Cooper Pair Transport Research Articles

From nonreciprocal to charge-4e supercurrent in Ge-based Josephson devices with tunable harmonic content

Hybrid superconductor(S)-semiconductor(Sm) devices bring a range of functionalities into superconducting circuits. In particular, hybrid parity-protected qubits and Josephson diodes were recently proposed and experimentally demonstrated. Such devices leverage the nonsinusoidal character of the Josephson current-phase relation (CPR) in highly transparent S-Sm-S junctions. Here, we report an experimental study of superconducting quantum-interference devices (SQUIDs) embedding Josephson field-effect transistors fabricated from a SiGe/Ge/SiGe heterostructure grown on a 200-mm silicon wafer. The single-junction CPR shows up to three harmonics with gate-tunable amplitude. In the presence of microwave irradiation, the ratio of the first two dominant harmonics, corresponding to single and double Cooper-pair transport processes, is consistently reflected in relative weight of integer and half-integer Shapiro steps. A combination of magnetic-flux and gate-voltage control enables tuning the SQUID functionality from a nonreciprocal Josephson-diode regime with 27% asymmetry to a π-periodic Josephson regime suitable for the implementation of parity-protected superconducting qubits. These results illustrate the potential of Ge-based hybrid devices as versatile and scalable building blocks of superconducting quantum circuits. Published by the American Physical Society 2024

One-dimensional proximity superconductivity in the quantum Hall regime.

Extensive efforts have been undertaken to combine superconductivity and the quantum Hall effect so that Cooper-pair transport between superconducting electrodes in Josephson junctions is mediated by one-dimensional edge states1-6. This interest has been motivated by prospects of finding new physics, including topologically protected quasiparticles7-9, but also extends into metrology and device applications10-13. So far it has proven challenging to achieve detectable supercurrents through quantum Hall conductors2,3,6. Here we show that domain walls in minimally twisted bilayer graphene14-18 support exceptionally robust proximity superconductivity in the quantum Hall regime, allowing Josephson junctions to operate in fields close to the upper critical field of superconducting electrodes. The critical current is found to be non-oscillatory and practically unchanging over the entire range of quantizing fields, with its value being limited by the quantum conductance of ballistic, strictly one-dimensional, electronic channels residing within the domain walls. The system described is unique in its ability to support Andreev bound states at quantizingfields and offers many interesting directions for further exploration.

Interplay of Andreev Reflection and Coulomb Blockade in Hybrid Superconducting Single-Electron Transistors.

We study the interplay between Coulomb blockade and superconductivity in a tunable superconductor-superconductor-normal-metal single-electron transistor. The device is realized by connecting the superconducting island via an oxide barrier to the normal-metal lead and with a break junction to the superconducting lead. The latter enables Cooper pair transport and (multiple) Andreev reflection. We show that these processes are relevant also far above the superconducting gap and that signatures of Coulomb blockade may reoccur at high bias while they are absent for small bias in the strong-coupling regime. Our experimental findings agree with simulations using a rate equation approach in combination with the full counting statistics of multiple Andreev reflection.

Parity-conserving Cooper-pair transport and ideal superconducting diode in planar germanium

Superconductor/semiconductor hybrid devices have attracted increasing interest in the past years. Superconducting electronics aims to complement semiconductor technology, while hybrid architectures are at the forefront of new ideas such as topological superconductivity and protected qubits. In this work, we engineer the induced superconductivity in two-dimensional germanium hole gas by varying the distance between the quantum well and the aluminum. We demonstrate a hard superconducting gap and realize an electrically and flux tunable superconducting diode using a superconducting quantum interference device (SQUID). This allows to tune the current phase relation (CPR), to a regime where single Cooper pair tunneling is suppressed, creating a sin left(2varphi right) CPR. Shapiro experiments complement this interpretation and the microwave drive allows to create a diode with ≈ 100% efficiency. The reported results open up the path towards integration of spin qubit devices, microwave resonators and (protected) superconducting qubits on the same silicon technology compatible platform.

