Recent experiments using the quantum dot coupled to the topological superconducting nanowire [Deng et al., Science 354, 1557 (2016)] revealed that the zero-energy bound state coalesces from the Andreev bound states. Such quasiparticle states, present in the quantum dot, can be controlled by magnetic and electrostatic means. We use a microscopic model of the quantum-dot–nanowire structure to reproduce the experimental results, applying the Bogoliubov–de Gennes technique. This is done by studying the gate voltage dependence of the various types of bound states and mutual influence between them. We show that the zero-energy bound states can emerge from the Andreev bound states in the topologically trivial phase and can be controlled using various means. In the nontrivial topological phase we show the possible resonance between these zero-energy levels with Majorana bound states. We discuss and explain this phenomenon as a result of dominant spin character of discussed bound states. Presented results can be applied in experimental studies by using the proposed nanodevice.

Fe-based superconductors (FeSC) exhibit all the properties of systems that allow the formation of a superconducting phase with oscillating order parameter, called the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase. By the analysis of the Cooper pair susceptibility in two-band FeSC, such systems are shown to support the existence of a FFLO phase, regardless of the exhibited order parameter symmetry. We also show the state with nonzero Cooper pair momentum, in superconducting FeSC with ∼cos(k _x )⋅cos(k _y ) symmetry, to be the ground state of the system in a certain parameter range.

Systems containing the ideal kagome lattice can exhibit several distinct and novel exotic states of matter. One example of such systems is a recently discovered $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, and Cs) family of compounds. Here the coexistence of the charge density wave (CDW) and superconductivity is observed. In this paper, we study the dynamic properties of the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ systems in context of origin of the CDW phase. We show and discuss the structural phase transition from $P6/mmm$ to $C2/m$ symmetry that is induced by the presence of phonon soft modes. We conclude that the CDW observed in this family of compounds is a consequence of the atom displacement, from the high-symmetry position of the kagome net, in the low-temperature phase. Additionally, using the numerical ab initio methods, we discuss the charge distribution on the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ surface. We show that the observed experimental stripelike modulation of the surface can be related to surface reconstruction and manifestation of the three-dimensional $2\times 2\times 2$ bulk CDW. Finally, the consequence of realization of the $C2/m$ structure on the electronic properties is discussed. We show that the electronic band structure reconstruction and the accompanying modification of density of states correspond well to the experimental data.

The recently discovered heavy fermion ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ compound crystallizes in nonsymmorphic $P4/nmm$ symmetry, which enables the occurrence of topological protection. Experimental results show that this material exhibits unusual behavior, which is manifested by the appearance of two superconducting phases. In this Letter, we uncover and discuss the role of ${\mathrm{Rh}}_2{\mathrm{As}}_2$ layers and their impact on the electronic and dynamical properties of the system. The location of Ce atoms between two nonequivalent layers allows for the realization of orbital order. We point out that the electronic band structure around the Fermi level is associated mostly with Ce $4f$ and Rh $4d$ orbitals and suggest the occurrence of the Lifshitz transition induced by an external magnetic field. We discuss also the role played by the $f-d$ orbital hybridization in the electronic band structure.

Honeycomb and kagome lattices exhibit extraordinary electronic properties. It is a natural consequence of additional discrete degree of freedom associated with a valley or the occurrence of electronic flat bands. The combination of both types of lattices, observed in CoSn-like compounds, leads not only to the topological electronic behavior, but also to the emergence of chiral phonon modes. We study CoSn-like compounds and show that chiral phonons are realized here. Previous theoretical studies demonstrated that the chiral phonons can be found in ideal two-dimensional honeycomb or kagome lattices. Recent experimental results support such a prediction as the chiral phonons were observed in the transition metal dichalcogenide ${\mathrm{WSe}}_2$. It turns out that in the case of CoSn-like systems with the $P6/mmm$ symmetry, the kagome lattice formed by $d$-block element is decorated by the additional $p$-block atom. As a result one finds a two-dimensional triangular lattice of atoms with nonequal masses and the absence of chiral phonons in the kagome plane. Contrary to this, the interlayer honeycomb lattice of $p$-block atoms is preserved and allows for the realization of chiral phonons. In this paper we discuss the properties of such chiral phonons in seven CoSn-like compounds and demonstrate that they do not depend on the atomic mass ratio or the presence of intrinsic magnetic order. The chiral phonons of $d$-block atoms can be restored by removing the inversion symmetry. The latter is possible in the crystal structure of CoGe and RhPb with the reduced symmetry ($P\overline{6}2m$) and in distorted-kagome-like lattice.

We study the topography of the spin-polarized bound states of magnetic impurities embedded in a triangular lattice of a superconducting host. Such states have been observed experimentally in $2\mathrm{H}\text{−}{\mathrm{NbSe}}_2$ crystal [G. C. Ménard et al., Nat. Phys. 11, 1013 (2015)], and they revealed oscillating particle-hole asymmetry extending to tens of nanometers. Using the Bogoliubov–de Gennes approach, we explore the Yu-Shiba-Rusinov states in the presence of spin-orbit interaction. We also study the bound states of double impurities for several relative positions in a triangular lattice.