# Publications

Highlights and most important publications

*E. Bocquillon, V. Freulon, J.-M Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, G. Fève*

#### Coherence and Indistinguishability of Single Electrons Emitted by Independent Sources, *Science 339*, 1054 (2013)

The on-demand emission of coherent and indistinguishable electrons by independent synchronized sources is a challenging task of quantum electronics, in particular regarding its application for quantum information processing. Using two independent on-demand electron sources, we triggered the emission of two single-electron wave packets at different inputs of an electronic beam splitter. Whereas classical particles would be randomly partitioned by the splitter, we observed two-particle interference resulting from quantum exchange. Both electrons, emitted in indistinguishable wave packets with synchronized arrival time on the splitter, exited in different outputs as recorded by the low-frequency current noise. The demonstration of two-electron interference provides the possibility of manipulating coherent and indistinguishable single-electron wave packets in quantum conductors. |

*E. Bocquillon, V. Freulon, J.-M. Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, G. Fève*

#### Separation of neutral and charge modes in one-dimensional chiral edge channels, *Nat Commun 4*, 1839 (2013)

Coulomb interactions have a major role in one-dimensional electronic transport. They modify the nature of the elementary excitations from Landau quasiparticles in higher dimensions to collective excitations in one dimension. Here we report the direct observation of the collective neutral and charge modes of the two chiral co-propagating edge channels of opposite spins of the quantum Hall effect at filling factor 2. Generating a charge density wave at frequency f in the outer channel, we measure the current induced by inter-channel Coulomb interaction in the inner channel after a 3-mm propagation length. Varying the driving frequency from 0.7 to 11 GHz, we observe damped oscillations in the induced current that result from the phase shift between the fast charge and slow neutral eigenmodes. We measure the dispersion relation and dissipation of the neutral mode from which we deduce quantitative information on the interaction range and parameters. |

*J. Wiedenmann, E. Bocquillon, R.S. Deacon, S. Hartinger1, O. Herrmann, T.M. Klapwijk, L. Maier, C. Ames, C. Brüne, C. Gould, A. Oiwa, K. Ishibashi, S. Tarucha, H. Buhmann1 & L.W. Molenkamp*

#### 4pi-periodic Josephson supercurrent in HgTe-based topological Josephson junctions, *Nat Commun 7*, 10303 (2016)

The Josephson effect describes the generic appearance of a supercurrent in a weak link between two superconductors. Its exact physical nature deeply influences the properties of the supercurrent. In recent years, considerable efforts have focused on the coupling of superconductors to the surface states of a three-dimensional topological insulator. In such a material, an unconventional induced p-wave superconductivity should occur, with a doublet of topologically protected gapless Andreev bound states, whose energies vary 4p-periodically with the superconducting phase difference across the junction. In this article, we report the observation of an anomalous response to rf irradiation in a Josephson junction made of a HgTe weak link. The response is understood as due to a 4p-periodic contribution to the supercurrent, and its amplitude is compatible with the expected contribution of a gapless Andreev doublet. Our work opens the way to more elaborate experiments to investigate the induced superconductivity in a three-dimensional insulator. |

*Erwann Bocquillon, Russell S. Deacon, Jonas Wiedenmann, Philipp Leubner, Teunis M. Klapwijk, Christoph Brüne, Koji Ishibashi, Hartmut Buhmann and Laurens W. Molenkamp*

#### Gapless Andreev bound states in the quantum spin Hall insulator HgTe, *Nat. Nanotech 12*, 137–143 (2016)

In recent years, Majorana physics has attracted considerable attention because of exotic new phenomena and its prospects for fault-tolerant topological quantum computation. To this end, one needs to engineer the interplay between superconductivity and electronic properties in a topological insulator, but experimental work remains scarce and ambiguous. Here, we report experimental evidence for topological superconductivity induced in a HgTe quantum well, a 2D topological insulator that exhibits the quantum spin Hall (QSH) effect. The a.c. Josephson effect demonstrates that the supercurrent has a 4π periodicity in the superconducting phase difference, as indicated by a doubling of the voltage step for multiple Shapiro steps. In addition, this response like that of a superconducting quantum interference device to a perpendicular magnetic field shows that the 4π-periodic supercurrent originates from states located on the edges of the junction. Both features appear strongest towards the QSH regime, and thus provide evidence for induced topological superconductivity in the QSH edge states. |

#### Dynamical Separation of Bulk and Edge Transport in HgTe-Based 2D Topological Insulators, *Phys. Rev. Lett. 124*, 076802 (2020)

Matthieu C. Dartiailh, S. Hartinger, A. Gourmelon, K. Bendias, H. Bartolomei, H. Kamata, J.-M. Berroir, G. Fève, B. Plaçais, L. Lunczer, R. Schlereth, H. Buhmann, L. W. Molenka, Erwann Bocquillon

Topological effects in edge states are clearly visible on short lengths only, thus largely impeding their studies. On larger distances, one may be able to dynamically enhance topological signatures by exploiting the high mobility of edge states with respect to bulk carriers. Our work on microwave spectroscopy highlights the response of the edges which host very mobile carriers, while bulk carriers are drastically slowed down in the gap. Though the edges are denser than expected, we establish that charge relaxation occurs on short timescales and suggest that edge states can be addressed selectively on timescales over which bulk carriers are frozen. |