arXiv subjects

Rok Žitko

Publications and source records attributed to Rok Žitko.

At least 19 recordsLinked to original sources

arXiv2026

Hubbard vs. Emery model: spectra, transport and relevance for cuprates

Understanding the transport properties of cuprate superconductors is one of the central challenges in the physics of strongly correlated electrons. The most common approach is to define and solve a low-energy lattice model, but it is still unclear what the minimal model is to capture all relevant mechanisms and provide quantitative predictions. The main uncertainty concerns the choice of the orbital degrees of freedom to be included in the model, as well as the definition of the effective coupling. In this paper, we study the two most commonly considered models, namely the single-orbital Hubbard model and the three-orbital Emery model. We investigate and compare their spectral and transport properties, and find that the two models present a similar, but not the same, physical picture. We identify several strong quantitative differences which might allow one to discriminate between the two models by comparing theory with experiments. We compare our results for several physical quantities with 7 different experiments on 3 different La$_2$CuO$_4$-based cuprates, and in general find excellent agreement. The dc resistivity and the effective mass results suggest that the coupling constant in the effective Hubbard model is larger than expected. We find several more properties that are sensitive to the precise value of the coupling constant, including the critical doping for the Lifshitz transition, and the local spectral weight in the vicinity of the Fermi level; the latter provides a promising way to estimate the effective coupling constant in future photoemission experiments.

cond-mat.str-el↗

arXiv2026

Strongly correlated Josephson junction: proximity effect in the single-layer Hubbard model

We study the proximity effect in the Hubbard model coupled to BCS superconductors describing a single-layer strongly correlated electron system in a phase-biased Josephson junction. We find two distinct gapped solutions, one Mott-like insulating (M-phase) and one proximitized superconducting phase (S-phase), separated by first-order transition with hysteresis. In the M-phase the large correlation charge gap strongly suppresses the critical current, while the S-phase behaves as a $0$-junction, with a proximitized gap that closes for $ϕ=π$ to yield a correlated metal. Phase bias and junction transparency can thus serve as tuning knobs to switch between conducting and insulating regimes. Working within the dynamical mean field theory using the numerical renormalization group as the impurity solver, we associate M- and S-phase solutions with the doublet and singlet fixed points of the underlying superconducting Anderson impurity problem. We obtain detailed insight into the spectral structure on all energy scales. In the M-phase, the self-energy has sub-gap resonances symmetrically located around the Fermi level resulting from the splitting of the ''mid-gap pole'' found in Mott insulators; this structure accounts for phase insensitivity.

cond-mat.str-el↗

arXiv2026

Effects of electron-electron interaction and spin-orbit coupling on Andreev pair qubits in quantum dot Josephson junctions

We investigate the superconducting Anderson impurity model for interacting quantum dot Josephson junctions with spin-orbit coupling and a term accounting for tunnelling through higher-energy orbitals. These elements establish the conditions required for spin polarization in the absence of external magnetic field at finite superconducting phase bias. This Hamiltonian has been previously used to model the Andreev spin qubit, where quantum information is encoded in spinful odd-parity subgap states. Here we instead analyse the even-parity sector, i.e., the Andreev pair qubit based on Andreev bound states (ABS). The model is solved using the zero-bandwidth approximation and the numerical renormalization group, with further insight from variational calculations. Electron-electron interaction admixes single-occupancy Yu-Shiba-Rusinov (YSR) components into the ABS states, thereby strongly enhancing spin transitions in the presence of spin-orbit coupling. The ABS states can thus become sensitive to local magnetic field fluctuations, which has implications for decoherence in Andreev pair qubits. For strong interaction $U$, especially in the cross-over region between the ABS and YSR regimes for $U \sim 2Δ$, charge, spin, and inductive transitions can all become strong, offering avenues for spin control and quantum transduction.

cond-mat.mes-hall↗

arXiv2026

Andreev bound state spectroscopy of a quantum-dot-based Aharonov-Bohm interferometer with superconducting terminals

