arXiv subjects

Karol I. Wysokiński

Publications and source records attributed to Karol I. Wysokiński.

12 recordsLinked to original sources

arXiv2026

Search for Majorana Bound States in Short Chains of Proxmitised Quantum Dots

Majorana zero modes (MZM) appearing at the ends of artificially created one-dimensional p-wave superconductors have been intensively studied recently both theoretically and experimentally. Among possible platforms, proximitised semiconducting wires, and short chains of quantum dots with a superconductor in between were investigated. Here, we propose a different platform consisting of a chain of quantum dots (QDs) sandwiched between an s-wave superconductor and a strong spin-orbit semiconductor, subject to a Zeeman magnetic field. Neglecting spin-conserving hopping processes between QDs and local on-dot superconducting correlations induced by the superconducting proximity effect, reduces the Hamiltonian to the sum of two equivalent Hamiltonians with two independent Hilbert spaces. The resulting model has a staggered structure due to spin-flipping processes $t_{so}$ and cross-Andreev reflections $Δ_{CAR}$ between neighbouring dots. Our central result is the phase diagram of a short chain consisting of four QDs and coupled to two external reservoirs, obtained by means of the Green function in chiral Majorana representation. The modulus of the retarded Green function, probing the whole chain and calculated for zero energy, is shown to contain information on topology and spatial character of Majorana zero modes. The features observed in the Green function nicely agree with those obtained from the transfer matrix approach. In particular the region in parameter space in which Majorana zero modes display oscillatory wave functions are well reproduced. Likewise the borders of the fermion parity changes obtained by the Green function agree with those obtained by other means.

cond-mat.mes-hall↗

arXiv2026

Puzzling superconductivity in strontium ruthenate: then and now

Strontium ruthenate is a very interesting low temperature superconductor with relatively simple normal state and very puzzling superconducting state properties. Despite over thirty years of intensive research, even the precise symmetry of the order parameter is not known. In this paper we briefly review some of the key developments, focussing on some of the newer experiments, especially those which challenged the previous understanding that it is a spin triplet odd parity chiral p-wave superconductor. Since Sr$_2$RuO$_4$ now appears most probably a spin singlet superconductor we have calculated the Kerr effect for one candidate $d$-wave pairing state. We find that for the chiral $d$-wave $E_g$ pairing state the calculated Hall conductance is non-zero and qualitatively similar to that found earlier under the assumption of a chiral p-wave $E_u$ order parameter. We characterize the Hall conductance in relation to two sum rules, one related to Berry curvatures in the Bogoliubov quasiparticle states, and the other $f$-sum rule indicating the presence of inter-orbital pairing.

cond-mat.supr-con↗

arXiv2026

Interplay of spin orbit interaction and Andreev reflection in proximized quantum dots

We investigate a hybrid device consisting of two quantum dots placed between a BCS superconductor and a semiconductor with a strong spin-orbit interaction. Assuming charge tunneling between quantum dots through spin-flip processes, we study the molecular Andreev bound states appearing in the proximized quantum dots. We show that the spin-orbit coupling splits a pair of the Andreev states into four in-gap quasiparticles. For the appropriate set of model parameters, two of these internal quasiparticle states merge, forming the zero-energy state. Under such circumstances, we obtain fully spin-polarized versions of the Majorana quasiparticles, localized on different quantum dots. This happens solely when the spin-orbit interaction is equally strong to the magnitude of crossed Andreev reflections, i.e. in the sweet spot. Otherwise, these processes are competitive, as can be observed in changes of the expectation values of the corresponding order parameters. We analyze signatures of such competition manifested under the nonequilibrium conditions for various configurations of the bias voltage. In particular, for the symmetric bias voltage between the normal electrodes and the Cooper pair splitter bias configuration, we reveal duality in the transport properties. Charge transport through the zero-energy state at the sweet spot is contributed by perfectly entangled electrons with an (almost) ideal transmission. Transport studies would thus enable empirical detection of the molecular quasiparticle states and the efficiency of dissipation processes caused by the external normal electrodes.

cond-mat.mes-hall↗

arXiv2026

Beyond Hubbard: the role of correlated hopping interaction in superconductors and quantum dot devices

