Robust zero-energy modes in an electronic higher-order topological insulator.

Quantum simulators are essential tools for understanding complex quantum materials. Platforms based on ultracold atoms in optical lattices and photonic devices have led the field so far, but the basis for electronic quantum simulators is now being developed. Here, we experimentally realize an electronic higher-order topological insulator (HOTI). We create a breathing kagome lattice by manipulating carbon monoxide molecules on a Cu(111) surface using a scanning tunnelling microscope. We engineer alternating weak and strong bonds to show that a topological state emerges at the corner of the non-trivial configuration, but is absent in the trivial one. Different from conventional topological insulators, the topological state has two dimensions less than the bulk, denoting a HOTI. The corner mode is protected by a generalized chiral symmetry, which leads to a particular robustness against perturbations. Our versatile approach to designing artificial lattices holds promise for revealing unexpected quantum phases of matter.

Hybrid Oleate-Iodide Ligand Shell for Air-Stable PbSe Nanocrystals and Superstructures.

A postsynthetic treatment is presented to improve the air stability of PbSe nanocrystals (NCs) and PbSe square superstructures. The addition of z-type Pb(oleate)2 ligands together with x-type iodide ligands creates a hybrid ligand shell containing both ligands. The air stability of the PbSe NCs is checked by enduring absorption spectroscopy under ambient conditions. With a combined NaI + Pb(oleate)2 treatment, the absorption spectrum remains unchanged for several days under ambient conditions. Fourier transform infrared spectroscopy shows that the surface coordination of the oleate ligands changes by the chemical treatment: from mixed chelating bidentate + bridging to Pb for the pristine nanocrystals to almost exclusive chelating bidentate coordination after chemical passivation. The shift of the C-H stretching vibration shows that the oleate hydrocarbon layer is in a more liquidlike state after the chemical treatment, suggesting that oleate and iodide ligands are often present on adjacent surface positions.

Design and characterization of electrons in a fractal geometry.

The dimensionality of an electronic quantum system is decisive for its properties. In one dimension electrons form a Luttinger liquid and in two dimensions they exhibit the quantum Hall effect. However, very little is known about the behavior of electrons in non-integer, or fractional dimensions1. Here, we show how arrays of artificial atoms can be defined by controlled positioning of CO molecules on a Cu (111) surface2-4, and how these sites couple to form electronic Sierpinski fractals. We characterize the electron wave functions at different energies with scanning tunneling microscopy and spectroscopy and show that they inherit the fractional dimension. Wave functions delocalized over the Sierpinski structure decompose into self-similar parts at higher energy, and this scale invariance can also be retrieved in reciprocal space. Our results show that electronic quantum fractals can be artificially created by atomic manipulation in a scanning tunneling microscope. The same methodology will allow future study to address fundamental questions about the effects of spin-orbit interaction and a magnetic field on electrons in non-integer dimensions. Moreover, the rational concept of artificial atoms can readily be transferred to planar semiconductor electronics, allowing for the exploration of electrons in a well-defined fractal geometry, including interactions and external fields.

Triangular nanoperforation and band engineering of InGaAs quantum wells: a lithographic route toward Dirac cones in III-V semiconductors.

The design of two-dimensional periodic structures at the nanoscale has renewed attention for band structure engineering. Here, we investigate the nanoperforation of InGaAs quantum wells epitaxially grown on InP substrates using high-resolution e-beam lithography and highly plasma based dry etching. We report on the fabrication of a honeycomb structure with an effective lattice constant down to 23 nm by realising triangular antidot lattice with an ultimate periodicity of 40 nm in a 10 nm thick InGaAs quantum well on a p-type InP. The quality of the honeycomb structures is discussed in detail, and calculations show the possibility to measure Dirac physics in these type of samples. Based on the statistical analysis of the fluctuations in pore size and periodicity, calculations of the band structure are performed to assess the robustness of the Dirac cones with respect to distortions of the honeycomb lattice.

Transport Properties of a Two-Dimensional PbSe Square Superstructure in an Electrolyte-Gated Transistor.

Self-assembled nanocrystal solids show promise as a versatile platform for novel optoelectronic materials. Superlattices composed of a single layer of lead-chalcogenide and cadmium-chalcogenide nanocrystals with epitaxial connections between the nanocrystals, present outstanding questions to the community regarding their predicted band structure and electronic transport properties. However, the as-prepared materials are intrinsic semiconductors; to occupy the bands in a controlled way, chemical doping or external gating is required. Here, we show that square superlattices of PbSe nanocrystals can be incorporated as a nanocrystal monolayer in a transistor setup with an electrolyte gate. The electron (and hole) density can be controlled by the gate potential, up to 8 electrons per nanocrystal site. The electron mobility at room temperature is 18 cm2/(V s). Our work forms a first step in the investigation of the band structure and electronic transport properties of two-dimensional nanocrystal superlattices with controlled geometry, chemical composition, and carrier density.

