**Carmine Autieri** (Warsaw)*Berry phase engineering at oxide interfaces*

Geometric phases in condensed matter play a central role in topological transport phenomena such as the quantum, spin and Anomalous Hall Effect (AHE). In contrast to the quantum Hall effect – which is characterized by a topological invariant and robust against perturbations – the AHE depends on the Berry curvature of occupied bands at the Fermi level and is therefore highly sensitive to subtle changes in the band structure.

A unique platform for its manipulation is provided by transition metal oxide heterostructures, where engineering of emergent electrodynamics becomes possible at atomically sharp interfaces. We demonstrate that the Berry curvature and its corresponding vector potential can be manipulated by interface engineering of the correlated itinerant ferromagnet SrRuO_3 (SRO). Measurements of the AHE reveal the presence of two interface-tunable spin-polarized conduction channels. Using theoretical calculations, we show that the tunability of the AHE at SRO interfaces arises from the competition between two topologically non-trivial bands. Our results demonstrate how reconstructions at oxide interfaces can be used to control emergent electrodynamics on a nanometer-scale, opening new routes towards spintronics and topological electronics.[1]

We discuss the evolution of the anomalous Hall conductivity as a function of the orientation of the magnetization encoded in the angle with respect to the z-axis perpendicular to the electron motion plane. We argue that the maximal of the anomalous Hall conductivity is obtained at a finite value of the angle due to the interplay the orbital Rashba field, the anisotropy, the topological bands and the magnetization.

[1] D. J. Groenendijk, C. Autieri, T. C. van Thiel, W. Brzezicki, N. Gauquelin, P. Barone, K. H. W. van den Bos, S. van Aert, J. Verbeeck, A. Filippetti, S. Picozzi, M. Cuoco and A. D. Caviglia, “Berry phase engineering at oxide interfaces”, arXiv:1810.05619 (preprint).

**Wojciech Brzezicki** (Warsaw)**Topology in a non-Hermitian chiral chain**

We consider a class of one-dimensional (1D) non-Hermitian models with a special type of a chiral symmetry which is related to pseudo-Hermiticity [1]. We show that the topology of a Hamiltonian belonging to this symmetry class is determined by a hidden Chern number described by an effective two-dimensional Hermitian Hamiltonian $H^{eff}(k,\eta)$, where $\eta$ is the imaginary part of the energy. This Chern number manifests itself as topologically protected in-gap end states at zero real part of the energy. We show that the bulk-boundary correspondence coming from the hidden Chern number is robust and immune to non-Hermitian skin effect. We introduce a minimal model Hamiltonian supporting topologically nontrivial phases in this symmetry class, derive its topological phase diagram and calculate the end states originating from the hidden Chern number. We show that such a model can be realized in the framework of polariton lattices.

[1] W. Brzezicki, T. Hyart, Phys. Rev. B **100**, 161105(R) (2019).

**Timo** **Hyart** (Warsaw)*Opening words and ongoing investigations of unconventional topological phase transitions*

After opening words and highlighting some of the MagTop research activities I will discuss our ongoing investigations related to unconventional topological phase transitions. I will discuss our prediction of a phase with spontaneously broken time-reversal symmetry separating the topologically trivial and nontrivial phases in band-inverted electron-hole bilayers [1]. In particular, I will focus on our current studies of the consequences of this transition on the transport experiments and realization of Majorana zero modes [2]. Finally, I will show that similar transitions can appear also in other systems [3] and I will put forward a hypothesis that perhaps a more exotic state of matter can be realized at a topological phase transition in superconductors.

[1] D. I. Pikulin and T. Hyart, Phys. Rev. Lett. **112**, 176403 (2014).

[2] T. Paul, V. F. Becerra, M. Płodzien, D. I. Pikulin and T. Hyart, in preparation.

[3] D. I. Pikulin, P. G. Silvestrov, T. Hyart, Nature Communications **7**, 10462 (2016).

