Topological insulators are a newly discovered phase of matter characterized by a gapped bulk surrounded by novel conducting boundary states [1,2,3]. Since their theoretical discovery, these materials have encouraged intense efforts to study their properties and capabilities. Among the most striking results of this activity are proposals to engineer a new variety of superconductor at the surfaces of topological insulators [4,5]. These topological superconductors would be capable of supporting localized Majorana fermions, particles whose braiding properties have been proposed as the basis of a fault-tolerant quantum computer [6]. Despite the clear theoretical motivation, a conclusive realization of topological superconductivity remains an outstanding experimental goal.Here we present measurements of superconductivity induced in two-dimensional HgTe/HgCdTe quantum wells, a material which becomes a quantum spin Hall insulator when the well width exceeds dC = 6.3 nm [7]. In wells that are 7.5 nm wide, we find that supercurrents are confined to the one-dimensional sample edges as the bulk density is depleted. However, when the well width is decreased to 4.5 nm the edge supercurrents cannot be distinguished from those in the bulk. These results provide evidence for superconductivity induced in the helical edges of the quantum spin Hall effect, a promising step toward the demonstration of one-dimensional topological superconductivity.Our results also provide a direct measurement of the widths of these edge channels, which range from 180 nm to 408 nm.Topological superconductors, like topological insulators, possess a bulk energy gap and gapless surface states. In a topological superconductor, the surface states are predicted to manifest as zero-energy Majorana fermions, fractionalized modes which pair to form conventional fermions. Due to their non-Abelian braiding statistics, achieving control of these Majorana modes is desirable both fundamentally and for [9], and on their direct engineering using s-wave superconductors combined with topological insulators or semiconductors [10,11]. Particularly appealing are implementations in one-dimensional (1D) systems, where Majorana modes would be localized to the ends of a wire. In such a 1D system, restriction to a single spin degree of freedom combined with proximity to an s-wave superconductor would provide the basis for topological superconductivity [12]. Effort in this direction has been advanced by studies of nanowire systems [13,14,15,16,17,18] and by excess current measurements on InAs/GaSb devices [19]. Given the wide interest in Majorana fermions in one dimension, it is essential to expand the search to other systems whose properties are suited toward their control.An attractive route toward a 1D topological superconductor uses as its starting point the twodimensional (2D) quantum spin Hall (QSH) insulator. This topological phase of matter was recently predicted [20,21] and observed [22,23] in HgTe/HgCdTe quantum wells thicker than a critical thickness d C = 6...

The on-demand generation and separation of entangled photon pairs are key components of quantum information processing in quantum optics [1][2][3] . In an electronic analogue, the decomposition of electron pairs represents an essential building block for using the quantum state of ballistic electrons in electron quantum optics [4][5][6][7] . The scattering of electrons has been used to probe the particle statistics of stochastic sources in Hanbury Brown and Twiss experiments 8,9 and the recent advent of on-demand sources further offers the possibility to achieve indistinguishability between multiple sources in Hong-Ou-Mandel experiments [10][11][12][13][14][15] . Cooper pairs impinging stochastically at a mesoscopic beamsplitter have been successfully partitioned, as verified by measuring the coincidence of arrival [16][17][18][19][20][21] . Here, we demonstrate the splitting of electron pairs generated on demand. Coincidence correlation measurements allow the reconstruction of the full counting statistics, revealing regimes of statistically independent, distinguishable or correlated partitioning, and have been envisioned as a source of information on the quantum state of the electron pair [22][23][24][25][26] . The high pair-splitting fidelity opens a path to future on-demand generation of spin-entangled electron pairs from a suitably prepared two-electron quantum-dot ground state.The few-electron source is based on a single-parameter non-adiabatic quantized charge pump [27][28][29] , which enables the deterministic generation of single electrons and electron pairs with tunable emission energy 12,30 . Non-equilibrium electrons propagate along the edge of a quantum Hall sample with minimal inelastic scattering. The device and measurement set-up are presented in Fig. 1. An energy-selective detector barrier splits the incoming beam of electrons into two detector paths. The coincidence of arrival of electrons in the two detector channels leads to positive correlation between the time-dependent current signals. These correlations are inferred from a measurement of the zero-frequency cross-correlation shot noise. Although an oscillator-controlled electron source is noiseless 31 , the splitting of electron pairs generates partitioning noise and enables tomography of the probability distribution for the partitioning outcomes within each emission cycle.The generation and energy-selective detection of on-demand non-equilibrium electrons was demonstrated with the electron source configured to emit one electron with charge e and repetition frequency f of 280 MHz. Figure 2 shows the transmitted current I T as a function of barrier energy. The maximum level of I T is 2% below the emission current I P = 1 ef due to residual inelastic scattering events on the 2-µm-long path to the barrier (the emission error of the source is <1 × 10 −4). For energies greater than 57 meV, the current is pinched off as all of the emitted electrons are reflected at the beamsplitter. The emission energy is defined by the exit barrier height and ca...

Feedback control of quantum mechanical systems is rapidly attracting attention not only due to fundamental questions about quantum measurements, but also because of its novel applications in many fields in physics. Quantum control has been studied intensively in quantum optics but progress has recently been made in the control of solid-state qubits as well. In quantum transport only a few active and passive feedback experiments have been realized on the level of single electrons, although theoretical proposals exist. Here we demonstrate the suppression of shot noise in a single-electron transistor using an exclusively electronic closed-loop feedback to monitor and adjust the counting statistics. With increasing feedback response we observe a stronger suppression and faster freezing of charge current fluctuations. Our technique is analogous to the generation of squeezed light with in-loop photodetection as used in quantum optics. Sub-Poisson single-electron sources will pave the way for high-precision measurements in quantum transport similar to optical or optomechanical equivalents.

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Interacting electrons confined to only one spatial dimension display a wide range of unusual many-body quantum phenomena, ranging from Peierls instabilities to the breakdown of the canonical Fermi liquid paradigm to even unusual spin phenomena. The underlying physics is not only of tremendous fundamental interest, but may also have bearing on device functionality in future micro- and nanoelectronics with lateral extensions reaching the atomic limit. Metallic adatoms deposited on semiconductor surfaces may form self-assembled atomic nanowires, thus representing highly interesting and well-controlled solid-state realizations of such 1D quantum systems. Here we review experimental and theoretical investigations on a few selected prototypical nanowire surface systems, specifically Ge(0 0 1)-Au and Si(hhk)-Au, and the search for 1D quantum states in them. We summarize the current state of research and identify open questions and issues.