I will present examples of metals, which have topologically protected crossings in the phonon spectrum. I will show how the topological invariant of such crossings is defined and will show that the presence of such crossings puts the hosting metals among the best known thermoelectric metallic compounds.

Apart from that I will introduce the notion of non-abelian topological charge, defined in...

Weyl semimetal is a topological nontrivial phase of condensed matter which hosts 2-fold degenerate Weyl nodes formed by unavoidable crossings of linearly dispersive bands. The tilted Weyl cone, Lorentz invariance violation and unusual transport properties distinguish the type-II WSM from its type-I counterpart. By combining ARPES study and first-principles calculations, we present the...

Topological materials have attracted great interest in solid state physics due to their ability to support robust quantum states at their boundaries. Recently, it has been predicted that localized zero energy modes can be obtained at junctions of topologically dissimilar graphene nanoribbons (GNR). Within a surface-assisted bottom-up approach using rationally designed molecular precursors, we...

Many topological band structures can be understood as consequences of a quantized Berry phase along phase-space trajectories, which arises from charge polarization. The theory relating topology and polarization has been recently extended to higher-order multipolar moments. Although originally based on the concept of charge polarization, the same theory can also be used to characterize the...

Using super-structures one can effectively change the way that sound waves propagates in space. Topological band theory, known from the description of electrons in solids, provides us with a powerful design-principle for such acoustic metamaterials. Weyl points are robust conical band crossings in three dimensional materials that are monopoles of Berry curvature. When a magnetic field is...

Linear Weyl nodes are classified in type-I and type-II. The Fermi surface, described by a $2^{nd}$ order algebraic surface, has a well define morphology for each type of Weyl point. When the $C_4$ and $C_6$ rotation symmetries forbid linear energy dispersion, as it happens in the composite Weyl nodes, terms with a quadratic or cubic dispersion must be included into the Hamiltonian....

The 6-dimensional Quantum Hall effect offers rich physics that generalize the concepts developed over decades for its 2-dimensional cousin. Using modern technological advances that allow for the study of systems with additional synthetic dimensions, higher-dimensional physics that was previously deemed to be of purely theoretical interest can now be accessed. In this talk, I will show how a...

Iridium oxides with $d^5$ configuration have attracted considerable interest in the last decade due to the realisation of spin-orbit-coupled (SOC) $j_{eff}=1/2$ insulating ground states. Recently, a new class of 5$d^4$ iridates with a singlet ($j_{eff}=0$) ground states have been realised in (Ba/Sr)$_2$YIrO$_6$. Here, we propose a new honeycomb lattice compound Ba$_3$CaIr$_2$O$_9$ in...

Bond-dependent interactions between magnetic moments can lead to strong frustration and nontrivial ground states. In particular, the Kitaev-Heisenberg model has a rich phase diagram and can host a spin liquid state or different frozen states depending on the strength of the additional Heisenberg interactions. Experimentally such phase diagrams can be explored by modifying the relative...

The Weyl and Dirac semimetals are recently discovered topological quantum states of matter characterized by the unavoidable crossing of two non- or doubly-degenerate energy bands near the Fermi level, respectively. These crossing points (Weyl or Dirac nodes) are the source of exotic phenomena, including the realization of massless Dirac and Weyl fermions as quasiparticles in the bulk and the...

The theoretical prediction and experimental validation of Na3Bi and Cd3As2 Dirac semimetals, as well as the TaAs-class Weyl semimetals, stimulated considerable research efforts aiming at extending the family of topological semimetals. Several new classes of gapless topological phases such as the topological nodal-line, nodal-chain, and nodal-net systems as well as high-dimensional fermions...

Cd3As2 is generally considered as archetype of the three-dimensional Dirac semimetal phase, the 3D analogue of graphene with linearly dispersing bulk state. Our reinvestigation of its electronic properties calls for a revision of this simplistic description. Cd3As2 exhibits, in fact, both a surface state and two bulk bands, dispersing across the Fermi level. Hence, these states must all...

Fundamental research and technological applications of topological insulators are hindered by the rarity of materials exhibiting a robust topologically non-trivial phase, especially in two dimensions. Here, by means of extensive first-principles calculations, we propose a novel quantum spin Hall insulator (QSHI) with a sizeable band gap of ∼0.5 eV that is a monolayer of jacutingaite, a...

Magnetoresistance of both topologically trivial and nontrivial materials was extensively studied during past few years. Different mechanisms were proposed to explain the magnetotransport properties, such as the extremely large non-saturating magnetoresistance observed in a number of materials, without arriving to definitive conclusions. By combining of ab initio calculations based on DFT with...

We report a comprehensive study of the low-energy bandstructure of the nodal-line semimetals ZrSiX (X = Se,Te), combining angle-resolved photoemission spectroscopy (ARPES) and first-principle calculations. We discriminate between the existence of bulk and surface states, whose spin texture is revealed by the means of spin-resolved ARPES and confirmed by our calculations. Interestingly, a...

At an interface between a topological insulator (TI) and a conventional $s$-wave superconductor, the induced superconductivity in the TI surface state is expected to develop a complex $p$-wave order parameter which may allow to create Majorana Fermions inside vortex cores. These collective excitations are the basic element in a proposal for fault-tolerant quantum computing. Here we present...