**Aksel Kobiałka** (Lublin)**Dimerization-induced topological superconductivity in a Rashba nanowire**

In condensed matter physics, in order for Majorana Bound States to emerge, we need interaction between superconductivity, spin-orbit coupling and magnetic field in some nanoscopic system [1]. In finite 1D Rasha nanowires those states are manifested by emergence of a pair of zero-energy Majorana bound states [2]. In order to apply Majorana states in any tangible apparatus and devices, limits of the robustness of topological phase have to be pondered.Therefore, we analyze the influence of SSH-like dimerization [3] on the topological phases of a Rashba nanowire. We find that “dimerization-induced topological superconductivity” completely repels the topological phase of the uniform nanowire, whenever they happen to overlap. We also test stability of the topological superconducting phases against electrostatic disorder. Therefore, we investigate properties of such bound states in low dimensional dimerized 1D Rashba nanowire and bounded 2D surfaces, by means of local density of states and the parity operator that allows for deciphering the topological phase of the system.

[1] J. D. Sau, R. M. Lutchyn, S. Tewari, & S. Das Sarma, Phys. Rev. Lett. **104**, 040502 (2010).

[2] A. Ptok, A. Kobiałka & T. Domański, Phys. Rev. B. **96**, 195430 (2017)

[3] W. P. Su, J. R. Schrieffer, & A. J. Heeger, Phys. Rev. Lett. **42**, 1698 (1979).

**Mariusz Krawiec** (Lublin)*Emergent Dirac fermions in Si-Au *heterostructures

Silicene is a silicon counterpart of graphene [1]. Due to larger ionic radius of Si than C atoms, silicene features the mixed sp^{2}/sp^{3} bonding character. Thus its freestanding atomic structure is low-buckled, although planar, perfectly flat structure has also been predicted as a metastable phase [2]. So far silicene has been grown only on a few substrates in the epitaxial form, where its freestanding atomic structure has usually been destroyed and replaced by surface reconstruction [3].

Here we discuss the issue of the first experimental evidence of planar silicene, i.e. perfectly flat sp^{2}-bonded sheet of Si atoms. This new graphene-like silicon allotrope has been synthesized on Au(111) thin films grown on Si substrate in the process of surface segregation [4]. Its electronic structure is different than in a freestanding form, but also features linear Dirac-like bands.*Acknowledgments:* This work has been supported by the National Science Centre (Poland) under Grant No. DEC-2018/29/B/ST5/01572.

[1] K. Takeda, K. Shiraishi, Phys. Rev. B **50**, 14916 (1994).

[2] S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, S. Ciraci, Phys. Rev. Lett. **102**, 236804 (2009).

[3] M. Krawiec, J. Phys.: Condens. Matter **30**, 233003 (2018).

[4] A. Stępniak-Dybala, P. Dyniec, M. Kopciuszyński, R. Zdyb. M. Jałochowski, M. Krawiec, Adv. Funct. Mater. 1906053 (2019).

**Damian Krychowski** (Poznań)*Impact of multi-Majorana fermions on the SU(4) Kondo state in the carbon nanotube quantum dots*

We have proposed a realization of the single, double and triple Majorana fermions at the end of zig-zag carbon nanotube quantum wire in the superconducting coat without magnetic field. The Majorana fermions are coupled with the carbon nanotube quantum dot in the SU(4) Kondo state. Using Kotliar-Ruckenstein slave boson method for two-orbital Anderson model, we have analyzed the conductance, Kondo temperature, Fano factor, linear thermopower coefficient and the local Casmir operators. The giant thermopower in the Kondo – Majorana Kondo crossover range, and the fractional conductance in the strong coupling limit are observed. Majorana Kondo effect is a consequence of SU(3) Kondo state and one underscreened spin-orbital channel (interfering with Majorana fermion).