We analytically and numerically investigate an Aharonov-Bohm interferometer with two superconducting terminals and a strongly correlated quantum dot in one arm. Through a rigorous derivation, we prove that this double-path interferometer is spectrally equivalent to a simpler system: an interacting quantum dot coupled to a non-interacting side-coupled proximitized mode and a semiconductor lead. This equivalence reveals a simple interpretation of the interferometer's behavior through the competition of a geometric factor $χ$, a key parameter characterizing the anomalous part of the hybridization function, with the properties of the side-coupled mode. We identify the conditions for the formation of doublet chimney in the phase diagrams in more general setting. Moreover, we show how the obtained Andreev bound state spectra clearly indicate the presence of Josephson diode effect generated by interferometric phenomena.

cond-mat.mes-hall↗

arXiv2026

Systematic Schrieffer-Wolff-transformation approach to Josephson junctions: quasiparticle effects and Josephson harmonics

We use the Schrieffer-Wolff transformation (SWT) to analyze Josephson junctions between superconducting leads described by the charge-conserving BCS theory. Starting from the single-electron tunneling terms, we directly recover the conventional effective Hamiltonian, $-E_J\cos\hatφ$, with an operator-valued phase bias $\hatφ$. The SWT approach has the advantage that it can be systematically extended to more complex scenarios. We show that if a Bogoliubov quasiparticle is present its motion couples to that of Cooper pairs, introducing correlated dynamics that reshape the energy spectrum of the junction. Furthermore, higher-order terms in the SWT naturally describe Josephson harmonics, whose amplitudes are directly related to the microscopic properties of the superconducting leads and the junction. We derive expressions that could facilitate tuning the ratio between the different harmonics in a controlled way.

cond-mat.supr-con↗

arXiv2025

Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena

We propose a set of variational wavefunctions for the sub-gap spin-doublet and spin-singlet eigenstates of the particle-hole symmetric superconducting Anderson impurity model. The wavefunctions include up to two Bogoliubov quasiparticles in the continuum which is necessary to correctly capture the weak-coupling asymptotics in all parameter regimes. The eigenvalue problems reduce to solving transcendental equations. We investigate how the lowest singlet state evolves with increasing charge repulsion $U$, transitioning from a proximitized state (a superposition of empty and doubly occupied impurity orbitals, corresponding to an Andreev bound state) to a local moment that is Kondo screened by Bogoliubov quasiparticles (Yu-Shiba-Rusinov state). This change occurs for $U = 2Δ$, where $Δ$ is the BCS gap. At this point, the band-edge effects make the eigenenergy scale in a singular way as $Γ^{2/3}$, where $Γ$ is the hybridization strength. Away from this special point, regular $Γ$-linear behavior is recovered, but only for $Γ\lesssim (U/2-Δ)^2/Δ$. The singular behavior thus extends over a broad range of parameters, including those relevant for some quantum devices in current use. The singular state is an equal-superposition state with maximal fluctuations between the local impurity charge configurations. Accurately capturing the band-edge singularity requires a continuum model, and it cannot be correctly described by discrete (truncated) models such as the zero-bandwidth approximation or the superconducting atomic limit. We determine the region of parameter space where the second spin-singlet state exists: in addition to the whole $U<2Δ$ ABS region, it also includes a small part of the $U>2Δ$ YSR region for finite values of $Γ$, as long as some ABS wavefunction component is admixed.

cond-mat.supr-con↗

arXiv2024

Incommensurable matter-wave jets in quasi-1D geometry

Matter-wave jets are ejected from a Bose-Einstein condensate subjected to a modulation of the interaction strength. For sufficiently strong modulation additional higher harmonic matter-wave jets emerge. Here we report the first experimental observation of incommensurable "golden" $\frac{1+\sqrt{5}}{2}$ matter-wave jets in a Bose-Einstein condensate exposed to a single frequency interaction modulation. We study the formation of higher-order jets and the corresponding incommensurable density waves in quasi-one-dimensional geometry with numerical one dimensional (1D) Gross-Pitaevskii equation simulation. We explore the process of jet formation experimentally and theoretically for a wide range of modulation amplitudes and frequencies and establish a phase diagram delineating different regimes of jet formation.