We investigate the role of strong Coulomb interactions beyond the standard Hubbard model in two distinct physical contexts. First, we analyze the superconducting phase transition occurring near the Mott metal-insulator transition. Second, we study transport properties of artificial nano-scale structures containing quantum dots coupled to external electrodes. In both cases, we focus on the impact of the correlated (assisted) hopping (CH) interaction. For superconductors, CH acts as a driving mechanism for the phase transition and modifies the spectral properties of the system. We present the evolution of the spectral function as the system approaches the Mott-type transition under varying model parameters. In quantum-dot-based devices, CH influences the tunneling amplitude between the dot and metallic leads. We demonstrate that the characteristic changes in the conductance of a normal metal-quantum dot-normal metal structure provide a clear signature of the presence and sign of CH interaction.

cond-mat.str-el↗

arXiv2024

Signatures of the Correlated-Hopping Interaction in Non-Linear Transport through a Quantum Dot

In condensed matter systems with the Coulomb interaction playing an important role one expects, besides the on-site (local) Hubbard-type interaction, that also other (non-local) terms depending on the site occupancy, known as correlated or assisted hopping, exist. Even though such terms in quantum dots tunnel coupled to external electrodes may have quite an appreciable amplitude, the interpretation of experiments on these systems -- usually in the linear response regime -- seems not to require their presence. However, since the correlated-hopping term breaks the particle-hole symmetry of the standard Anderson model and modifies all transport characteristics of the system, the detailed knowledge of its influence on measurable characteristics, especially {\em in the non-linear regime}, is a prerequisite for its experimental detection. In this paper, we study the non-linear transport properties of junctions composed of a quantum dot tunnel coupled to external electrodes. We model the system by the single-impurity Anderson Hamiltonian with Hubbard on-site interaction and with a non-local correlated-hopping interaction. Using the previously found general expression for the spin-dependent transport and spectral Green functions as well as general formulae for charge and heat transport, we calculate relevant transport characteristics in the strongly non-linear regime

cond-mat.mes-hall↗

arXiv2023

Four terminal quantum dot as an efficient rectifier of heat and charge currents

We propose an efficient method of heat rectification in a simple system consisting of a quantum dot asymmetrically coupled to four mutually perpendicular electrodes. In such a device the Hall-like charge and heat currents appear in response to the voltage bias or temperature difference between one pair of electrodes. Even though both longitudinal (along the bias) and Hall-like (perpendicular to the bias) currents are rectified under appropriate conditions, the rectification factor is typically much bigger for the latter currents. This is true for heat and charge flow. The Hall-like currents are predicted to exist in linear as well as non-linear transport regimes and require broken mirror symmetry but not time reversal symmetry. The linear effect exists only in geometry which breaks two inversion symmetries along two pairs of electrically coupled terminals. The proposed system is attainable within current technology and provides novel platform of simultaneous heat and charge management at the nanoscale.

cond-mat.mes-hall↗

arXiv2021

Anomalous Hall conductivity of the holographic $\mathbb{Z}_2$ Dirac semimetals

The anomalous spin Hall conductivity in the holographic model of Dirac semimetals with two Dirac nodes protected by the crystal symmetry has been elaborated. Such system besides the chiral anomaly possesses another anomaly which is related to the $\mathbb{Z}_2$ topological charge of the system. The holographic model of the system contains matter action with two $U(1)$-gauge fields as well as the appropriate combination of the Chern-Simons gauge terms. We also allow for the coupling of two gauge fields {\it via} the kinetic mixing parametrised by the coupling $α$. The holographic approach in the probe limit enables us to obtain Hall conductivity. The aim of this work is to describe the phase transitions in the $\mathbb{Z}_2$ Dirac semimetals between the topologically trivial and non-trivial phases. Interestingly the anomalous Hall conductivity plays a role of the order parameter of this phase transition. The holographically found prefactor of the Hall conductivity in the topologically non-trivial phase, depends on the coupling $α$ and the Chern - Simons couplings.

hep-th↗

arXiv2021

Charge and heat transport through quantum dots with local and correlated-hopping interactions

