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

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)

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

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

Rectification of electronic heat current by a hybrid thermal diode

We report the realization of an ultra-efficient low-temperature hybrid heat current rectifier, thermal counterpart of the well-known electric diode. Our design is based on a tunnel junction between two different elements: a normal metal and a superconducting island. Electronic heat current asymmetry in the structure arises from large mismatch between the thermal properties of these two. We demonstrate experimentally temperature differences exceeding $60$ mK between the forward and reverse thermal bias configurations. Our device offers a remarkably large heat rectification ratio up to $\sim 140$ and allows its prompt implementation in true solid-state thermal nanocircuits and general-purpose electronic applications requiring energy harvesting or thermal management and isolation at the nanoscale.Comment: 8 pages, 6 color figure

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

Evidence of topological superconductivity in planar Josephson junctions

Majorana zero modes are quasiparticle states localized at the boundaries of topological superconductors that are expected to be ideal building blocks for fault-tolerant quantum computing. Several observations of zero-bias conductance peaks measured in tunneling spectroscopy above a critical magnetic field have been reported as experimental indications of Majorana zero modes in superconductor/semiconductor nanowires. On the other hand, two dimensional systems offer the alternative approach to confine Ma jorana channels within planar Josephson junctions, in which the phase difference {\phi} between the superconducting leads represents an additional tuning knob predicted to drive the system into the topological phase at lower magnetic fields. Here, we report the observation of phase-dependent zero-bias conductance peaks measured by tunneling spectroscopy at the end of Josephson junctions realized on a InAs/Al heterostructure. Biasing the junction to {\phi} ~ {\pi} significantly reduces the critical field at which the zero-bias peak appears, with respect to {\phi} = 0. The phase and magnetic field dependence of the zero-energy states is consistent with a model of Majorana zero modes in finite-size Josephson junctions. Besides providing experimental evidence of phase-tuned topological superconductivity, our devices are compatible with superconducting quantum electrodynamics architectures and scalable to complex geometries needed for topological quantum computing.Comment: main text and extended dat