# Publications

Highlights and most important publications

#### Propagation, dissipation, and breakdown in quantum anomalous Hall edge states probed by microwave edge plasmons, *Phys. Rev. B 110*, L161403 (2024)

Torsten Röper, Hugo Thomas, Daniel Rosenbach, Anjana Uday, Gertjan Lippertz, Anne Denis, Pascal Morfin, Alexey A. Taskin, Yoichi Ando and Erwann Bocquillon

The quantum anomalous Hall (QAH) effect, with its single chiral, topologically protected edge state, offers a platform for flying Majorana states as well as nonreciprocal microwave devices. While recent research showed the nonreciprocity of edge plasmons in Cr-doped (BixSb1−x )2Te3, the understanding of their dissipation remains incomplete. Our study explores edge plasmon dissipation in V-doped (BixSb1−x )2Te3 films, analyzing microwave transmission across various conditions. We identify interactions with charge puddles as a primary source, providing insights critical for developing improved QAH-based technologies. |

#### 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. |

*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. |

*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. |

*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. |

*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. |

# Theses

Bachelor-, Masters- and PhD theses

#### High-Frequency Filtering Systems for Noise Measurements, Bachelor Thesis (2024)

Paul Ruhrberg

The thesis is separated into three main parts. The first chapter focuses on using electrical components to construct a circuit known as a low-pass filter. Therefore, basic electronics knowledge is reiterated, followed by the theory of low-pass filters, and concluded with the design and construction of such a circuit. The second chapter introduces the copper powder filter. A short introduction to the theory of metal powder filters is followed by the design and optimization process. The third chapter combines both filter stages and focuses on the application of such a filter at low temperatures. A conclusion and outlook is given at the end of this thesis. |

#### Low-Temperature Atomic Layer Deposition of Hafnium Oxide Gate Dielectrics, Bachelor Thesis (2024)

Benjamin Roth

The quantum anomalous Hall effect (QAHE), first experimentally observed in 2013, is a fascinating quantum phenomenon that continues to be a focus of active research. The QAHE is characterized by a single chiral edge state. To suppress bulk transport, the Fermi level is tuned in the bulk’s band gap by electrostatic gating. However, the deposition of gate material often requires elevated temperatures, at which our samples degrade. Hence, we develop and optimize the low-temperature (< 100 ◦C) atomic layer deposition of hafnium oxide (HfO2) gate dielectrics. We found relative permittivities ϵr of 6 to 10, which were significantly lower than in other studies. Current-voltage measurements showed strong asymmetry, with electrical breakdowns occurring at Ebd ∼ 1.5MVcm−1 and up to Ebd ∼ 6MVcm−1 depending on the voltage polarity. Finally, we deposited HfO2 at 80 ◦C on a quantum anomalous Hall insulator (QAHI), where a successful gating effect was shown at T ≈ 14 mK. These results highlight the potential for atomic layer deposition of hafnium oxide for temperature-sensitive gating applications. |