Condensed Matter Physics Seminars

In this talk we will focus on atomic chains in different topological phases and geometries placed on different substrates. We will show basic electrical properties of this kind of nanostructures and show theoretical calculation methods of these properties. In particular there will be analysed modified SSH chains (straight, zig-zag and armchair edge geometries) connected to different types of 2D electrodes (electron reservoirs): characterized by a flat band structure or with van Hove singularities, which are common in real 2D structures like graphene, silicene, antimonene or other atomic layers. There will be shown how topological SSH states are influenced by the DOS singularities of 2D substrates and verified if these states are robust to these singularities and if the space and energetic symmetries of 1D edge states survive in the presence of 2D substrates. Moreover, there will be discussed if the SSH topological states can appear outside the electrode’s DOS.

We introduce three new analytical and semi-analytical tools that allow one to determine the topological character of impurity Shiba chains. The analytical methods are based on calculating the effective Green's function of an infinite embedded chain using the T-matrix formalism and describing the chain as a line impurity. We thus provide a solution to the longstanding size-effects problem affecting the only general alternative method, the numerical tight-binding analysis. As an example we consider a chain of magnetic impurities deposited on an s-wave superconducting substrate with Rashba spin-orbit and we calculate its topological phase diagram as a function of the magnetic impurity strength and the chemical potential. We find a perfect agreement between all our new techniques and a numerical analysis. We go on to analyse the effects that topologically non-trivial substrates have on the possible formation of topological chains.

The transport properties of junctions composed of a central region tunnel-coupled to external electrodes are frequently studied within the single-impurity Anderson model with Hubbard on-site interaction. In the present work, we supplement the model with an important ingredient, namely, the charge-bond interaction, also known as correlated or assisted hopping. Correlated hopping enters the second-quantized Hamiltonian, written in the Wannier representation, as an off-diagonal many-body term. Using the equation of motion technique, we study the effect of correlated hopping on the spectral and transport characteristics of a two-terminal quantum dot. Two different mutually coupled Green functions (GFs) appear: one of them describes the spectral properties of the quantum dot, the other the transport properties of the system. We calculate conductance, Seebeck coefficient, and other transport characteristics of the system. Since the correlated-hopping term breaks the particle-hole symmetry of the model and modifies all transport characteristics of the system, the detailed knowledge of its influence on measurable characteristics is a prerequisite for its experimental detection. Simple, experimentally feasible methods are proposed.

The dispersion relation of a one-dimensional magnonic crystal is composed of the sequence of the non-overlapping bands. The calculation of the Zak phases [1,2] for the bands below the selected gap allows identifying if the gap is supportive to the existence of edge modes [3] in terminated structures. In this work, we have calculated Zak phases for magnonic crystal operating in exchange regime, composed of the two alternatively repeated magnetic layers. An expression for the dispersion relation of such magnonic crystals has been derived and the corresponding Bloch function has been found. We determined the Zak phases of the successive bands by analysing the symmetries of the Bloch in a centrosymmetric unit cell, at the edges of bands (i.e., for the wavenumbers in the center and edges of the Brillouin zone). For this, we have used an important result from J. Zak’s work [1] for 1D one- dimensional crystals with inversion symmetry [1], which were generalized to a magnonic system. In conclusion, we have presented a general approach for studying the topological properties of Bloch bands in 1D magnonic crystals in an exchange regime.

References:
[1] J. Zak, Phys. Rev. Lett. 62, 2747 (1989)
[2] M. Xiao, Z. Q. Zhang, C. T. Chan, Phys. Rev. X 4, 021017 (2014)
[3] J. Rychły, J. W. Kłos, J. Phys. D: Appl. Phys. 50 164004 (2017)

Hybrids comprising quantum dots and topological chains are considered as scalable platforms for topological quantum computation. To determine how fast such devices can perform dynamic operations, it is important to evaluate time required for the transfer of quantum state between subsystems. In the seminar the dynamics of the system comprising a quantum dot deposited on a s-wave superconductor and tunnel coupled to one end of the topological chain will be analyzed. In particular it will be shown how long it takes for the Majorana zero mode to be induced in the region of quantum dot and how charge transfer properties change over time under abrupt change of model parameters e.g. the gate voltage.

The phase diagram of the conventional 2-impurity Kondo model and its relevance to correlated lattice models have been a subject of a long debate. It is now clear that it features a quantum phase transition (QPT) between the Kondo and the RKKY phase only in the model extended with a specially designed counter-term. I will present results obtained for a different extension of the standard 2-impurity model, where each of the impurities is coupled to a different host, and the hosts (not impurities) are directly coupled by spin-spin exchange. The model exhibits Jones-Varma QPT even away from the particle-hole symmetry point. Moreover, a second QPT occurs upon tuning the same inter-host coupling to very high values, where the system forms 2-impurity version of a spin-liquid. I will discuss the possibilities for realization of this scenario in quantum-dot structures and heavy-fermion materials.

We investigate dynamical phase transition which can be driven by two types of quantum quenches acting on a correlated quantum dot embedded between superconducting and metallic reservoirs. Under stationary conditions the proximity induced on-dot pairing competing with the Coulomb repulsion prefers the quantum dot to be either in the singly occupied (spinful) or BCS-type (spinless) ground state configuration. We study the dynamical evolution upon traversing such phase boundary due to quantum quenches by means of the time dependent numerical renormalization group approach, revealing non-analytic features in the return rate. Since quench protocols can be realized in a controllable manner, we propose empirically feasible methods for detecting this dynamical singlet-doublet phase transition which should be manifested in the subgap (Andreev) tunneling.

In the final slot this semester we will meet to discuss some different ideas about the shape our condensed matter seminars will take in the coming semester.