Josephson Junction π-0 Transition Induced by Orbital Hybridization in a Double Quantum Dot.

In this Letter, we manipulate the phase shift of a Josephson junction using a parallel double quantum dot (QD). By employing a superconducting quantum interference device, we determine how orbital hybridization and detuning affect the current-phase relation in the Coulomb blockade regime. For weak hybridization between the QDs, we find π junction characteristics if at least one QD has an unpaired electron. Notably the critical current is higher when both QDs have an odd electron occupation. By increasing the inter-QD hybridization the critical current is reduced, until eventually a π-0 transition occurs. A similar transition appears when detuning the QD levels at finite hybridization. Based on a zero-bandwidth model, we argue that both cases of phase-shift transitions can be understood considering an increased weight of states with a double occupancy in the ground state and with the Cooper pair transport dominated by local Andreev reflection.

Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor

We analyze the time-dependent solution of master equations by exploiting fermionic duality, a dissipative symmetry applicable to a large class of open systems describing quantum transport. Whereas previous studies mostly exploited duality relations after partially solving the evolution equations, we here systematically exploit the invariance under the fermionic duality mapping from the very beginning when setting up these equations. Moreover, we extend the resulting simplifications -so far applied to the local state evolution- to non-local observables such as transport currents. We showcase the exploitation of fermionic duality for a quantum dot with strong interaction -covering both the repulsive and attractive case- proximized by contact with a large-gap superconductor which is weakly probed by charge and heat currents into a wide-band normal-metal electrode. We derive the complete time-dependent analytical solution of this problem involving non-equilibrium Cooper pair transport, Andreev bound states and strong interaction. Additionally exploiting detailed balance we show that even for this relatively complex problem the evolution towards the stationary state can be understood analytically in terms of the stationary state of the system itself via its relation to the stationary state of a dual system with inverted Coulomb interaction, superconducting pairing and applied voltages.

Nonequilibrium Green’s function approach to multi-band Cooper-pair transport: linear magnetoresistance effect due to nonunitary superconductivity

Many-body transport has emerged as an efficient tool for understanding interaction effects in quantum materials with a multi-band electronic structure. This paper proposes a formula for the two-particle transmission coefficient for Cooper-pair transport between multi-band normal and superconducting materials. The approach employs a tight-binding nonequilibrium Green’s function technique, allowing a direct calculation of the two-particle current, without invoking the paradigm of Andreev reflection. As an application of the theory, we demonstrate a low-field linear magnetoresistance effect for superconductors with an induced nonunitary order parameter. These results uncover an unexplored route for detecting unconventional nonunitary superconductivity in quantum materials of current theoretical and experimental interest.

Thermal signature of the Majorana fermion in a Josephson junction

Existence of distinctive correlation between the thermal conductance and the Josephson current across a 1-D topological Josephson junction (T-JJ) is established and an expression connecting the two is derived in the short junction limit. It is shown that the three terminal T-JJ provides us with an ideal set-up for exploiting the distinctive correlations which aid in identifying hallmarks of Majorana bound state localized at the junction. Our approach combines information form sub-gap Cooper pair transport and transport of above-gap thermally excited quasiparticle which is complementary to the existing studies.

Current correlations of Cooper-pair tunneling into a quantum Hall system

We study Cooper pair transport through a quantum point contact between a superconductor and a quantum Hall edge state at integer and fractional filling factors. We calculate the tunnelling current and its finite-frequency noise to the leading order in the tunneling amplitude for dc and ac bias voltage in the limit of low temperatures. At zero temperature and in case of tunnelling into a single edge channel both the conductance and differential shot noise vanish as a result of Pauli exclusion principle. In contrast, in the presence of two edge channels, this Pauli blockade is softened and a non-zero conductance and shot noise are revealed.

