arXiv subjects

Bogdan R. Bułka

Publications and source records attributed to Bogdan R. Bułka.

11 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

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↗

arXiv2023

Detection of persistent current correlation in cavity-QED

We simulated the radiative response of the cavity quantum electrodynamics (QED) inductively coupled to the ring pierced by magnetic flux, and analyzed its spectral dependence to get insight into persistent current dynamics. Current fluctuations in the ring induce changes in the microwave resonator: shifting the resonant frequency and changing its damping. We use the linear response theory and calculate the current response function by means of the Green function technique. Our model contains two quantum dots which divide the ring into two arms with different electron transfers. There are two opposite (symmetric and asymmetric) components of the persistent current, which interplay can be observed in the response functions. The resonator reflectance shows characteristic shifts in the dispersive regime and avoided crossings at the resonance points. The magnitude of the resonator frequency shift is greater for coupling to the arm with higher transparency. Fluctuations of the symmetric component of the persistent current are relevant for a wide range of the Aharovov-Bohm phase $ϕ$, while the asymmetric component becomes dominant close to $ϕ\approx π$ (when the total persistent current changes its orientation)

cond-mat.mes-hall↗

arXiv2022

Cooper pair splitter in a photonic cavity: Detection of Andreev scatterings

We simulated the radiative response of the cavity quantum electrodynamics (QED) coupled to the double quantum dot Cooper pair splitter and analyzed its spectral dependence to get insight into dynamics of the Cooper pair transfers. The model is confined to the energy subspace where two entangled electrons are transferred to two normal electrodes through the inter-dot singlet state on two proximitized quantum dots. Our research is focused on the Andreev scatterings in the subgap regime, for which the local charge susceptibility $Π(ω_p)$ is derived, by means of Keldysh Green functions, in a whole bias voltage range. In particular, in the large voltage limit the spectrum of $Π(ω_p)$ is expressed by a simple analytical formula, which shows various dissipation processes related with photon-induced transitions between the Andreev bound states.

cond-mat.mes-hall↗

arXiv2021

Formation of Fano resonance in double quantum dot system

Transient electron dynamics and the Fano resonance formation over time in transport through a two quantum dot system in a T-shape geometry (2QD-T) are analysed for free electrons. Time evolution of the transport characteristics are different for a weak and a strong inter-dot coupling with respect to the dot-electrode coupling. When the dot-dot coupling is weak, we find that transport dynamics is governed by two channel tunneling processes with two different relaxation times and buildup of the Fano resonance is developed much slower, with the longer relaxation time. In the opposite limit, the transmission evolves with a single relaxation time, from the single peak resonance structure into the structure with two asymmetric peaks. One observes large dot-electrode charge oscillations, which can temporarily change direction of transient currents. We find also that the time evolution of entanglement is different in both coupling regimes; in particular rapid Rabi oscillations caused by coherent electron transfer between the 2QD states can be seen for the strong dot-dot coupling.

cond-mat.mes-hall↗

arXiv2021

Coherent current correlations in a double-dot Cooper pair splitter

Exact analytical formulas are derived, by means of Keldysh Green functions, for currents and current correlation functions in a Cooper pair splitter modelled on a double quantum dot system coherently coupled to a superconductor and two normal metallic electrodes. Confining to the subspace with the inter-dot singlet we show perfect entanglement of split electrons in two separated crossed Andreev reflection processes. The studies are focused on the noise power spectrum in a whole bias voltage range. In particular, in the large voltage limit shot noise dominates and its spectrum exhibits two extraordinary side dips related to resonant inter-level current correlations caused by coherent electron-hole recombination processes accompanied by emission and absorption of photons. In the linear response limit we derived the frequency dependent admittance which shows different interference patterns for the cross and the auto current correlations.

cond-mat.mes-hall↗

arXiv2021

Quantum coherence in noise power spectrum in two quantum dots

We present studies of quantum interference in a noise power spectrum in the system of two quantum dots (2QD) in a T-geometry. Performing the spectral decomposition we are able to separate local currents and distinguish between the intra- and inter-level current correlation contributions to the noise power spectrum. In particular, we analyzed the large bias regime and show that for a weak coupling of 2QD with the electrodes the noise power spectrum has dips at frequencies characteristic to inter-level excitations. For a strong coupling the electron transport changes its nature and the dynamics of the current correlations is different: there are two coherently coupled relaxators with different relaxation frequencies. These two regimes of current dynamics are separated by a quantum critical point, in which the noise power spectrum shows a specific frequency dependence. In the linear response limit the noise power spectrum is related to the admittance, which shows characteristics different, due to quantum interference, for the weak and strong coupling case.

cond-mat.mes-hall↗

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

Current Correlations in a Quantum Dot Ring: A Role of Quantum Interference

We present studies of the electron transport and circular currents induced by the bias voltage and the magnetic flux threading a ring of three quantum dots coupled with two electrodes. Quantum interference of electron waves passing through the states with opposite chirality plays a relevant role in transport, where one can observe Fano resonance with destructive interference. The quantum interference effect is quantitatively described by local bond currents and their correlation functions. Fluctuations of the transport current are characterized by the Lesovik formula for the shot noise, which is a composition of the bond current correlation functions. In the presence of circular currents, the cross-correlation of the bond currents can be very large, but it is negative and compensates for the large positive auto-correlation functions.

cond-mat.mes-hall↗

arXiv2018

Two-qubit logical operations in three quantum dots system

We consider a model of two interacting always-on, exchange-only qubits for which controlled phase ($CPHASE$), controlled NOT ($CNOT$), quantum Fourier transform ($QFT$) and $SWAP$ operations can be implemented only in a few electrical pulses in a nanosecond time scale. Each qubit is built of three quantum dots (TQD) in a triangular geometry with three electron spins which are always kept coupled by exchange interactions only. The qubit states are encoded in a doublet subspace and are fully electrically controlled by a voltage applied to gate electrodes. The two qubit quantum gates are realized by short electrical pulses which change the triangular symmetry of TQD and switch on exchange interaction between the qubits. We found an optimal configuration to implement the $CPHASE$ gate by a single pulse of the order 2.3 ns. Using this gate, in combination with single qubit operations, we searched for optimal conditions to perform the other gates: $CNOT$, $QFT$ and $SWAP$. Our studies take into account environment effects and leakage processes as well. The results suggest that the system can be implemented for fault tolerant quantum computations.

cond-mat.mes-hall↗

arXiv2010

Current rectification in molecular junctions produced by local potential fields

The transport properties of a octane-dithiol (ODT) molecule coupled to Au(001) leads are analyzed using density functional theory and non-equilibrium Green functions. It is shown that a symmetric molecule can turn into a diode under influence of a local electric field created by an external charged probe. The origin of the asymmetry of the current--voltage ($I-V$) dependence is traced back to the appearance of a probe induced quasi--local state in the pseudogap of the ODT molecule. The induced state affects electron transport, provided it is close to the Fermi level of the leads. An asymmetric placement of the charged probe along the alkane chain makes the induced quasi--local state in the energy gap very sensitive to the bias voltage and results in rectification of the current. The results based on DFT are supported by independent calculations using a simple one--particle model Hamiltonian.

cond-mat.mes-hall↗