# General information about the project

Nearly half a century has passed since P. W. Anderson published in Science his seminal paper *More is Different*. In this paper Anderson discusses the hierarchical structure of science and puts forward the conjecture that the knowledge of behavior of a few particles cannot be extrapolated to predict the behavior of more complex systems. This straightforwardly leads to the conclusion that with increasing the system’s complexity, some completely new properties may emerge. In fact, over recent decades we have witnessed several astonishing discoveries, with topologically protected states of matter (Nobel awarded to Thouless, Haldane and Kosterlitz in 2016) being a very important example. Such states are very robust against local perturbations, since they are protected by symmetry, and can extend over entire sample. This makes them very promising for quantum spintronics and quantum computation and, in fact, puts their investigations in the forefront of nowadays physics. Besides, topological materials also constitute an excellent playground for more fundamental research. In particular, it turns out that the long-searched Majorana fermions, i.e. particles that are their own antiparticles, predicted by Ettore Majorana already in 1937, can emerge at the ends of topological superconducting wires as zero-energy quasiparticles.

**The Majorana quasiparticles and their interactions with strongly correlated low-dimensional systems are the central object of interest of this research project.**

The emergence of Majorana quasiparticles at the ends of topological superconducting nanowires can be confirmed by performing transport spectroscopy experiments, where their presence gives rise to a zero-bias peak in the differential conductance of the device. Moreover, Majorana quasiparticles can also affect the transport behavior of side-attached zero-dimensional systems, such as quantum dots, where the leakage of Majorana modes results in fractional value of the conductance. In fact, such hybrid, coupled zero and one-dimensional systems provide an exceptional opportunity to test fundamental interactions between topologically-protected states of matter and various electronic correlations, such as the ones leading to the Kondo effect. The Kondo effect emerges when a magnetic impurity interacts with continuum of states and its signature is an additional resonance in the local density of states of the impurity. The studies of the interplay between the Kondo and Majorana physics have been so far mainly restricted to relatively simple models. Nevertheless, since to understand the behavior of real systems minimal descriptions are not necessarily sufficient, it is important to address the question of what are the transport properties of considered hybrid systems, where more exotic Kondo phenomena can emerge.
The investigations will be performed by using the state-of-the-art numerical and analytical methods, which will be appropriately adapted to determine the transport behavior of considered hybrid systems. These methods include, among others, the density-matrix numerical renormalization group method – the approach known for its accuracy in determining the transport properties of nanostructures, or the Keldysh nonequilibrium Green’s function formalism.

**Realization period:** 21.01.2019 - 20.09.2023

# Research team:

** Prof. Ireneusz Weymann ** (PI, Leader of the UAM node)

** Prof. Tadeusz Domański ** (Leader of the UMCS node)

Dr. Krzysztof Wójcik

Dr. Sakineh Vosoughi-nia

Dr. Grzegorz Górski

MSc. Piotr Majek

# List of publications

**PUBLICATIONS:**

Spin effects on transport and zero-bias anomaly in a hybrid Majorana wire-quantum dot system

Sci. Rep.**13**, 17279 (2023)

Quantum spin liquid in an RKKY-coupled two-impurity Kondo system

Phys. Rev. B**107**, L121111 (2023)

Asymmetry effects on the phases of RKKY-coupled two-impurity Kondo systems

Phys. Rev. B**107**, 125146 (2023)

Majorana Coupling and Kondo Screening of Localized Spins

Acta Phys. Pol. A**143**, 207 (2023)

Synergy of Semiconductor Physics and Electron Pairing: Route Towards Novel Topological Materials

Acta Phys. Pol. A**142**, 679 (2022)

Hallmarks of Majorana mode leaking into a hybrid double quantum dot

Phys. Rev. B**106**, 155123 (2022)

Majorana-Kondo competition in a cross-shaped double quantum dot-topological superconductor system

J. Magn. Magn. Mater.**549**, 168935 (2022)

Spin-resolved thermal signatures of Majorana-Kondo interplay in double quantum dots

Phys. Rev. B**105**, 075418 (2022)

Majorana mode leaking into a spin-charge entangled double quantum dot

Phys. Rev. B**104**, 085416 (2021)

Dynamical leakage of Majorana mode into side-attached quantum dot

Phys. Rev. B**103**, 235416 (2021)

Subgap dynamics of double quantum dot coupled between superconducting and normal leads

Sci. Rep.**11**, 1-15 (2021)

Transient effects in a double quantum dot sandwiched laterally between superconducting and metallic leads

Phys. Rev. B**103**, 165430 (2021)

Quench dynamics of a correlated quantum dot sandwiched between normal-metal and superconducting leads

Phys. Rev. B**103**, 155420 (2021)

Magnetization dynamics in a Majorana-wire-quantum-dot setup

Phys. Rev. B**103**, 125413 (2021)

Magnetic field effect on trivial and topological bound states of superconducting quantum dot

J. Phys.: Cond. Matter**32**, 445803 (2020)

Majorana-Kondo interplay in T-shaped double quantum dots

Phys. Rev. B**101**, 235404 (2020)

Leakage of Majorana mode into correlated quantum dot nearby its singlet-doublet crossover

J. Phys.: Cond. Matter**32**, 025302 (2019)

Delocalisation of Majorana quasiparticles in plaquette-nanowire hybrid system

Sci. Rep.**9**, 12933 (2019)

Quasiparticles of a periodically driven quantum dot coupled between superconducting and normal leads

Phys. Rev. B**100**, 085414 (2019)