Controlling quantum dot emission by plasmonic nanoarrays.

Metallic nanoparticle arrays support localized surface plasmon resonances (LSPRs) and propagating surface lattice resonances (SLRs). We study the control of quantum dot (QD) emission coupled to the optical modes of silver nanoparticle arrays, both experimentally and numerically. With a hybrid lithography-functionalization method, the QDs are deposited in the vicinity of the nanoparticles. Directionality and enhancement of the emission are observed in photoluminescence spectra and fluorescence lifetime measurements, respectively. Similar features are also demonstrated in the numerical simulations. The tunable emission of this type of hybrid structures could lead to potential applications in light sources.

Topological states in multi-orbital HgTe honeycomb lattices.

Research on graphene has revealed remarkable phenomena arising in the honeycomb lattice. However, the quantum spin Hall effect predicted at the K point could not be observed in graphene and other honeycomb structures of light elements due to an insufficiently strong spin-orbit coupling. Here we show theoretically that 2D honeycomb lattices of HgTe can combine the effects of the honeycomb geometry and strong spin-orbit coupling. The conduction bands, experimentally accessible via doping, can be described by a tight-binding lattice model as in graphene, but including multi-orbital degrees of freedom and spin-orbit coupling. This results in very large topological gaps (up to 35 meV) and a flattened band detached from the others. Owing to this flat band and the sizable Coulomb interaction, honeycomb structures of HgTe constitute a promising platform for the observation of a fractional Chern insulator or a fractional quantum spin Hall phase.

Long-range orientation and atomic attachment of nanocrystals in 2D honeycomb superlattices.

Oriented attachment of synthetic semiconductor nanocrystals is emerging as a route for obtaining new semiconductors that can have Dirac-type electronic bands such as graphene, but also strong spin-orbit coupling. The two-dimensional (2D) assembly geometry will require both atomic coherence and long-range periodicity of the superlattices. We show how the interfacial self-assembly and oriented attachment of nanocrystals results in 2D metal chalcogenide semiconductors with a honeycomb superlattice. We present an extensive atomic and nanoscale characterization of these systems using direct imaging and wave scattering methods. The honeycomb superlattices are atomically coherent and have an octahedral symmetry that is buckled; the nanocrystals occupy two parallel planes. Considerable necking and large-scale atomic motion occurred during the attachment process.

Electron-phonon coupling and intervalley splitting determine the linewidth of single-electron transport through PbSe nanocrystals.

The linewidth of the resonances in the single-electron tunneling spectra has been investigated for PbSe semiconductor nanocrystals (NCs) with scanning tunneling spectroscopy at low temperature. The linewidth of the resonances corresponding to tunneling through the first conduction and valence levels is found to increase with decreasing size of the NCs. Based on theoretical calculations, this broadening is mainly induced by the coupling between the tunneling electrons and the longitudinal optical phonon mode of the NC, and by the splitting of the degenerate electronic levels between the different L-valleys in the Brillouin zone. For the smallest sizes, it is shown that the intervalley splitting is the major source of broadening.

Polarization, microscopic origin, and mode structure of luminescence and lasing from single ZnO nanowires.

The emission spectrum of individual single crystalline ZnO nanowires shows three regimes characterized by distinct polarization properties and spatial emission patterns along the length of the wire. In the visible range below 2.9 eV, emission is polarized along the long axis of the wire, along the c-axis (E//c). In the second regime between 2.9 and 3.22 eV, Fabry-Pérot guided modes polarized perpendicular to the wire (E perpendicularc) prevail. From their dispersion, it is clear that these modes signify strong coupling between the B-exciton and linearly polarized transverse electric modes that are guided by the wire and trapped between the wire end facets. The third regime is characterized by uniform emission along the wire and a marked dip in the polarization at around the electronic band gap at 3.3 eV. Lasing is observed only in the second regime in which strong light-matter interaction prevails.

Nature of sub-band gap luminescent eigenmodes in a ZnO nanowire.

