Quench dynamics of Fano-like resonances in the presence of the on-dot superconducting pairing.

We explore the electron dynamics of a system composed of double quantum dot embedded between metallic and superconducting leads in a "T-shape" geometry. In nanoscopic systems, where electron transfer between electrodes can be realized via different paths, interference effects play an important role. For double quantum dot system in the chosen geometry, interference of electrons transferred between electrodes via the interfacial quantum dot and electrons scattered on the side dot gives rise to Fano-like interference. If such a system is additionally coupled to a superconducting electrode, together with the well-understood Fano resonance an additional resonance appears on the opposite side of the Fermi level. In the recent work (Baranski et al. in Sci Rep 10:2881, 2020), we showed that this resonance occurs solely as a result of the local pairing of non-scattered electrons with scattered ones. In this work, considering the quench dynamics, we explore how much time is required for formation of each of these resonances. In particular, (i) we analyze the charge oscillations between subsystems; (ii) we estimate the time required for each resonance to achieve stable equilibrium upon an abrupt change of interdot connection; (iii) we discuss a typical energy and time scales for experiments on similar architectures.

Charge-Order on the Triangular Lattice: A Mean-Field Study for the Lattice S = 1/2 Fermionic Gas.

The adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111) surface of face-cubic center crystals. In the present work, an extension of the lattice gas model to S=1/2 fermionic particles on the two-dimensional triangular (hexagonal) lattice is analyzed. In such a model, each lattice site can be occupied not by only one particle, but by two particles, which interact with each other by onsite U and intersite W1 and W2 (nearest and next-nearest-neighbor, respectively) density-density interaction. The investigated hamiltonian has a form of the extended Hubbard model in the atomic limit (i.e., the zero-bandwidth limit). In the analysis of the phase diagrams and thermodynamic properties of this model with repulsive W1>0, the variational approach is used, which treats the onsite interaction term exactly and the intersite interactions within the mean-field approximation. The ground state (T=0) diagram for W2≤0 as well as finite temperature (T>0) phase diagrams for W2=0 are presented. Two different types of charge order within 3×3 unit cell can occur. At T=0, for W2=0 phase separated states are degenerated with homogeneous phases (but T>0 removes this degeneration), whereas attractive W2<0 stabilizes phase separation at incommensurate fillings. For U/W1<0 and U/W1>1/2 only the phase with two different concentrations occurs (together with two different phase separated states occurring), whereas for small repulsive 0

Extended Falicov-Kimball model: Hartree-Fock vs DMFT approach.

In this work, we study the extended Falicov-Kimball model at half-filling within the Hartree-Fock approach (HFA) (for various crystal lattices) and compare the results obtained with the rigorous ones derived within the dynamical mean field theory (DMFT). The model describes a system, where electrons with spin-↓ are itinerant (with hopping amplitude t), whereas those with spin-↑ are localized. The particles interact via on-site U and intersite V density-density Coulomb interactions. We show that the HFA description of the ground state properties of the model is equivalent to the exact DMFT solution and provides a qualitatively correct picture also for a range of small temperatures. It does capture the discontinuous transition between ordered phases at U = 2V for small temperatures as well as correct features of the continuous order-disorder transition. However, the HFA predicts that the discontinuous boundary ends at the isolated-critical point (of the liquid-gas type) and it does not merge with the continuous boundary. This approach cannot also describe properly a change of order of the continuous transition for large V as well as various metal-insulator transitions found within the DMFT.

Electronic properties of Bi2Se3 dopped by 3d transition metal (Mn, Fe, Co, or Ni) ions.

Topological insulators are characterized by the existence of band inversion and the possibility of the realization of surface states. Doping with a magnetic atom, which is a source of the time-reversal symmetry breaking, can lead to realization of novel magneto-electronic properties of the system. In this paper, we study effects of substitution by the transition metal ions (Mn, Fe, Co and Ni) into Bi2Se3 on its electric properties. Using the ab inito supercell technique, we investigate the density of states and the projected band structure. Under such substitution the shift of the Fermi level is observed. We find the existence of nearly dispersionless bands around the Fermi level associated with substituted atoms, especially, in the case of the Co and Ni. Additionally, we discuss the modification of the electron localization function as well as charge and spin redistribution in the system. Our study shows a strong influence of the transition metal-Se bond on local modifications of the physical properties. The results are also discussed in the context of the interplay between energy levels of the magnetic impurities and topological surface states.

Anomalous Fano Resonance in Double Quantum Dot System Coupled to Superconductor.

We analyze the influence of a local pairing on the quantum interference in nanoscopic systems. As a model system we choose the double quantum dot coupled to one metallic and one superconducting electrode in the T-shape geometry. The analysis is particularly valuable for systems containing coupled objects with considerably different broadening of energy levels. In such systems, the scattering of itinerant electrons on a discrete (or narrow) energy level gives rise to the Fano-type interference. Systems with induced superconducting order, along well understood Fano resonances, exhibit also another features on the opposite side of the Fermi level. The lineshape of these resonances differs significantly from their reflection on the opposite side of the Fermi level, and their origin was not fully understood. Here, considering the spin-polarized tunneling model, we explain a microscopic mechanism of a formation of these resonances and discuss the nature of their uncommon lineshapes. We show that the anomalous Fano profiles originate solely from the pairing of nonscattered electrons with scattered ones. We investigate also the interplay of each type of resonances with the Kondo physics and discuss the resonant features in differential conductivity.

Phase separations induced by a trapping potential in one-dimensional fermionic systems as a source of core-shell structures.

Ultracold fermionic gases in optical lattices give a great opportunity for creating different types of novel states. One of them is phase separation induced by a trapping potential between different types of superfluid phases. The core-shell structures, occurring in systems with a trapping potential, are a good example of such separations. The types and the sequences of phases which emerge in such structures can depend on spin-imbalance, shape of the trap and on-site interaction strength. In this work, we investigate the properties of such structures within an attractive Fermi gas loaded in the optical lattice, in the presence of the trapping potential and their relations to the phase diagram of the homogeneous system. Moreover, we show how external and internal parameters of the system and parameters of the trap influence their properties. In particular, we show a possible occurrence of the core-shell structure in a system with a harmonic trap, containing the BCS and FFLO states. Additionally, we find a spatial separation of two superfuild states in the system, one in the BCS limit as well as the other one in the tightly bound local pairs (BEC) regime.

Diversity of charge orderings in correlated systems.

The phenomenon associated with inhomogeneous distribution of electron density is known as a charge ordering. In this work, we study the zero-bandwidth limit of the extended Hubbard model, which can be considered as a simple effective model of charge ordered insulators. It consists of the on-site interaction U and the intersite density-density interactions W_{1} and W_{2} between nearest neighbors and next-nearest neighbors, respectively. We derived the exact ground state diagrams for different lattice dimensionalities and discuss effects of small finite temperatures in the limit of high dimensions. In particular, we estimated the critical interactions for which new ordered phases emerge (laminar or stripe and four-sublattice-type). Our analysis show that the ground state of the model is highly degenerated. One of the most intriguing finding is that the nonzero temperature removes these degenerations.