arXiv subjects

A. Zazunov

Publications and source records attributed to A. Zazunov.

At least 19 recordsLinked to original sources

arXiv2024

Nonreciprocal charge transport and subharmonic structure in voltage-biased Josephson diodes

We study charge transport in voltage-biased single-channel junctions involving helical superconductors with finite Cooper pair momentum. For a Josephson junction, the equilibrium current-phase relation shows a superconducting diode effect: the critical current depends on the propagation direction. We formulate a scattering theory for voltage-biased Josephson diodes and show that multiple Andreev reflection processes cause a rich subharmonic structure in the DC current-voltage curve at low temperatures and small voltages due to Doppler shifts of the spectral gap. In the current-biased case, the diode efficiency has maximal rectification efficiency $η_0\approx 0.4$ for this model. In the voltage-biased case, however, the rectification efficiency can reach the ideal value $η=1$. We also discuss charge transport for NS junctions between a normal metal and a helical superconductor and comment on related models with spin-orbit interactions and magnetic Zeeman fields.

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arXiv2024

Approaching ideal rectification in superconducting diodes through multiple Andreev reflections

We analyze the rectification properties of voltage-biased Josephson junctions exhibiting the superconducting diode effect. Taking into account multiple Andreev reflection (MAR) processes in our scattering theory, we consider a short weak link of arbitrary transparency between two superconductors with finite Cooper pair momentum $2q$. In equilibrium, the diode efficiency is bounded from above in this model, with maximal efficiency $η_0\approx 0.4$. Out of equilibrium, we find a rich subharmonic structure in the current-voltage curve. For high transparency and low bias voltage $V$, the rectification efficiency $η(V)$ approaches the ideal value $η=1$ for $qξ\to 1$ (with coherence length $ξ$).

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arXiv2020

Towards dark space stabilization and manipulation in driven dissipative Majorana platforms

We propose driven dissipative Majorana platforms for the stabilization and manipulation of robust quantum states. For Majorana box setups, in the presence of environmental electromagnetic noise and with tunnel couplings to quantum dots, we show that the time evolution of the Majorana sector is governed by a Lindblad master equation over a wide parameter regime. For the single-box case, arbitrary pure states (`dark states') can be stabilized by adjusting suitable gate voltages. For devices with two tunnel-coupled boxes, we outline how to engineer dark spaces, i.e., manifolds of degenerate dark states, and how to stabilize fault-tolerant Bell states. The proposed Majorana-based dark space platforms rely on the constructive interplay of topological protection mechanisms and the autonomous quantum error correction capabilities of engineered driven dissipative systems. Once a working Majorana platform becomes available, only standard hardware requirements are needed to implement our ideas.

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arXiv2020

Driven Dissipative Majorana Dark Spaces

Pure quantum states can be stabilized in open quantum systems subject to external driving forces and dissipation by environmental modes. We show that driven dissipative (DD) Majorana devices offer key advantages for stabilizing degenerate state manifolds (`dark spaces') and for manipulating states in dark spaces, both with respect to native (non-DD) Majorana devices and to DD platforms with topologically trivial building blocks. For two tunnel-coupled Majorana boxes, using otherwise only standard hardware elements (e.g., a noisy electromagnetic environment and quantum dots with driven tunnel links), we propose a dark qubit encoding. We anticipate exceptionally high fault tolerance levels due to a conspiracy of DD-based autonomous error correction and topology.

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arXiv2020

Theory of non-equilibrium noise in general multi-terminal superconducting hydrid devices: application to multiple Cooper pair resonances