cond-mat.quant-gas↗

arXiv2024

Higher order spin interactions mediated by the substrate

Since the seminal works in the fifties it has been known that a bath of non-interacting electrons mediates an interaction between local moments (such as nuclear spins or magnetic impurities) coupled to distant sites of the lattice. Recent efforts in simultaneous control of multi-qubit arrays rely on defining quantum dots in environments which likewise contain electrons capable of mediating effective interactions. It is therefore interesting to analyze systems with more than two impurities in higher orders of perturbation theory. Here we derive and discuss the significance of the effective spin interactions between four impurities in fourth order of the coupling between the impurities and the substrate, mediated by conduction electrons of a two-dimensional square lattice. This effective interaction resembles the ring exchange -- a coupling of four spins appearing in perturbative treatment of the Hubbard model. Despite it being a higher-order effect, it can dramatically influence the magnetic ordering. We show that as an effective interaction between impurity spins, the ring exchange can also compete with the more familiar two-spin interactions.

cond-mat.mes-hall↗

arXiv2024

Inelastic tunneling through normal and superconducting junctions in the presence of photonic bath within Lindbladian formalism

An electron tunneling across a junction integrated into an electric circuit can generate an excitation in the photonic field (electromagnetic environment) and lose energy in the process. Such inelastic tunneling of particles is commonly described using the $P(E)$ theory. In the conventional approach to this theory, the tunneling rate and the electric current through the junction are derived using Fermi's golden rule and by averaging over the environmental photonic degrees of freedom. In this work, we address the same problem of inelastic tunneling due to photonic environment in Lindbladian formalism and we present how the photonic degrees of freedom are traced out in quantum master equation approach. The resulting quantum master equation is parameterized by the same $P(E)$ function and enables us to obtain not only the electric current but various other quantities, for instance the heat current, in a systematic and convenient way. We also demonstrate that the Lindbladian formalism provides a comprehensive description of Bogoliubov quasiparticle tunneling through superconducting junctions and that it properly accounts for the coherence factors. The coherence factors become important if the normal-state density of states is particle-hole asymmetric.

cond-mat.mes-hall↗

arXiv2024

Generalized transmon Hamiltonian for Andreev spin qubits

We solve the problem of an interacting quantum dot embedded in a Josephson junction between two superconductors with finite charging energy described by the transmon (Cooper pair box) Hamiltonian. The approach is based on the flat-band approximation of the Richardson model, which reduces the Hilbert space to the point where exact diagonalisation is possible while retaining all states that are necessary to describe the low energy phenomena. The presented method accounts for the physics of the quantum dot, the Josephson effect and the Coulomb repulsion (charging energy) at the same level. In particular, it captures the quantum fluctuations of the superconducting phase as well as the coupling between the superconducting phase and the quantum dot (spin) degrees of freedom. The method can be directly applied for modelling Andreev spin qubits embedded in transmon circuits in all parameter regimes, for describing time-dependent processes, and for the calculation of transition matrix elements for microwave-driven transmon, spin-flip and mixed transitions that involve coupling to charge or current degree of freedom.

cond-mat.mes-hall↗

arXiv2024

Strong-coupling theory of quantum dot Josephson junctions: role of the residual quasiparticle

We consider an interacting quantum dot strongly coupled to two superconducting leads in a Josephson junction geometry. By defining symmetry-adapted superpositions of states from the leads, we formulate an effective Hamiltonian for the strong-hybridisation regime with a single orbital directly coupled to the dot and three additional indirectly coupled orbitals. This minimal basis set allows to account for the quasiparticles in the vicinity of the dot as well as those further away in the leads, and to describe how their role evolves as a function of coupling strength and phase bias $ϕ$. This formulation also reveals the changing nature of the spin-doublet state for the experimentally relevant coupling strengths. The binding of a nearly decoupled quasiparticle in the vicinity of the QD explains the "doublet chimney" in the phase diagram for $ϕ\sim π$, in contrast to $ϕ\sim 0$ where the residual quasiparticle escapes to infinity and plays no active role.

