Towards phase-coherent caloritronics in superconducting circuits

The emerging field of phase-coherent caloritronics (from the Latin word "calor", i.e., heat) is based on the possibility to control heat currents using the phase difference of the superconducting order parameter. The goal is to design and implement thermal devices able to master energy transfer with a degree of accuracy approaching the one reached for charge transport by contemporary electronic components. This can be obtained by exploiting the macroscopic quantum coherence intrinsic to superconducting condensates, which manifests itself through the Josephson and the proximity effect. Here, we review recent experimental results obtained in the realization of heat interferometers and thermal rectifiers, and discuss a few proposals for exotic non-linear phase-coherent caloritronic devices, such as thermal transistors, solid-state memories, phase-coherent heat splitters, microwave refrigerators, thermal engines and heat valves. Besides being very attractive from the fundamental physics point of view, these systems are expected to have a vast impact on many cryogenic microcircuits requiring energy management, and possibly lay the first stone for the foundation of electronic thermal logic.Comment: 11 pages, 6 colour figure

Phase-tunable Josephson thermal router

Since the the first studies of thermodynamics, heat transport has been a crucial element for the understanding of any thermal system. Quantum mechanics has introduced new appealing ingredients for the manipulation of heat currents, such as the long-range coherence of the superconducting condensate. The latter has been exploited by phase-coherent caloritronics, a young field of nanoscience, to realize Josephson heat interferometers, which can control electronic thermal currents as a function of the external magnetic flux. So far, only one output temperature has been modulated, while multi-terminal devices that allow to distribute the heat flux among different reservoirs are still missing. Here, we report the experimental realization of a phase-tunable thermal router able to control the heat transferred between two terminals residing at different temperatures. Thanks to the Josephson effect, our structure allows to regulate the thermal gradient between the output electrodes until reaching its inversion. Together with interferometers, heat diodes and thermal memories, the thermal router represents a fundamental step towards the thermal conversion of non-linear electronic devices, and the realization of caloritronic logic components.Comment: 9 pages, 5 figure

0-π\pi phase-controllable thermalthermal Josephson junction

Two superconductors coupled by a weak link support an equilibrium Josephson electrical current which depends on the phase difference $\varphi$ between the superconducting condensates [1]. Yet, when a temperature gradient is imposed across the junction, the Josephson effect manifests itself through a coherent component of the heat current that flows oppositely to the thermal gradient for $\varphi <\pi/2$ [2-4]. The direction of both the Josephson charge and heat currents can be inverted by adding a $\pi$ shift to $\varphi$. In the static electrical case, this effect was obtained in a few systems, e.g. via a ferromagnetic coupling [5,6] or a non-equilibrium distribution in the weak link [7]. These structures opened new possibilities for superconducting quantum logic [6,8] and ultralow power superconducting computers [9]. Here, we report the first experimental realization of a thermal Josephson junction whose phase bias can be controlled from $0$ to $\pi$. This is obtained thanks to a superconducting quantum interferometer that allows to fully control the direction of the coherent energy transfer through the junction [10]. This possibility, joined to the completely superconducting nature of our system, provides temperature modulations with unprecedented amplitude of $\sim$ 100 mK and transfer coefficients exceeding 1 K per flux quantum at 25 mK. Then, this quantum structure represents a fundamental step towards the realization of caloritronic logic components, such as thermal transistors, switches and memory devices [10,11]. These elements, combined with heat interferometers [3,4,12] and diodes [13,14], would complete the thermal conversion of the most important phase-coherent electronic devices and benefit cryogenic microcircuits requiring energy management, such as quantum computing architectures and radiation sensors.Comment: 10 pages, 9 color figure

A normal metal tunnel-junction heat diode

We propose a low-temperature thermal rectifier consisting of a chain of three tunnel-coupled normal metal electrodes. We show that a large heat rectification is achievable if the thermal symmetry of the structure is broken and the central island can release energy to the phonon bath. The performance of the device is theoretically analyzed and, under the appropriate conditions, temperature differences up to $\sim$ 200 mK between the forward and reverse thermal bias configurations are obtained below 1 K, corresponding to a rectification ratio $\mathcal{R} \sim$ 2000. The simplicity intrinsic to its design joined with the insensitivity to magnetic fields make our device potentially attractive as a fundamental building block in solid-state thermal nanocircuits and in general-purpose cryogenic electronic applications requiring energy management.Comment: 4.5 pages, 4 color figure

Electrostatic tailoring of magnetic interference in quantum point contact ballistic Josephson junctions

The magneto-electrostatic tailoring of the supercurrent in quantum point contact ballistic Josephson junctions is demonstrated. An etched InAs-based heterostructure is laterally contacted to superconducting niobium leads and the existence of two etched side gates permits, in combination with the application of a perpendicular magnetic field, to modify continuously the magnetic interference pattern by depleting the weak link. For wider junctions the supercurrent presents a Fraunhofer-like interference pattern with periodicity h/2e whereas by shrinking electrostatically the weak link, the periodicity evolves continuously to a monotonic decay. These devices represent novel tunable structures that might lead to the study of the elusive Majorana fermions.Comment: 4.5 pages, 4 color figure