**Arkadiusz Kuroś** (Kraków)**Condensed matter physics in time domain**

Periodically driven quantum many-body systems can be employed to model crystalline structure in time do-main. It is possible to investigate Anderson localization [1], dynamical quantum phase transitions [2] and exotic long-range interaction [3]. In this work we propose a simple implementation of non-separate two-dimensional lattices. We show that such lattices can be placed on M ̈obius strip manifesting itself in the time domain. We present these concepts by creating three-band Lieb lattice model with a well separated flat band [4], where we can modulate contact interactions by periodic changes of s-wave scattering length using Feshbach resonance mechanism.

[1] K . Sacha and D. Delande, Phys. Rev. A **94**, 023633 (2016).

[2] A . Kosior and K. Sacha, Phys. Rev. A **97**, 053621 (2018).

[3] K . Giergiel, A. Miroszewski, and K. Sacha, Phys. Rev. Lett. **120**, 140401 (2018).

[4] S . Taie, H. Ozawa, T. Ichinose, T. Nishio, S. Nakajima, and Y. Takahashi, Science Advances **1** (2015).

**Alexander Lau** (Warsaw)**3D pseudo-Landau flat band in a nodal-line semimetal**

Nodal-line semimetals are a class of three-dimensional topological semimetals featuring two-fold degenerate band-crossing points that form closed loops in the Brillouin zone of the material. Based on an effective low-energy theory, I will show how strain can be used to induce a set of 3D pseudo-Landau levels in nodal-line semimetals and discuss their properties. Of particular interest is the zeroth Landau level as it realizes a three-dimensional flat band which is expected to give rise to various correlated phases due to strong electron-electron interactions. Finally, I will give a brief outlook on the current research directions and open questions.

**Piotr Majek** (Poznań)*Thermopower of a double quantum dot – Majorana system*

We investigate theoretically the thermoelectric transport properties of a T-shaped double quantum dot side-coupled to a topological superconducting nanowire hosting Majorana zero-energy modes. By using the numerical renormalization group method, we determine the transport coefficients, such as conductance, thermopower and thermoelectric figure of merit, focusing on the Kondo regime. We show that the thermopower exhibits unique signatures due to the presence of Majorana quasiparticles.

**Maciej M. Maśka** (Katowice)**“Topofilia” in a one-dimensional spin-fermion model with proximity-induced superconductivity**

We study a simple model, where a chain of localized magnetic moments is coupled to itinerant electrons and deposited on superconducting material. By performing Monte Carlo simulations we demonstrate that the moments adjust themselves in response to changing external conditions, so that the system self-tunes into the topological phase. We estimate the critical temperature up to which the system remains in this phase.

**Teemu Ojanen** (Tampere, Finland)*Magnetically covered NbSe_2 as an experimental platform of chiral superconductivity*

The recent breakthrough in growing 2d van der Waals magnets has opened intriguing possibilities in fabrication of designer topological materials. In particular, magnetically covered NbSe_2 has been identified as a promising candidate for different topological superconducting phases. In my talk I will introduce a model of NbSe_2 covered with a 2d magnet with out-of-plane magnetization and argue that this system is a plausible candidate for chiral superconductivity with Chern number C=3. I will also explain how this prediction is supported by recent experimental observations of edge modes on magnetic islands on NbSe_2.

**Marcin Płodzień** (Warsaw)*Machine learning assisted identification of topological invariants in disordered systems*

We will consider topological systems supporting non-trivial Chern numbers in the presence of the disorder. We will discuss our preliminary results of machine learning assisted Chern number identification from LDOS for models belonging to different symmetry classes.

**Andrzej Ptok** (Kraków)*Majorana bound states in magnetic chain : **“to be or not to be” ?*

Recent experiments have shown the signatures of Majorana bound states at the ends of magnetic chains deposited on a superconducting substrate. Here, we employ first principles calculations to directly investigate the topological properties of 3d transition metal nanochains (i.e., Mn, Cr, Fe and Co) for isolated and surface–deposited wires. From the obtained band structure, we found the exact tight binding model in the Wannier orbital basis with realistic parameters. For these models, we calculate topological invariant of Z_2 phase. Additionally, we discuss non-collinear magnetic moments as a source of the non–trivial topological phase. We also discuss the influence of the substrate on the band structure and magnetic properties of the nanochain’s atoms. We show that the coupling of the chain to substrate leads to suppression of the magnetic moment value and to strong modification of the band structures.