cond-mat.mes-hall↗

arXiv2023

Richardson model with complex level structure and spin-orbit coupling for hybrid superconducting islands: stepwise suppression of pairing and magnetic pinning

An epitaxial semiconductor-superconductor nanowire is a superconducting system with a complex level structure originating from hybridization: in addition to a dense set of higher-energy states derived predominantly from the metallic superconducting shell above the bulk gap $Δ$, there is a smaller number of lower-energy proximitized states from the semiconducting core that define the induced gap $Δ^*$. Nanostructures built from such nanowires can furthermore incorporate quantum dots in order to obtain localized spins for storing and manipulating quantum information. We discuss the magnetic field dependence in three devices with different combinations of embedded quantum dots and superconducting islands. For strong fields, they show pinning of excitation energies to a uniform spacing, even if for weak fields they have non-universal properties with different behaviors for even and odd number of confined electrons. We propose a quantum impurity model for hybrid devices that incorporates all relevant physical effects. We show that the model accounts for the key observations and permits unambiguous interpretation in terms of many-particle states. In particular, we study the replicas of the Yu-Shiba-Rusinov states in the hybrid gap, their collapse and oscillation around zero bias with increasing field, and the strong smoothing effect of the spin-orbit coupling (SOC) on these oscillations. We propose that the SOC-induced mixing of many-body states is a generic mechanism and that magnetic pinning is likely to be a ubiquitous feature in hybrid nanowires.

cond-mat.mes-hall↗

arXiv2023

Exchange interaction between two quantum dots coupled through a superconducting island

We present a theoretical study of a system consisting of a superconducting island and two quantum dots, a possible platform for building qubits and Cooper pair splitters, in the regime where each dot hosts a single electron and, hence, carries a magnetic moment. We focus on the case where the dots are coupled to overlapping superconductor states and we study whether the spins are ferromagnetically or antiferromagnetically aligned. We show that if the total number of particles is even, the spins align antiferromagnetically in the flatband limit, i.e., when the bandwidth of the superconductor is negligibly small, but ferromagnetically if the bandwidth is finite and above some value. If the total number of particles is odd, the alignment is ferromagnetic independently from the bandwidth. This implies that the results of the flatband limit are applicable only within restricted parameter regime for realistic superconducting qubit systems and that some care is required in applying simplified models to devices such as Cooper pair splitters.

cond-mat.mes-hall↗

arXiv2023

Impurity Knight shift in quantum dot Josephson junctions

Spectroscopy of a Josephson junction device with an embedded quantum dot reveals the presence of a contribution to level splitting in external magnetic field that is proportional to $\cos ϕ$, where $ϕ$ is the gauge-invariant phase difference across the junction. To elucidate the origin of this unanticipated effect, we systematically study the Zeeman splitting of spinful subgap states in the superconducting Anderson impurity model. The magnitude of the splitting is renormalized by the exchange interaction between the local moment and the continuum of Bogoliubov quasiparticles in a variant of the Knight shift phenomenon. The leading term in the shift is linear in the hybridisation strength $Γ$ (quadratic in electron hopping), while the subleading term is quadratic in $Γ$ (quartic in electron hopping) and depends on $ϕ$ due to spin-polarization-dependent corrections to the Josephson energy of the device. The amplitude of the $ϕ$-dependent part is largest for experimentally relevant parameters beyond the perturbative regime where it is investigated using numerical renormalization group calculations. Such magnetic-field-tunable coupling between the quantum dot spin and the Josephson current could find wide use in superconducting spintronics.

cond-mat.mes-hall↗

arXiv2023

Entanglement between quasiparticles in superconducting islands mediated by a single spin

