## Tesi etd-01132013-183035 |

Thesis type

Tesi di laurea magistrale

Author

FORNIERI, ANTONIO

URN

etd-01132013-183035

Title

Josephson effect in ballistic semiconductor nanostructures

Struttura

FISICA

Corso di studi

FISICA

Supervisors

**relatore**Dott. Giazotto, Francesco

**relatore**Dott. Pellegrini, Vittorio

Parole chiave

- Josephson
- ballistic
- 2DEG

Data inizio appello

28/01/2013;

Consultabilità

Completa

Riassunto analitico

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).

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).

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