**Nicholas Sedlmayr** (Lublin)**The bulk-boundary correspondence and unprotected Majorana zero modes**

The bulk-boundary correspondence establishes a connection between the bulk topological index of an insulator or superconductor, and the number of topologically protected edge bands or states. In particular for topological superconductors in two dimensions the first Chern number is related to the number of protected bands within the bulk energy gap, and is therefore assumed to give the number of Majorana zero modes in the system. Here we show that this is not necessarily the case. We demonstrate that despite the high Chern numbers that can be seen in some 2D topological superconductors these do not strictly always contain Majorana zero modes. Furthermore on the edge of any realistic 2D system the Majorana zero modes gap each other out. It is an open question whether any signature of their strange nature is left in the topologically protected band of mid-gap states.

**Mircea Trif **Warsaw)*Non-Abelian dynamics in the presence of a quantum cavity field*

In this talk, I will present the general framework for describing the dynamics of a degenerate quantum system in the presence of a quantum cavity field. I will show explicitly the effective coupling between the non-Abelian Berry curvature associated with the system and the photonic field [1] which can be detected by dispersive readout techniques. As an application, I will address the dynamical process of braiding Majorana bound states (MBS) in the presence of the coupling to photons in a microwave cavity. I will show theoretically that the $\pi/4$ phase associated with the braiding of MBS, as well as the parity of the ground state are imprinted into the photonic field of the cavity[2]. If time permits, I will briefly address the effect of dissipation based on the full density matrix of the low‐energy states [3]. These manifestations are purely dynamical and they occur in the absence of any splitting of the (degenerate) ground states.

[1] Mircea Trif, Marcin Wysokiński, Marcin Płodzień (in preparation).

[2] Mircea Trif and Pascal Simon, Phys. Rev. Lett. **122**, 236803 (2019).

[3] Mircea Trif and Pascal Simon, Adv. Quantum Technol., in press, **2019**

**Ireneusz Weymann** (Poznań)**Majorana-Kondo interplay in double quantum dots**

We analyze the transport behavior of a double quantum dot attached to a topological superconducting wire hosting Majorana zero-energy modes. At low temperatures and in the absence of topological superconductor, the considered system exhibits the two-stage Kondo effect, characterized by a nonmonotonic temperature dependence of the conductance. We show that the coupling to Majorana wire enhances the exchange interaction between the dots, giving rise to a subtle interplay between the first and second-stage Kondo effects and the half-fermionic nature of Majorana quasiparticles.

**Andrzej Więckowski** (Wrocław)*Majorana phase-gate based on the geometric phase*

We study dynamics of a single qubit encoded in two pairs of Majorana modes, whereby each pair is hosted on a trijunction described by the Kitaev model extended by many-body interactions. We demonstrated that the challenging phase-gate may be efficiently implemented via braiding of partially overlapping modes. Although such qubit acquires both geometric and dynamical phases during the braiding protocol, the latter phase may be eliminated if the Majorana modes are hosted by systems with appropriate particle-hole symmetry.*Acknowledgments:* This work was supported by the National Science Centre (NCN, Poland) under Grant No. 2016/23/B/ST3/00647.

**Kacper Wrześniewski** (Poznań)*Quench dynamics in proximitized quantum dot system*

We study the quench dynamics in hybrid quantum dot system by means of the time-dependent numerical renormalization group method. The quantum dot is coupled to normal lead and either to superconducting one or is attached to the topological superconductor wire hosting Majorana zero-energy modes at its ends. Relevant time scales describing the dynamics are identified.

**Marcin M. Wysokiński** (Warsaw)*Electrical control of entanglement for spin 3/2*

t.b.a.