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### **Topological protection demonstrated via microwave measurements**

### **High kinetic inductance superconducting nanowires**

### **Revealing ballistic transport in topological bismuth nanowires**

### **Electronic interactions make noise !**

### **How to control the magnetic state of a quantum dot with the superconducting phase?**

### **Funding**

The electronic properties of mesoscopic samples are modified by electronic interference if their size is smaller than the phase coherence length. Our team probes systems for which the quantum effects are particularly important such as topological insulator, grahene or carbon nanotube. We list below some of our latest results.

Demonstrating the topological protection of Andreev states in Josephson junctions is an experimental challenge. It was predicted that low temperature ac susceptibility measurements could reveal the topological protection of quantum spin Hall edge states by probing their phase-dependent, low-energy Andreev spectrum at finite frequency. Topological protection leads to a perfect Andreev level crossing at a phase difference of pi, which translates in a peaked dissipative response at pi.

We have performed such a microwave probing of a phase-biased Josephson junction built around a bismuth nanowire, a predicted second order topological insulator, in which we previously detected one-dimensional ballistic edge states. We find absorption peaks at the Andreev level crossings, whose temperature and frequency dependencies point to protected topological crossings with an accuracy limited by the electronic temperature of our experiment.

*Reference :*
A. Murani et al, Phys. Rev. Lett. **122**, 076802 (2019) (Pdf)

Joint efforts involving two teams from the LPS have demonstrated that beam-assisted deposition of superconducting materials with a He-based focused ion beam (He-FIB) can be used to design and deposit superconducting nano-objects with a versatile direct write process. In particular, nanowires could be made very thin (5nm), narrow (35nm) and long (400µm), demonstrating a very high kinetic inductance, 250 times larger than the geometrical one.

This technological breakthrough was made possible by the unique properties and stability of a recently acquired helium focused ion beam machine. These nanowires hold a great promise for superconducting circuits applications.

*Reference :*
J. Basset et al., Appl. Phys. Lett. **114**, 102601 (2019) (Pdf)

The current through two-dimensional topological insulators is predicted to run only through a few, perfectly conducting, narrow channels. We have used superconducting electrodes to reveal the ballistic nature of the current through bismuth nanowires, suggesting they are good topological insulator candidates.

We have exploited this sensitivity of the current phase relation to probe conduction through topological insulators. The current through such materials is predicted to run only through a few perfectly ballistic channels, called topological edge states. The topological insulator candidate is a monocrystalline bismuth nanowire whose crystalline orientation is chosen such that it contains two topological surfaces, each with one-dimensional edge states. And indeed, we have found that the supercurrent through a 1.4 micrometer-long monocrystalline bismuth nanowire has just such a sawtooth-shaped dependence on the phase difference between the superconductors at its ends. The fact that transport is ballistic over such a long distance hints to a possible topological protection against scattering in those wires.

*References :*

Frank Schindler et al, Nature Physics **14**, 918–924 (2018).(Pdf)

Anil Murani et al, Nature Communications **8**, 15941 (2017)

Although electronic interactions are generally negligible in metals, confinement of electrons in a quantum dot, such as a carbon nanotube, enhances them. A striking consequence of electronic interactions in a metal is the Kondo effect, where the spin of magnetic impurities is screened by conduction electrons at low enough temperature. This same effect emerges for a quantum dot coupled to metallic electrodes: the spin of the quantum dot is screened by the conduction electrons of the electrodes resulting in a singlet state of spin zero.

Thanks to a collaboration between the LPS and Osaka University (Japan), it was possible to measure the shot noise, i.e. the fluctuations in the backscattered current due to the variations in the number of charges reflected by the quantum dot. Our experiment was realized in a carbon nanotube connected to metallic electrodes. Two signatures of the Kondo state emerged. First, at low current the delocalized state transmits perfectly the current through the dot, without any backscattering. The quantum dot is thus totally silent. At high current, noise increases rapidly and non-linearly. The non-linear shot noise measures the effective charge of the backscattered carriers. Our measurement of the effective charge, e*=5/3 ± 5%, is in perfect agreement with theory, and demonstrates the appearance of electrons pairs. Moreover we have shown that this value is universal for any spin ½ Kondo system.

*References :*

Meydi Ferrier et al, Phys. Rev. Lett. **118**, 196803 (2017) (Pdf)

Meydi Ferrier et al, Nature Physics **12**, 230–235 (2016) (Pdf)

We have demonstrated the control by the superconducting phase of the magnetic state of a quantum dot connected to two superconducting reservoirs. It happens in the regime of strongest competition between the Kondo effect (screening of the dot spin by the conduction electrons of the reservoirs) and the superconducting proximity effect. This has spectacular consequences on the relation between the supercurrent and the superconducting phase: the current phase relation. Indeed the junction behaves both as a regular junction ("0" junction) and junction with opposite sign ("pi" junction). To create this experiment, a carbon nanotube, which acts as a quantum dot, is inserted in a SQUID and measured at very low temperature. The current-phase relation is extracted from the supercurrent of the SQUID which is modulated by the phase difference controlled by a magnetic field. A successful comparison with theoretical prediction was carried out. This experiment demonstrates the control of the magnetic state of a quantum dot by the superconducting phase and paves the way to current phase relation measurements in strongly correlated mesoscopic systems.

*References :*

R. Delagrange et al., Phys. Rev. B **93**, 195437 (2016) (Pdf)

R. Delagrange et al. Phys. Rev. B **91**, 241401(R) (2015). (Pdf)

We acknowledge financial support from ANR, ERC, the Labex PALM and NanoSaclay and the DIM SIRTEQ.