We consider the out-of-equilibrium behavior of a general class of mesoscopic devices composed of several superconducting or/and normal metal leads separated by quantum dots. Starting from a microscopic Hamiltonian description, we provide a non-perturbative approach to quantum electronic transport in the tunneling amplitudes between dots and leads: using the equivalent of a path integral formulation, the lead degrees of freedom are integrated out in order to compute both the current and the current correlations (noise) in this class of systems, in terms of the dressed Green's function matrix of the quantum dots. In order to illustrate the efficiency of this formalism, we apply our results to the "all superconducting Cooper pair beam splitter", a device composed of three superconducting leads connected via two quantum dots, where crossed Andreev reflection operates Cooper pair splitting. Commensurate voltage differences between the three leads allow to obtain expressions for the current and noise as a function of the Keldysh Nambu Floquet dressed Green's function of the dot system. This voltage configuration allows the occurrence of non-local processes involving multiple Cooper pairs which ultimately lead to the presence of non-zero DC currents in an out-of-equilibrium situation. We investigate in details the results for the noise obtained numerically in the specific case of opposite voltages, where the transport properties are dominated by the so called "quartet processes", involving the coherent exchange of two Cooper pairs among all three superconducting terminals. We show that these processes are noiseless in the non-resonant case, and that this property is also observed for other voltage configurations. When the dots are in a resonant regime, the noise characteristics change qualitatively, with the appearance of giant Fano factors.

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arXiv2020

Multi-particle interferometry in the time-energy domain with localized topological quasiparticles

We propose multi-particle interference protocols in the time-energy domain which are able to probe localized topological quasiparticles. Using a set of quantum dots tunnel-coupled to a topologically nontrivial system, the time dependence of the dot level energies defines a many-body interferometry platform which (to some extent) is similar to the Hong-Ou-Mandel (HOM) interferometer. We demonstrate that for a superconducting island harboring at least four Majorana bound states, the probability distribution of the final dot occupation numbers will exhibit a characteristic interferometric pattern with robust and quantized $π$ phase shifts. This pattern is shown to be qualitatively different for topologically trivial variants of our setup. Apart from identifying the presence of topological quasiparticles, the interferometer can be used to manipulate the quantum state in the topologically nontrivial sector by means of post-selection.

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arXiv2020

Boundary Green's function approach for spinful single-channel and multichannel Majorana nanowires

The boundary Green's function (bGF) approach has been established as a powerful theoretical technique for computing the transport properties of tunnel-coupled hybrid nanowire devices. Such nanowires may exhibit topologically nontrivial superconducting phases with Majorana bound states at their boundaries. We introduce a general method for computing the bGF of spinful multi-channel lattice models for such Majorana nanowires, where the bGF is expressed in terms of the roots of a secular polynomial evaluated in complex momentum space. In many cases, those roots, and thus the bGF, can be accurately described by simple analytical expressions, while otherwise our approach allows for the numerically efficient evaluation of bGFs. We show that from the behavior of the roots, many physical quantities of key interest can be inferred, e.g., the value of bulk topological invariants, the energy dependence of the local density of states, or the spatial decay of subgap excitations. We apply the method to single- and two-channel nanowires of symmetry class D or DIII. In addition, we study the spectral properties of multi-terminal Josephson junctions made out of such Majorana nanowires.

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arXiv2019

Finite frequency noise in a normal metal - topological superconductor junction

A topological superconductor nanowire bears a Majorana bound state at each of its ends, leading to unique transport properties. As a way to probe these, we study the finite frequency noise of a biased junction between a normal metal and a topological superconductor nanowire. We use the non-equilibrium Keldysh formalism to compute the finite frequency emission and absorption noise to all order in the tunneling amplitude, for bias voltages below and above the superconducting gap. We observe noticeable structures in the absorption and emission noise, which we can relate to simple transport processes. The presence of the Majorana bound state is directly related to a characteristic behavior of the noise spectrum at low frequency. We further compute the noise measurable with a realistic setup, based on the inductive coupling to a resonant LC circuit, and discuss the impact of the detector temperature. We have also computed the emission noise for a non-topological system with a resonant level, exhibiting a zero-energy Andreev bound state, in order to show the specificities of the topological case. Our results offer an original tool for the further characterization of the presence of Majorana bound states in condensed matter systems.

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arXiv2019

Giant shot noise from Majorana zero modes in topological trijunctions

The clear-cut experimental identification of Majorana bound states in transport measurements still poses experimental challenges. We here show that the zero-energy Majorana state formed at a junction of three topological superconductor wires is directly responsible for giant shot noise amplitudes, in particular at low voltages and for small contact transparency. The only intrinsic noise limitation comes from the current-induced dephasing rate due to multiple Andreev reflection processes.