Phase-controlled spin and charge currents in a superconductor-ferromagnet hybrid

We investigate spin-dependent quasiparticle and Cooper-pair transport through a central node interfaced with two superconductors and two ferromagnets. We demonstrate that voltage biasing of the ferromagnetic contacts induces superconducting triplet correlations on the node and reverses the supercurrent flowing between the two superconducting contacts. We further find that such triplet correlations can mediate a tunable spin current flow into the ferromagnetic contacts. Our key finding is that unequal spin-mixing conductances for the two interfaces with the ferromagnets result in equal-spin triplet correlations on the node, detectable via a net charge current between the two magnets. Our proposed device thus enables the generation, control, and detection of the typically elusive equal-spin triplet Cooper pairs.

High transparency Bi2Se3 topological insulator nanoribbon Josephson junctions with low resistive noise properties

Bi2Se3 nanoribbons, grown by catalyst-free Physical Vapor Deposition, have been used to fabricate high quality Josephson junctions with Al superconducting electrodes. The conductance spectra (dI/dV) of the junctions show clear dip-peak structures characteristic of multiple Andreev reflections. The temperature dependence of the dip-peak features reveals a highly transparent Al/Bi2Se3 topological insulator nanoribbon interface and Josephson junction barrier. This is supported by the high values of the Bi2Se3 induced gap and of IcRn (where Ic is the critical current and Rn is the normal resistance of the junction) product both of the order of 160 μeV, a value close to the Al gap. The devices present an extremely low relative resistance noise below 1 × 10−12 μm2/Hz comparable to the best Al tunnel junctions, which indicates a high stability in the transmission coefficients of transport channels. The ideal Al/Bi2Se3 interface properties, perfect transparency for Cooper pair transport in conjunction with low resistive noise, make these junctions a suitable platform for further studies of the induced topological superconductivity and Majorana bound states physics.

Quasiparticle Screening near a Bosonic Superconductor-Insulator Transition Revealed by Magnetic Impurity Doping.

Experiments show that the Cooper pair transport in the insulator phase that forms at thin film superconductor to insulator transitions (SIT) is simply activated. The activation energy T_{0} depends on the microscopic factors that drive Cooper pair localization. To test proposed models, we investigated how a perturbation that weakens Cooper pair binding, magnetic impurity doping, and phase frustration affects T_{0}. The data show that T_{0} decreases monotonically with doping in films tuned farther from the SIT and increases and peaks in films that are closer to the SIT critical point. The observations provide strong evidence that the bosonic SIT in thin films is a Mott transition driven by Coulomb interactions that are screened by virtual quasiparticle excitations. This dependence on underlying fermionic degrees of freedom distinguishes these SITs from those in microfabricated Josephson Junction arrays, cold atom systems, and likely in high temperature superconductors with nodes in their quasiparticle density of states.

Aharonov-Bohm and Aharonov-Casher effects in a double quantum dot Josephson junction

We analyze a Josephson junction between two superconductors interconnected through a normal-state nanostructure made of two parallel nanowires with embedded quantum dots. We study the influence of interference effects due to the Aharonov-Bohm (AB) and Aharonov-Casher (AC) phases for local and nonlocal (split) Cooper pairs. In the AB effect the phase of electron is affected by magnetic flux, while in the AC effect the phase of the electron in solid state can be modified due to the Rashba spin-orbit coupling. In the low-transmission regime the AB and AC effects can be related to only local or nonlocal Cooper pair transport, respectively. We demonstrate that by the addition of the quantum dots the Cooper pair splitting can be made perfectly efficient, and that the AC phase is different for non-spin-flip and spin-flip transport processes.

Aharonov-Bohm and Aharonov-Casher effects for local and nonlocal Cooper pairs

We study combined interference effects due to the Aharonov-Bohm (AB) and Aharonov-Casher (AC) phases in a Josephson supercurrent of local and nonlocal (split) Cooper pairs. We analyze a junction between two superconductors interconnected through a normal-state nanostructure with either (i) a ring, where single-electron interference is possible, or (ii) two parallel nanowires, where the single-electron interference can be absent, but the cross Andreev reflection can occur. In the low-transmission regime in both geometries the AB and AC effects can be related to only local or nonlocal Cooper pair transport, respectively.