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-quantised Hamiltonian, written in the Wannier representation, as an off-diagonal many-body term. Using the equation of motion technique, we study the effect of the correlated hopping on the spectral and transport characteristics of a two-terminal quantum dot. Two different Green functions (GFs) appear: one of them describes the spectral properties of the quantum dot, the other the transport properties of the system. The calculation of the transport GF requires the knowledge of the spectral one. We use decoupling procedures similar to those which properly describe the standard Anderson model within the Kondo regime and outside of it. For an arbitrary ratio $x$ between the amplitudes of correlated and single-particle hopping terms, the transport GF fulfils the $x \leftrightarrow 2-x$ symmetry of the model. The average occupation of the dot also obeys this symmetry, albeit the spectral function of the quantum dot, calculated within an analogous decoupling scheme as for the transport GF, does not. We identify the physical reason for this behavior, and propose a way to cure it. 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.

cond-mat.mes-hall↗

arXiv2020

Holographic DC SQUID in the presence of dark matter

The gauge-gravity duality has been applied to examine the properties of holographic superconducting quantum device (SQUID), composed of two S-N-S Josephson junctions, influenced by dark sector modelled by the additional $U(1)$-gauge field coupled to the ordinary Maxwell one. The dark matter sector is known to affect the properties of superconductors and is expected to enter the current-phase relation. The kinetic mixing between two gauge fields provides a mechanism allowing for the conceivable observation of the effect. We find small but visible effect of the dark matter particle traversing the device, which shows up as a change of its maximal current.

hep-th↗

arXiv2020

Statistical correlations of currents flowing via proximized quantum dot

Statistical properties of the electron transport flowing through nanostructures are strongly influenced by the interactions, geometry of the system and/or by type of the external electrodes. These factors affect not only the average current induced in the system but also contribute to fluctuations in the flux of charges and their correlations. Due to possible applications of the hybrid nano-systems, containing one or more superconducting electrodes, a detailed understanding of the flow of charge and its fluctuations seems to be of primary importance. Coulomb repulsion between electrons usually strongly affect the current-current correlation function. In this work we study the correlations in the charge flow through such interacting quantum dot contacted to one superconducting and two normal electrodes. This set-up allows for analysis of the Andreev scattering events in the correlations of currents flowing between external electrodes and, in particular, gives access to cross-correlations between currents from/to different normal electrodes. Our approach relies on the master equation technique, which properly captures the Coulomb interactions. We study the finite frequency correlations and find the relaxation processes, related to the high frequency charge and low frequency polarisation fluctuations. The multiterminal structure of here studied single electron device allows to analyze a competition between the intra- and inter-channel correlations. In the appropriate limit of the interacting quantum dot embedded between two normal electrodes our calculations quantitatively describe the recent experimental data on the frequency dependent correlations. This shows a promising potential of the method for description of the hybrid systems with superconducting electrode(s).

cond-mat.mes-hall↗

arXiv2019

Multi-terminal far-from-equilibrium thermoelectric nano-devices in the Kondo regime

The quest for good thermoelectric materials and/or high-efficiency thermoelectric devices is of primary importance from theoretical and practical points of view. Low-dimensional structures with quantum dots or molecules are promising candidates to achieve the goal. Interactions between electrons, far-from-equilibrium conditions and strongly non-linear transport are important factors affecting the usefulness of the devices. This paper analyses the thermoelectric power of a two-terminal quantum dot under large thermal $ΔT$ and voltage $V$ biases as well as the performance of the three-terminal system as a heat engine. To properly characterise the non-linear effects under these conditions, two different Seebeck coefficients are introduced, generalizing the linear response expression. The direct calculations of thermally induced electric and heat currents show, in agreement with recent work, that the efficiency of the thermoelectric heat engine as measured by the delivered power is maximal far from equilibrium. Moreover, the strong Coulomb interactions between electrons on the quantum dot are found to diminish the efficiency at maximum power and the maximal value of the delivered power, both in the Kondo regime and outside of it.

cond-mat.mes-hall↗

arXiv2008

Real space Bogolubov-de Gennes equations study of the boson-fermion model

The boson-fermion (BF) model has been proposed to describe superconductivity in short coherence length superconductors. In this work we use it to study impurity induced inhomogeneities in high temperature superconductors (HTS) as found in numerous scanning tunnelling measurements. The model has been formulated in real space and solved with help of Bogolubov-de Gennes approach. Disorder in the boson or fermion subsystem is directly coupled to the superconducting order parameter and leads to severe changes of superconducting properties like local order parameter and density of states. We present the results for many impurities randomly distributed over otherwise clean and periodic two-dimensional square lattice.

cond-mat.supr-con↗