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arXiv2018

Fermi liquid approach for superconducting Kondo problems

We present a Fermi liquid approach to superconducting Kondo problems applicable when the Kondo temperature is large compared to the superconducting gap. To illustrate the theory, we study the current-phase relation and the Andreev level spectrum for an Anderson impurity between two $s$-wave superconductors. In the particle-hole symmetric Kondo limit, we find a $4π$ periodic Andreev spectrum. The $4π$ periodicity persists under a small voltage bias which however causes an asymmetric distortion of Andreev levels. The latter distinguishes the present $4π$ effect from the one in topological Majorana junctions.

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arXiv2018

Unified scattering approach to Josephson current and thermal noise in BCS and topological superconducting junctions

We present a unified description of a junction between $s$-wave (BCS) superconductors and a junction between $p$-wave superconductors in a topologically nontrivial phase, which relies on a scattering state expansion. We compute Josephson current and thermal noise in the two kinds of junction and exhibit some characteristic features for a junction of two topological superconductors hosting Majorana zero-energy modes.

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arXiv2018

Josephson effect in junctions of conventional and topological superconductors

We present a theoretical analysis of the equilibrium Josephson current-phase relation in hybrid devices made of conventional s-wave spin-singlet superconductors (S) and topological superconductor (TS) wires featuring Majorana end states. Using Green's function techniques, the topological superconductor is alternatively described by the low-energy continuum limit of a Kitaev chain or by a more microscopic spinful nanowire model. We show that for the simplest S-TS tunnel junction, only the s-wave pairing correlations in a spinful TS nanowire model can generate a Josephson effect. The critical current is much smaller in the topological regime and exhibits a kink-like dependence on the Zeeman field along the wire. When a correlated quantum dot (QD) in the magnetic regime is present in the junction region, however, the Josephson current becomes finite also in the deep topological phase as shown for the cotunneling regime and by a mean-field analysis. Remarkably, we find that the S-QD-TS setup can support $φ_0$-junction behavior, where a finite supercurrent flows at vanishing phase difference. Finally, we also address a multi-terminal S-TS-S geometry, where the TS wire acts as tunable parity switch on the Andreev bound states in a superconducting atomic contact.

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arXiv2017

Josephson effect in multiterminal topological junctions

We study the Josephson effect in a trijunction formed by two topological superconductor (TS) wires and a conventional $s$-wave superconductor. Using a boundary Green's function formalism, analytical results for the current-phase relation are obtained in various limiting cases by modeling the TS wires via the low-energy limit of a Kitaev chain. We show that Josephson transport critically depends on the spin canting angle $θ$ between the boundary spin polarizations of the TS wires, which in turn suggests that the spin structure of Majorana states can be accessed through supercurrent measurements. We also extend the boundary Green's function approach to a more microscopic spinful wire model and thereby compute the dependence of $θ$ on experimentally accessible parameters such as the Zeeman field and/or the chemical potential. Furthermore, we show that the equilibrium current-phase relation between both TS wires exhibits a robust $4π$-periodicity since the conventional superconducting lead effectively locks the fermion parity of the trijunction.

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arXiv2017

Hanbury Brown and Twiss noise correlations in a topological superconductor beam splitter

We study Hanbury-Brown and Twiss current cross-correlations in a three-terminal junction where a central topological superconductor (TS) nanowire, bearing Majorana bound states at its ends, is connected to two normal leads. Relying on a non-perturbative Green function formalism, our calculations allow us to provide analytical expressions for the currents and their correlations at subgap voltages, while also giving exact numerical results valid for arbitrary external bias. We show that when the normal leads are biased at voltages $V_1$ and $V_2$ smaller than the gap, the sign of the current cross-correlations is given by $-\mbox{sgn}(V_1 \, V_2)$. In particular, this leads to positive cross-correlations for opposite voltages, a behavior in stark contrast with the one of a standard superconductor, which provides a direct evidence of the presence of the Majorana zero-mode at the edge of the TS. We further extend our results, varying the length of the TS (leading to an overlap of the Majorana bound states) as well as its chemical potential (driving it away from half-filling), generalizing the boundary TS Green function to those cases. In the case of opposite bias voltages, $\mbox{sgn}(V_1 \, V_2)=-1$, driving the TS wire through the topological transition leads to a sign change of the current cross-correlations, providing yet another signature of the physics of the Majorana bound state.