InAs nanowire superconducting tunnel junctions: spectroscopy, thermometry and nanorefrigeration

We demonstrate an original method -- based on controlled oxidation -- to create high-quality tunnel junctions between superconducting Al reservoirs and InAs semiconductor nanowires. We show clean tunnel characteristics with a current suppression by over $4$ orders of magnitude for a junction bias well below the Al gap $\Delta_0 \approx 200\,\mu {\rm eV}$. The experimental data are in close agreement with the BCS theoretical expectations of a superconducting tunnel junction. The studied devices combine small-scale tunnel contacts working as thermometers as well as larger electrodes that provide a proof-of-principle active {\em cooling} of the electron distribution in the nanowire. A peak refrigeration of about $\delta T = 10\,{\rm mK}$ is achieved at a bath temperature $T_{bath}\approx250-350\,{\rm mK}$ in our prototype devices. This method opens important perspectives for the investigation of thermoelectric effects in semiconductor nanostructures and for nanoscale refrigeration.Comment: 6 pages, 4 color figure

Scaling of Majorana Zero-Bias Conductance Peaks

We report an experimental study of the scaling of zero-bias conductance peaks compatible with Majorana zero modes as a function of magnetic field, tunnel coupling, and temperature in one-dimensional structures fabricated from an epitaxial semiconductor-superconductor heterostructure. Results are consistent with theory, including a peak conductance that is proportional to tunnel coupling, saturates at $2e^2/h$, decreases as expected with field-dependent gap, and collapses onto a simple scaling function in the dimensionless ratio of temperature and tunnel coupling.Comment: Accepted in Physical Review Letter

Josephson effect in ballistic semiconductor nanostructures

The Josephson effect [1] is one of the most remarkable macroscopic manifestations of quantum mechanics. It consists in the dissipationless flowing of a phase-coherent current between two superconducting leads, coupled by a weak-link. The weak-link can be made of a thin insulating layer (S-I-S junctions) or a short section of normal conducting material (S-N-S junctions) [2]. In recent years, semiconducting weak-links have been the focus of increasing interest driven by the fast development of semiconductor electronic devices. Research on such hybrid superconductor/semiconductor devices has been further expanded by the realization of Two-Dimensional Electron Gases (2DEGs) in semiconductor heterostructures, in which carrier density can be finely controlled and large mobilities can be achieved. This, in particular, has opened the way to the fabrication of ballistic hybrid junctions [3]. In these devices new quantum effects can be observed, which rely on the large Fermi wave-length and electron mean free path of 2DEGs compared to purely metallic structures. A prominent example was the observation of the Josephson current quantization, obtained in a superconducting Quantum Point Contact (QPC) constriction [4]. In this thesis work we have investigated the transport properties of ballistic S-2DEG-S junctions, in which the 2DEG is hosted in an InAs-based quantum well. We studied two different designs of the InAs-based semiconducting region: a QPC and a Quantum Ring (QR). First, we fabricated normal QPCs and QRs observing conductance quantization [5] and the magneto-electrostatic Aharonov-Bohm (AB) interference effect [6]. Then, we replaced the normal contacts with Nb leads, thereby fabricating S-QPC-S and S-QR-S junctions. In both these junctions we were able to manipulate the Josephson current by applying external magneto-electrostatic fields. In the case of S-QPC-S junctions, we observed a magnetic interference pattern of the supercurrent and we electrically tailored it by using side gates [7]. We qualitatively confirmed the theoretical predictions made by Barzykin and Zagoskin [8] for the evolution of the interference pattern as a function of the gate voltage and temperature. In S-QR-S junctions, we found that the magnetic modulation of the Josephson current displays a periodicity h/e [9] (where h is the Planck’s constant and e is the electron charge) typical of the AB effect, in contrast to the standard h/2e period observed in conventional Superconducting Quantum Interference Devices (SQUIDs), implemented either with two Josephson junctions in parallel [2] or with metallic rings in the diffusive regime [10]. This difference stems from the topology and the ballistic nature of our junction, which consists of a single ring-shaped weak-link connecting the same superconducting leads. Within the ballistic weak-link the electrons are influenced by the external magnetic field as in a normal QR, thus giving rise to the AB periodicity of the supercurrent interference pattern. The obtained result agrees with the theoretical analysis made by Dolcini and Giazotto [11] for this particular system and offer the first experimental verification of this effect. The investigated devices can be sought as promising building blocks to implement fully controllable Josephson -junctions [11], which are of great interest in quantum computing. In addition, such ballistic superconducting interferometers might pave the way to the experimental investigation of topological superconductors, that may support the existence of Majorana fermions [12]. [1] B. D. Josephson, Phys. Lett. 1, 251 (1962). [2] M. Tinkham, Introduction to superconductivity, McGraw-Hill, 1996. [3] T. Schäpers, Superconductor/semiconductor junctions, Springer, 2001. [4] H. Takayanagi et al., Phys. Rev. Lett. 75, 3533 (1995). [5] B. J. van Wees et al., Phys. Rev. Lett. 60, 848 (1988). [6] Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959). [7] M. Amado et al., in preparation. [8] V. Barzykin and A. M. Zagoskin, Superlattices Microstruct. 25, 797 (1999). [9] A. Fornieri et al., arXiv: 1211.1629v1. [10] J. Wei et al., Phys. Rev. B 84, 224519 (2011) [11] F. Dolcini, F. Giazotto, Phys. Rev. B 75, 140511 (2007). [12] J. Alicea, Rep. Prog. Phys. 75, 076501 (2012)

