Boundaries between distinct topological phases of matter support robust, yet exotic quantum states such as spin-momentum locked transport channels or Majorana fermions. The idea of using such states in spintronic devices or as qubits in quantum information technology is a strong driver of current research in condensed matter physics. The topological properties of quantum states have helped to explain the conductivity of doped trans-polyacetylene in terms of dispersionless soliton states. In their seminal paper, Su, Schrieffer and Heeger (SSH) described these exotic quantum states using a one-dimensional tight-binding model. Because the SSH model describes chiral topological insulators, charge fractionalization and spin-charge separation in one dimension, numerous efforts have been made to realize the SSH Hamiltonian in cold-atom, photonic and acoustic experimental configurations. It is, however, desirable to rationally engineer topological electronic phases into stable and processable materials to exploit the corresponding quantum states. Here we present a flexible strategy based on atomically precise graphene nanoribbons to design robust nanomaterials exhibiting the valence electronic structures described by the SSH Hamiltonian. We demonstrate the controlled periodic coupling of topological boundary states at junctions of graphene nanoribbons with armchair edges to create quasi-one-dimensional trivial and non-trivial electronic quantum phases. This strategy has the potential to tune the bandwidth of the topological electronic bands close to the energy scale of proximity-induced spin-orbit coupling or superconductivity, and may allow the realization of Kitaev-like Hamiltonians and Majorana-type end states.

Hexagonal boron nitride (hBN) is an emerging material in nanophotonics and an attractive host for color centers for quantum photonic devices. Here, we show that optical emission from individual quantum emitters in hBN is spatially correlated with structural defects and can display ultranarrow zero-phonon line width down to 45 μeV if spectral diffusion is effectively eliminated by proper surface passivation. We demonstrate that undesired emission into phonon sidebands is largely absent for this type of emitter. In addition, magneto-optical characterization reveals cycling optical transitions with an upper bound for the g-factor of 0.2 ± 0.2. Spin-polarized density functional theory calculations predict possible commensurate transitions between like-spin electron states, which are in excellent agreement with the experimental nonmagnetic defect center emission. Our results constitute a step toward the realization of narrowband quantum light sources and the development of spin-photon interfaces within 2D materials for future chip-scale quantum networks.

Black phosphorus (BP) is a highly anisotropic allotrope of phosphorus with great promise for fast functional electronics and optoelectronics. We demonstrate the controlled structural modification of few-layer BP along arbitrary crystal directions with sub-nanometer precision for the formation of few-nanometer-wide armchair and zigzag BP nanoribbons. Nanoribbons are fabricated, along with nanopores and nanogaps, using a combination of mechanical–liquid exfoliation and in situ transmission electron microscopy (TEM) and scanning TEM nanosculpting. We predict that the few-nanometer-wide BP nanoribbons realized experimentally possess clear one-dimensional quantum confinement, even when the systems are made up of a few layers. The demonstration of this procedure is key for the development of BP-based electronics, optoelectronics, thermoelectrics, and other applications in reduced dimensions.

A tunable band gap in phosphorene extends its applicability in nanoelectronic and optoelectronic applications. Here, we propose to tune the band gap in phosphorene by patterning antidot lattices, which are periodic arrays of holes or nanopores etched in the material, and by exploiting quantum confinement in the corresponding nanoconstrictions. We fabricated antidot lattices with radii down to 13 nm in few-layer black phosphorus flakes protected by an oxide layer and observed suppression of the in-plane phonon modes relative to the unmodified material via Raman spectroscopy. In contrast to graphene antidots, the Raman peak positions in few-layer BP antidots are unchanged, in agreement with predicted power spectra. We also use DFT calculations to predict the electronic properties of phosphorene antidot lattices and observe a band gap scaling consistent with quantum confinement effects. Deviations are attributed primarily to self-passivating edge morphologies, where each phosphorus atom has the same number of bonds per atom as the pristine material so that no dopants can saturate dangling bonds. Quantum confinement is stronger for the zigzag edge nanoconstrictions between the holes as compared to those with armchair edges, resulting in a roughly bimodal band gap distribution. Interestingly, in two of the antidot structures an unreported self-passivating reconstruction of the zigzag edge endows the systems with a metallic component. The experimental demonstration of antidots and the theoretical results provide motivation to further scale down nanofabrication of antidots in the few-nanometer size regime, where quantum confinement is particularly important.

We report a temperature-dependent Raman spectroscopy study of few-layer black phosphorus (BP) with varied incident polarization and sample thickness. The Raman-active modes Ag 1, B2g, and Ag 2 exhibit a frequency downshift, while their line width tends to increase with increasing temperature. To understand the details of these phenomena, we perform first-principles density functional theory calculations on freestanding monolayer BP. The effect of thermal expansion is included by constraining the temperature-dependent lattice constant. The study of the temperature-induced shift of the phonon frequencies is carried out using ab initio molecular dynamics simulations. The normal-mode frequencies are calculated by identifying the peak positions from the magnitude of the Fourier transform of the total velocity autocorrelation. Anharmonicity induces a frequency shift for each individual mode, and the three- and four-phonon process coefficients are extracted. These results are compared with those obtained from many-body perturbation theory, giving access to phonon lifetimes and lattice thermal conductivity. We establish that the frequency downshift is primarily due to phonon–phonon scattering while thermal expansion only contributes indirectly by renormalizing the phonon–phonon scattering. Overall, the theoretical results are in excellent agreement with experiment, thus showing that controlling phonon scattering in BP could result in better thermoelectric devices or transistors that dissipate heat more effectively when confined to the nanoscale.

Poly(para-phenylene) obtained by a three-step Ullmann coupling: two distinct 1D and 2D organometallic phases are reported.

The modification of an idealized infinite bulk system by dimensional reduction or structural distortion results in quantum confinement effects (QCEs). For example, dimensional reduction of a black phosphorus structure leads to the realization of few-layer systems, creation of edges and surfaces, nanoribbons, quantum dots, and antidot lattices while structural distortion involves simple bending (including nanotubes) and rippling. Black phosphorus ('phosphorene' in the single-layer limit) has been of recent interest due to its relatively large charge carrier mobility and moderate semiconducting band gap, which remains direct irrespective of the number of layers. In this review the state-of-the-art properties of black phosphorus in its dimensionally reduced and structurally distorted forms are discussed, with emphasis on how quantum confinement impacts the material's properties.

The finite-temperature stability of single-layer black (BP) and blue (bP) phosphorus deposited on a gold substrate is investigated using first-principles calculations. In contrast to previous studies, a density functional theory (DFT) treatment including van der Waals (vdW) corrections predicts that the thermo-structural properties do not lead to a phase transition from BP to bP. To account for entropic (i.e. finite temperature) effects on the stability of materials deposited on a substrate within a first-principles framework, we develop an algorithm to investigate phonons properties at the interface between the phosphorus layers and a metallic substrate. This approach greatly reduces the computational cost and makes it possible to use DFT to model vibrational properties of systems with hundreds of atoms, and especially those that can be separated into weakly interacting sub-systems. It also allows for the description of interfacial shear and breathing-like modes, which enter in the evaluation of finite temperature effects via the Helmholtz free energy. In contrast to the freestanding case, we find that bP is energetically more stable than BP adsorbed on Au(1 1 1) with an energy difference between these two phases equal to 46 meV/atom at room temperature.