Condensed matter is composed of a small set of identical units, yet it shows an immense range of behaviour. Recently, an array of cold atoms was used to generate long-range quantum entanglement, a property of topological matter. Another approach to strong non-local correlations employs the macroscopic coherence of superconductors. Impurity spins in superconductors are thought to be unamenable to the formation of long-range spin entanglement because each spin tends to be screened by binding to a quasiparticle from the superconductor to form a local singlet. Here we demonstrate that it is possible to attach a second quasiparticle to the spin, overscreening it into a doublet state carrying ferromagnetic correlations between two quasiparticles over a micrometer distance. To demonstrate this effect, which is strongest for equal binding, we symmetrically couple the spin of a quantum dot to two ultrasmall superconducting islands. The overscreened state requires sufficiently large Coulomb repulsion and exchange binding to become well defined. We predict that this state will carry long-range correlations for an alternating chain of quantum dots and superconducting islands, opening a new route to controllable large-scale entanglement in the solid state.

cond-mat.mes-hall↗

arXiv2022

Quantum capacitance of a superconducting subgap state in an electrostatically floating dot-island

We study a hybrid device defined in an InAs nanowire with an epitaxial Al shell that consists of a quantum dot in contact with a superconducting island. The device is electrically floating, prohibiting transport measurements, but providing access to states that would otherwise be highly excited and unstable. Radio-frequency reflectometry with lumped-element resonators couples capacitatively to the quantum dot, and detects the presence of discrete subgap states. We perform a detailed study of the case with no island states, but with quantum-dot-induced subgap states controlled by the tunnel coupling. When the gap to the quasi-continuum of the excited states is small, the capacitance loading the resonator is strongly suppressed by thermal excitations, an effect we dub "thermal screening". The resonance frequency shift and changes in the quality factor at charge transitions can be accounted for using a single-level Anderson impurity model. The established measurement method, as well as the analysis and simulation framework, are applicable to more complex hybrid devices such as Andreev molecules or Kitaev chains.

cond-mat.mes-hall↗

arXiv2022

Spectroscopy of spin-split Andreev levels in a quantum dot with superconducting leads

We use a hybrid superconductor-semiconductor transmon device to perform spectroscopy of a quantum dot Josephson junction tuned to be in a spin-1/2 ground state with an unpaired quasiparticle. Due to spin-orbit coupling, we resolve two flux-sensitive branches in the transmon spectrum, depending on the spin of the quasi-particle. A finite magnetic field shifts the two branches in energy, favoring one spin state and resulting in the anomalous Josephson effect. We demonstrate the excitation of the direct spin-flip transition using all-electrical control. Manipulation and control of the spin-flip transition enable the future implementation of charging energy protected Andreev spin qubits.

cond-mat.mes-hall↗

arXiv2022

Direct manipulation of a superconducting spin qubit strongly coupled to a transmon qubit

Spin qubits in semiconductors are currently one of the most promising architectures for quantum computing. However, they face challenges in realizing multi-qubit interactions over extended distances. Superconducting spin qubits provide a promising alternative by encoding a qubit in the spin degree of freedom of an Andreev level. Such an Andreev spin qubit could leverage the advantages of circuit quantum electrodynamic, enabled by an intrinsic spin-supercurrent coupling. The first realization of an Andreev spin qubit encoded the qubit in the excited states of a semiconducting weak-link, leading to frequent decay out of the computational subspace. Additionally, rapid qubit manipulation was hindered by the need for indirect Raman transitions. Here, we exploit a different qubit subspace, using the spin-split doublet ground state of an electrostatically-defined quantum dot Josephson junction with large charging energy. Additionally, we use a magnetic field to enable direct spin manipulation over a frequency range of 10 GHz. Using an all-electric microwave drive we achieve Rabi frequencies exceeding 200 MHz. We furthermore embed the Andreev spin qubit in a superconducting transmon qubit, demonstrating strong coherent qubit-qubit coupling. These results are a crucial step towards a hybrid architecture that combines the beneficial aspects of both superconducting and semiconductor qubits.

quant-ph↗