In recent years novel materials with remarkable properties have attracted the interest of the scientific community, due to both their importance in terms of fundamental research and application impact.
Topological Insulators, i.e. insulator that exhibit conducting channels at the boundaries (i.e. at the surface or at the edges). These conducting channels are characterized by a connection between the electron motion direction and spin orientation, and by a topological protection to disorder and impurities. For these reasons, these materials are particularly promising for spintronics and quantum information. The first experimental evidence of Topological Insulator was observed in 2006 in HgTe/CdTe quantum wells. are materials that could be synthesized and investigated only recently.
Another remarkable example is carbon-based materials, like nanotubes or graphene. Graphene, first synthesized in 2004 by mechanical exfoliation technique, is a two-dimensional sheet of graphite exhibiting extraordinary electronic and mechanical properties. In graphene, for instance, it is possible to observe relativistic effects in Condensed Matter materials, where the speed of light is replaced by the Fermi velocity.
Furthermore, hybrid systems are realized when two or more systems with qualitatively different electronic properties are connected together. A typical example is hybrid junction between semiconductors and superconducting metals, which can be used -for instance- to realize tunable supercurrent transistors. We mainly investigate hybrid systems involving low-temperature superconductors and mesoscopic systems, where quantum phase coherence is preserved. In this respect, we consider both traditional and well established platforms (like semiconductors) and novel materials.
In Superconductors a macroscopic phase coherence is established among Cooper pairs, made up of electrons with opposite momenta and spin. In contrast, in superfluid exciton condensates, macroscopic phase coherence is established among pairs composed of electrons and holes in different bands. Exciton condensates have have been realized only recently and graphene bilayers seem quite promising platform for it.
In collaboration with Prof. A. H. MacDonald (Austin University, Texas), and the Research Group of Prof. R. Fazio at Scuola Normale Superiore in Pisa (Italy), we have investigated a hybrid junction between superconductors and bilayer exciton condensate. We have have demonstrated that perfect conversion between charged supercurrents in superconductors and neutral supercurrents in electron-hole pair condensates is possible via a new Andreev-like scattering mechanism. As a result, when two superconducting circuits are coupled through a bilayer exciton condensate, the superflow in both layers is drastically modified. Depending on the phase biases the supercurrents can be completely blocked (Exciton Blockade) or exhibit perfect drag (Superdrag) .
➤ Hybrid junctions between superconductors and a bilayer exciton condensate:
Converting Josephson current into excitonic current
Andreev reflection in a graphene nanoribbon / superconductor hybrid junction In collaboration with the Research Group of Prof. R. Fazio at Scuola Normale Superiore in Pisa (Italy), we have investigated the phenomenon of Andreev reflection in a graphene nanoribbon contacted to a superconductor.
Models for graphene typically consider an infinitely large 2D sheet (bulk case), which amounts to neglecting the energy scale associated with the finite width of the graphene sample. However, when a graphene ribbon is contacted to a superconductor, such energy scale is in fact of the same order of magnitude (or even bigger) than the Superconducting gap.
➤ Carbon nanotubes and Graphene nanoribbons
We have shown that finite-size effects lead to notable differences with respect to the bulk-graphene case. At subgap voltages, conservation of pseudoparity, a quantum number characterizing the ribbon states, yields either a suppression of Andreev reflection when the ribbon has an even
number of sites in the transverse direction or perfect Andreev reflection when the ribbon has an odd number of sites. In the former case the suppression of Andreev reflection induces an insulating behavior even when the junction is biased by a voltage; electron conduction can however be restored by applying a gate voltage.
These features remain valid, under some circumstances, also in the case of non-ideal nanoribbons in which the number of transverse sites varies along the transport direction.
i) We analyzed electron interferometry of edge states in Quantum Spin Hall effect (QSHE) bar. We showed that, realizing two quantum point contacts in a four terminal setup of a QSHE bar, it is possible to realize a full electrically controllable electron interferometer, where the magnitude of charge and spin linear conductances can be tuned by gate voltages, without applying magnetic fields. In particular we find that, under appropriate conditions, inter-boundary coupling can lead to negative values of the conductance.
ii) We investigated time-dependent perturbations of QSHE edge states and showed that the helical nature leads to the appearance of a forward scattering spin channel that is absent in other Luttinger liquid realizations. When these states are coupled at a constriction, suitably applied ac gate voltages can operate on the spin of electrons tunneling across the constriction, and induce in the dc tunneling current a cusp pattern that represents the signature of the edge state electronic interaction.
iii) We analyzed the problem of inelastic scattering due to phonons in QSHE edge states. In collaboration with B. Trauzettel (Wuerzburg) and P. Recher (Univ.of Braunschweig) we showed that, although there is no symmetry preventing inelastic backscattering as brought about by phonons in the presence of Rashba spin orbit coupling, the quantized conductivity of a single channel of helical Dirac electrons is protected even against this inelastic mechanism to leading order. We demonstrated that this result remains valid even when Coulomb interaction is included in the framework of helical Luttinger liquids.