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arXiv2017

$6π$ Josephson effect in Majorana box devices

We study Majorana devices featuring a competition between superconductivity and multi-channel Kondo physics. Our proposal extends previous work on single-channel Kondo systems to a topologically nontrivial setting of non-Fermi liquid type, where topological superconductor wires (with gap $Δ$) represent leads tunnel-coupled to a Coulomb-blockaded Majorana box. On the box, a spin degree of freedom with Kondo temperature $T_K$ is nonlocally defined in terms of Majorana states. For $Δ\gg T_K$, the destruction of Kondo screening by superconductivity implies a $4π$-periodic Josephson current-phase relation. Using a strong-coupling analysis in the opposite regime $Δ\ll T_K$, we find a $6π$-periodic Josephson relation for three leads, with critical current $I_c\approx eΔ^2/ \hbar T_K$, corresponding to the transfer of fractionalized charges $e^*=2e/3$.

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arXiv2016

Low-energy theory of transport in Majorana wire junctions

We formulate and apply a low-energy transport theory for hybrid quantum devices containing junctions of topological superconductor (TS) wires and conventional normal (N) or superconducting (S) leads. We model TS wires as spinless $p$-wave superconductors and derive their boundary Keldysh Green's function, capturing both the Majorana end state and continuum quasiparticle excitations in a unified manner. We also specify this Green's function for a finite-length TS wire. Junctions connecting different parts of the device are described by the standard tunneling Hamiltonian. Using this Hamiltonian approach, one also has the option to include many-body interactions in a systematic manner. For N-TS junctions, we provide the current-voltage ($I$-$V$) characteristics at arbitrary junction transparency and give exact results for the shot noise power and the excess current. For TS-TS junctions, analytical results for the thermal noise spectrum and for the $I$-$V$ curve in the high-transparency low-bias regime are presented. For S-TS junctions, we compute the entire $I$-$V$ curve and clarify the conditions for having a finite Josephson current.

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arXiv2016

Kondo physics from quasiparticle poisoning in Majorana devices

We present a theoretical analysis of quasiparticle poisoning in Coulomb-blockaded Majorana fermion systems tunnel-coupled to normal-conducting leads. Taking into account finite-energy quasiparticles, we derive the effective low-energy theory and present a renormalization group analysis. We find qualitatively new effects when a quasiparticle state with very low energy is localized near a tunnel contact. For $M=2$ attached leads, such "dangerous" quasiparticle poisoning processes cause a spin $S=1/2$ single-channel Kondo effect, which can be detected through a characteristic zero-bias anomaly conductance peak in all Coulomb blockade valleys. For more than two attached leads, the topological Kondo effect of the unpoisoned system becomes unstable. A strong-coupling bosonization analysis indicates that at low energy the poisoned lead is effectively decoupled and hence, for $M>3$, the topological Kondo fixed point re-emerges, though now it involves only $M-1$ leads. As a consequence, for $M=3$, the low-energy fixed point becomes trivial corresponding to decoupled leads.

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arXiv2015

Cooper pair splitting in a nanoSQUID geometry at high transparency

We describe a Josephson device composed of two superconductors separated by two interacting quantum dots in parallel, as a probe for Cooper pair splitting. In addition to sequential tunneling of electrons through each dot, an additional transport channel exists in this system: crossed Andreev reflection, where a Cooper pair from the source is split between the two dots and recombined in the drain superconductor. Unlike non-equilibrium scenarios for Cooper pair splitting which involves superconducting/normal metal "forks", our proposal relies on an Aharonov-Bohm measurement of the DC Josephson current when a flux is inserted between the two dots. We provide a path integral approach to treat arbitrary transparencies, and we explore all contributions for the individual phases ($0$ or $π$) of the quantum dots. We propose a definition of the Cooper pair splitting efficiency for arbitrary transparencies, which allows us to find the phase associations which favor the crossed Andreev process. Possible applications to experiments using nanowires as quantum dots are discussed.

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