Cosmic-ray transport in the Milky Way and related phenomenology

Tesis doctoral inédita cotutelada por la Università di Siena y la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura: 17-05-2021In this thesis, we aim at studying some of the open questions regarding the origin of the Cosmic Rays (CRs), as well as their transport properties. The exceptional quality of the experimentally measured cosmic-ray observables, especially at the recently-achieved energies in the range ∼O(100 GeV − 1 TeV), started to question the standard picture, based on a Supernova Remnant-(SNR)-only origin of the CRs and a diffusive propagation inspired by the Quasi-Linear Theory (QLT) of pitch-angle interaction against alfvénic turbulence. First, we reproduce the most relevant cosmic-ray observables to tune the propagation setup, numerically solving the transport equation with the DRAGON code. On top of this, to account for the rising of the e+ above ∼ 10 GeV, we fit a primary population of positrons originating in Pulsar Wind Nebulae, in a model-independent setup that considers the uncertainties in the pulsar injections mechanism. Since the all-lepton spectrum is still not reproduced above ∼ 50 GeV — and in particular the ∼ TeV break — we consider the contribution from a nearby source of e−, and conclude that an old (tage ∼ 105 yr) SNR, located between ∼ 600 pc and ∼ 1 kpc, is probably missing from the Catalogues. + Within the hypothesis of such old remnant in its radiative phase contributing to the e + e−, we search for its signature in the proton flux as well. To do this, we consider a phenomenological propagation setup that reproduces the hadronic spectral hardening at ∼ 200 GeV as a diffusive feature (D(E) ∝ Eδ(E)), and adopt it consistently for the large-scale background and for the nearby source. Within this framework, we account for the all-lepton spectrum, the proton spectrum and the cosmicray dipole anisotropy with the same old (tage =2 · 105 yr), nearby (d = 300 pc) remnant. We highlight that the progressively hardening diffusion coefficient is a crucial ingredient, since, in a single-power-law diffusion scenario, the dipole anisotropy data would be overshot by, at least, one order of magnitude. Finally, we explore the phenomenological implications of a change of paradigm in the standard cosmic-ray diffusion — based on wave-particle interaction with Alfvén fluctuations — considering a non-linear extension of the QLT that enhances the efficiency of CR-scattering with the other MagnetoHydro-Dynamic (MHD) modes. Indeed, assuming the anisotropy of the alfvénic cascade, its scattering rate at all energies below ∼ 100 TeV is not able to confine charged cosmic rays, and the fast magnetosonic modes alone shape the diffusion coefficient that particles experience in the Galaxy. Within such picture, we implement the resulting D(E) in DRAGON2, where two independent zones differently affect the evolution of the MHD cascade: the Halo (LHalo ∼ 5 − 6 kpc) and the Warm Ionized Medium (LWIM ∼ 1 kpc). We find that, with a reasonable choice of selected quantities, representing the physics of the environments, we can reproduce the hadronic fluxes, as well as the boron-over-carbon ratio, from ∼ 200 GeV above. We assign to the rising of the streaming instabilities the cosmic-ray transport below this energy

Nanoscale phase-engineering of thermal transport with a Josephson heat modulator

Macroscopic quantum phase coherence has one of its pivotal expressions in the Josephson effect [1], which manifests itself both in charge [2] and energy transport [3-5]. The ability to master the amount of heat transferred through two tunnel-coupled superconductors by tuning their phase difference is the core of coherent caloritronics [4-6], and is expected to be a key tool in a number of nanoscience fields, including solid state cooling [7], thermal isolation [8, 9], radiation detection [7], quantum information [10, 11] and thermal logic [12]. Here we show the realization of the first balanced Josephson heat modulator [13] designed to offer full control at the nanoscale over the phase-coherent component of thermal currents. Our device provides magnetic-flux-dependent temperature modulations up to 40 mK in amplitude with a maximum of the flux-to-temperature transfer coefficient reaching 200 mK per flux quantum at a bath temperature of 25 mK. Foremost, it demonstrates the exact correspondence in the phase-engineering of charge and heat currents, breaking ground for advanced caloritronic nanodevices such as thermal splitters [14], heat pumps [15] and time-dependent electronic engines [16-19].Comment: 6+ pages, 4 color figure