➤ Topological Materials: Electron Transport in edge States of Quantum Spin Hall effect Systems
In 2D Topological Insulators, realized in HgTe/CdTe quantum wells, edge states are one-dimensional channels where the electron spin is tightly connected to the electron motion direction (e.g. electrons traveling in one direction are characterized by spin-up, while electrons moving in the opposite direction are characterized by spin-down)
When a semiconductor quantum dot is contacted to two superconducting electrodes (see Figure 1 above) the subgap I-V curve is characterized by Andreev peaks, originating from the resonance of the dot level with a multiple Andreev reflection (MAR) trajectory, i.e. a sequence of odd Andreev reflections occurring at the interfaces between dot and superconductors.
Typical realization of quantum dots are based on semiconductors, where Rashba and Dresselhaus spin-orbit coupling play a relevant role. In particular, in the the presence of spin-orbit coupling the dot levels lack of a definite spin orientation. In collaboration with Luca Dell'Anna (SISSA) we analyzed the subgap structure of a multi-level quantum dot coupled to two superconductors, finding an extremely rich behavior for the current-voltage characteristics. Among various results, we show that due to the conservation of time-reversal symmetry the MAR subgap structure is modified but not suppressed by spin-orbit interaction. The resonance conditions and the linewidths change, affecting the location and the number of the Andreev peaks.
Furthermore we found that, when an in-plane magnetic field is applied to a strongly anisotropic dot, the peaks of the non-linear conductance oscillate as a function of the magnetic field angle φH, and the location of the maxima and minima allows for a straightforward read-out of the Dresselhaus/Rashba angle θ.
➤ Multiple Andreev reflections in a quantum dot contacted to superconductors
References
P. Sternativo and F. Dolcini, Tunnel junction of helical edge states: Determining and controlling spin-preserving and spin-flipping processes through transconductance, Phys. Rev. B 89, 035415 (2014)
J.C. Budich, F. Dolcini, P. Recher, and B. Trauzettel, Phonon-Induced Backscattering in Helical Edge States, Phys. Rev. Lett. 108, 086602 (2012)
F. Crépin, J.C. Budich, F. Dolcini, P. Recher, and B. Trauzettel, Renormalization Group approach for the scattering off a single Rashba impurity in a helical liquid, Phys. Rev. B 86, 121106(R) (2012)
F. Dolcini, Signature of interaction in dc Transport of ac gated Quantum Spin Hall edge states, Phys. Rev. B 85, 033306 (2012)
F. Dolcini, Full electrical control of Charge and Spin conductance through Interferometry of Edge States in Topological Insulators, Phys. Rev. B 83, 165304 (2011).
References
R.Rosati, F. Dolcini, and F. Rossi, Dispersionless propagation of electron wavepackets in single-walled carbon nanotubes, Appl. Phys. Lett. 106, 243101 (2015)
D. Rainis, F. Taddei, F. Dolcini, M. Polini, and R. Fazio, Andreev reflection in graphene nanoribbons, Phys. Rev. B 79, 115131 (2009).
References
H. Soller, F. Dolcini and A. Komnik, Nanotransformation and current fluctuations in exciton condensate junctions, Phys. Rev. Lett. 108, 156401 (2012)
S. Peotta, M. Gibertini, F. Dolcini, F. Taddei, M. Polini, L.B Ioffe, R. Fazio, and A. H. MacDonald, Josephson current in a four terminal superconductor - exciton condensate - superconductor system, Phys. Rev. B 84, 184528 (2011)
F. Dolcini, D. Rainis, F. Taddei, M. Polini, R. Fazio, and A. H. MacDonald, Blockade and Counterflow Supercurrent in exciton-condensate Josephson junctions, Phys. Rev. Lett. 104, 027004 (2010).
F. Dolcini, and L. Dell'Anna, Multiple Andreev reflections in a quantum dot coupled to superconducting leads: Effect of spin-orbit coupling, Phys. Rev. B 78, 024518 (2008).
F. Dolcini, and F. Giazotto, Switching the sign of Josephson current through Aharonov-Bohm interferometry, Phys. Rev. B 75, 140511 (2007).
S. Pugnetti, F. Dolcini, and R. Fazio, dc Josephson Effect in Metallic Single-Walled Carbon Nanotubes, Solid State Communications 144, 551 (2007).
Propagation of electron wavepackets in single-walled carbon nanotubes We have investigated the effects of electron-phonon coupling in the propagation of electron wavepackets in single-walled carbon nanotubes. Utilizing a Lindblad-based density-matrix approach that enables us to account for both dissipation and decoherence effects, we have shown that, while in semiconducting nanotubes the wavepacket experiences the typical dispersion of conventional materials, in metallic nanotubes its shape remains essentially unaltered, up to micron distances at room temperature. Such effect is due to the linear dispersion of metallic nanotubes, and is surprisingly robust to the presence of the electron-phonon coupling. This result can open up new interesting perspectives in nanoelectronics, where the generation of sequences of wavepackets that propagate coherently without overlapping to each other is crucial to realize an electronic alternative to photon-based quantum information processing.
Nanophysics and Quantum Systems