The emission spectrum of individual high-quality ZnO nanowires consists of a series of Fabry-Pérot-like eigenmodes that extend far below the band gap of ZnO. Spatially resolved luminescence spectroscopy shows that light is emitted predominantly at both wire ends, with identical spectra reflecting standing wave polariton eigenmodes. The intensity of the modes increases supralinearly with the excitation intensity, indicating that the mode population is governed by scattering among polaritons. Due to strong light-matter interaction, light emission from a ZnO nanowire is not dictated by the electronic band diagram of ZnO but depends also on the wire geometry and the excitation intensity. Delocalized polaritons provide a natural explanation for the pronounced subwavelength guiding in ZnO wires that has been reported previously.

Direct observation of electron-to-hole energy transfer in CdSe quantum dots.

We independently determine the subpicosecond cooling rates for holes and electrons in CdSe quantum dots. Time-resolved luminescence and terahertz spectroscopy reveal that the rate of hole cooling, following photoexcitation of the quantum dots, depends critically on the electron excess energy. This constitutes the first direct, quantitative measurement of electron-to-hole energy transfer, the hypothesis behind the Auger cooling mechanism proposed in quantum dots, which is found to occur on a 1 +/- 0.15 ps time scale.

Frequency-dependent spontaneous emission rate from CdSe and CdTe nanocrystals: influence of dark states.

We studied the rate of spontaneous emission from colloidal CdSe and CdTe nanocrystals at room temperature. The decay rate, obtained from luminescence decay curves, increases with the emission frequency in a supralinear way. This dependence is explained by the thermal occupation of dark exciton states at room temperature, giving rise to a strong attenuation of the rate of emission. The supralinear dependence is in agreement with the results of tight-binding calculations.

Wide energy-window view on the density of states and hole mobility in poly(p-phenylene vinylene).

Using an electrochemically gated transistor, we achieved controlled and reversible doping of poly(p-phenylene vinylene) in a large concentration range. Our data open a wide energy-window view on the density of states (DOS) and show, for the first time, that the core of the DOS function is Gaussian, while the low-energy tail has a more complex structure. The hole mobility increases by more than 4 orders of magnitude when the electrochemical potential is scanned through the DOS.

Effect of quantum confinement on the dielectric function of PbSe.

Monolayers of lead selenide nanocrystals of a few nanometers in height have been made by electrodeposition on a Au(111) substrate. These layers show a thickness-dependent dielectric function, which was determined using spectroscopic ellipsometry. The experimental results are compared with electronic structure calculations of the imaginary part of the dielectric function of PbSe nanocrystals. We demonstrate that the size-dependent variation of the dielectric function is affected by quantum confinement at well-identifiable points in the Brillouin zone, different from the position of the band-gap transition.

Optical transitions in artificial few-electron atoms strongly confined inside ZnO nanocrystals.

We have studied the optical transitions in artificial atoms consisting of one to ten electrons occupying the conduction levels in ZnO nanocrystals. We analyzed near IR absorption spectra of assemblies of weakly coupled ZnO nanocrystals for a gradually increasing electron number and found four allowed dipole transitions with oscillator strengths in quantitative agreement with tight-binding theory. Furthermore, this spectroscopy provides the single-particle energy separation between the conduction levels of the ZnO quantum dots.

Macroporous germanium by electrochemical deposition.

Germanium is electrodeposited in a template formed from a dried suspension of silica spheres. The germanium completely fills the pores of the silica matrix. The semiconductor, as deposited, is amorphous but can be crystallized by annealing. Selective dissolution of the silica template gives a macroporous germanium-air sphere matrix, which offers interesting possibilities for photonic applications.

Staircase in the electron mobility of a ZnO quantum dot assembly due to shell filling.

Electron transport in an assembly of ZnO quantum dots has been studied using an electrochemically gated transistor. The electron mobility shows a stepwise increase as a function of the electron occupation per quantum dot. When the occupation number is below two, transport occurs by tunneling between the S orbitals. Transport becomes 3 times faster when the occupation number is between two and eight; tunneling now occurs between the P orbitals. Electron transport is thus critically determined by the quantum properties of the building blocks.

Effects of crystal shape on the energy levels of zero-dimensional PbS quantum dots.

Nanometer-size PbS quantum dots have been made by electrodeposition on a Au(111) substrate. The deposited nanocrystals have a flattened cubic shape. We probed the single-electron energy-level spectrum of individual quantum dots by scanning tunneling spectroscopy and found that it deviates strongly from that of spherical PbS quantum dots. The measured energy-level spectrum is successfully explained by considering strong confinement in a flattened cubic box.