Zero energy states at a normal-metal/cuprate-superconductor interface probed by shot noise

We report measurements of the current noise generated in the optimally doped, $x=0.15$, Au-${\text{La}}_{2\ensuremath{-}x}{\text{Sr}}_{x}{\text{CuO}}_{4}$ junctions. For high transmission junctions on a (110) surface, we observed a split zero-bias conductance peak (ZBCP), accompanied by enhanced shot noise. We observed no enhanced noise neither in low-transmission junctions on a (110) surface nor in any junction on a (100) surface. We attribute the enhanced noise to Cooper pair transport through the junctions.

Electron and Cooper-pair transport across a single magnetic molecule explored with a scanning tunneling microscope

The interplay of magnetism and superconductivity gives rise to the emergence of various interesting phenomena in condensed matter physics, such as the Yu-Shiba-Rusinov in-gap modes created by local magnetic moments in superconducting hosts. Using normal-metal and superconducting tips the authors have formed contacts to an individual magnetic molecule adsorbed on a conventional superconductor. Spectroscopy of the differential conductance with tunable junction transparency has unveiled the crossover from quasiparticle tunneling, which probes the Bardeen-Cooper-Schrieffer energy gap as well as the Yu-Shiba-Rusinov levels, to the contact range where multiple Andreev reflection takes over.

Signatures of nonlocal Cooper-pair transport and of a singlet-triplet transition in the critical current of a double-quantum-dot Josephson junction

We study the critical Josephson current flowing through a double quantum dot weakly coupled to two superconducting leads. We use analytical as well as numerical methods to investigate this setup in the limit of small and large bandwidth leads in all possible charging states, where we account for on-site interactions exactly. Our results provide clear signatures of nonlocal spin-entangled pairs, which support interpretations of recent experiments [Deacon, R. S. et al., Nat. Commun. 6, 7446 (2015)]. In addition, we find that the ground state with one electron on each quantum dot can undergo a tunable singlet-triplet phase transition in the regime where the superconducting gap in the leads is not too large, which gives rise to an additional new signature of nonlocal Cooper pair transport.

Correlated Cooper pair transport and microwave photon emission in the dynamical Coulomb blockade

We study theoretically electromagnetic radiation emitted by inelastic Cooper-pair tunneling. We consider a dc-voltage-biased superconducting transmission line terminated by a Josephson junction. We show that the generated continuous-mode electromagnetic field can be expressed as a function of the time-dependent current across the Josephson junction. The leading-order expansion in the tunneling coupling, similar to the "$P(E)$-theory", has previously been used to investigate the photon emission statistics in the limit of sequential (independent) Cooper-pair tunneling. By explicitly evaluating the system characteristics up to the fourth-order in the tunneling coupling, we account for dynamics between consecutively tunneling Cooper pairs. Within this approach we investigate how temporal correlations in the charge transport can be seen in the first- and second-order coherences of the emitted microwave radiation.

Double Path Interference and Magnetic Oscillations in Cooper Pair Transport through a Single Nanowire.

We show that the critical current of the Josephson junction consisting of superconducting electrodes coupled through a nanowire with two conductive channels can reveal the multiperiodic magnetic oscillations. The multiperiodicity originates from the quantum mechanical interference between the channels affected by both the strong spin-orbit coupling and the Zeeman interaction. This minimal two-channel model is shown to explain the complicated interference phenomena observed recently in Josephson transport through Bi nanowires.

Pure second harmonic current-phase relation in spin-filter Josephson junctions

Higher harmonics in current-phase relations of Josephson Junctions are predicted to be observed when the first harmonic is suppressed. Conventional theoretical models predict higher harmonics to be extremely sensitive to changes in barrier thickness, temperature, and so on. Here we report experiments with Josephson junctions incorporating a spin-dependent tunnelling barrier, revealing a current-phase relation for highly spin polarized barriers that is purely second harmonic in nature and is insensitive to changes in barrier thickness. This observation implies that the standard theory of Cooper pair transport through tunnelling barriers is not applicable for spin-dependent tunnelling barriers.