibit an insulator to metal transition beyond certain disorder strength due to band gap closing as a result of the broadening of the zero energy states. For chiral symmetry breaking disorders, in both the cases the zero energy bulk states broaden and close the gap beyond certain critical disorder strength.

Tunable phase transitions in half-Heusler TbPtBi compound.

We report various phase transitions in half-Heusler TbPtBi compound using density functional theory. Specifically, the inclusion of spin-orbit coupling (SOC) leads to the band inversion resulting in the transition from the metallic to the topological semimetallic phase. However, in the presence of SOC, there is a phase transition from the topological semimetal to the trivial semimetal when the material is subjected to compressive strain-7%. Subsequently, under the further increase of compressive strain(⩾​​-7%), we find an opening of a direct band gap at the point, driving the system from the trivial semimetallic to a semiconducting state with changes in the sequence of the bands. In the absence of SOC, only the transition from the metallic to the semiconducting phase is noticed. Under tensile strain, the TbPtBi compound maintains its phase as in the unstrained condition but with an increase in the hole pocket at the Fermi level, both in the absence and presence of SOC. These tunable phase transitions (especially as a fraction of strain) make this compound very promising for application in various quantum devices, such as highly sensitive strain gauges.

The case of itinerant magnetism in CaMn2Al10: self-consistent renormalisation (SCR) theory study.

We have applied the powerful self-consistent renormalization theory of spin fluctuations for the system CaMn2Al10discovered in 2015 and was conjectured to be an itinerant magnet. We have calculated the inverse static i.e. (paramagnetic) susceptibility and have compared it with the experimental data (Steinkeet al2015Phys. Rev.B92020413). The agreement is very good. We have calculated spin fluctuations at various temperatures and have also estimated the strength of the electronic correlation i.e. (U = 0.3136 eV) in the Hubbard Hamiltonian. Based on our quantitative explanation of the inverse static i.e. (paramagnetic) susceptibility data within the framework of self-consistent renormalization theory, we can decisively conclude CaMn2Al10exhibits the phenomena of itinerant magnetism. Further, our density functional theory (DFT) and DFT + U calculations corroborate the strong Mn-Al hybridization which is the key to the itinerant magnetism in this system. Our estimated correlations strength will provide a foundation for further studies of itinerant magnetism in this system.