Chirality in curved polyaromatic systems

Carbon allotropes constituted of sp(2)-hybridised carbon atoms display a variety of properties that arise from their delocalised Pi-conjugated electronic structure. Apart from carbon's planar allotropic form graphene, bent or curved structures, such as carbon nanotubes or fullerenes, respectively, have been discovered. In this Tutorial Review, we analyse and conceptually categorise chiral synthetic molecular fragments of non-planar sp(2)-carbon allotropes, including hypothetical forms of carbon that have been proposed to exist as stable entities. Two types of molecular systems composed of equally or differently sized rings are examined: bent with zero Gaussian curvature and curved with positive or negative Gaussian curvature. To affirm that a system is chiral, two conditions must be fulfilled: (1) both reflective symmetry elements, an inversion centre and a mirror plane, must be absent and (2) the system must be stereochemically rigid. It is therefore crucial to not only consider the symmetry of a given system as if it was a rigid object but also its structural dynamics. These principles serve as guidelines for the design of molecular fragments that encode and transcribe chirality into larger systems

Determining Inversion Barriers in Atrop- isomers - A Tutorial for Organic Chemists

Dynamic behavior is a fascinating property of natural and artificial systems and its understanding has significantly impacted the transformation of molecular interchanges into controlled molecular motion. In this tutorial, the key descriptors of enantiomeric stability are examined in-depth. Enantiomerization and racemization are discussed and differentiated on a fundamental level proposing a unified and distinct nomenclature. Their mathematical meanings and relations are described and deduced cohesively in the context of atropisomerization. The calculation of inversion barriers from thermodynamic and kinetic data is demonstrated and the interdependences between the latter are explained mathematically. Using current examples from our group, the determination of rate constants and the thermodynamic parameters is shown in a step-by-step manner using the most common techniques. The tutorial is concluded with aspects and considerations concerning statistical data analysis and error determination of measurements including a practical guide to Monte-Carlo simulations

Fabrication of ballistic suspended graphene with local-gating

Herein we discuss the fabrication of ballistic suspended graphene nanostructures supplemented with local gating. Using in-situ current annealing, we show that exceptional high mobilities can be obtained in these devices. A detailed description is given of the fabrication of bottom and different top-gate structures, which enable the realization of complex graphene structures. We have studied the basic building block, the p-n junction in detail, where a striking oscillating pattern was observed, which can be traced back to Fabry-Perot oscillations that are localized in the electronic cavities formed by the local gates. Finally we show some examples how the method can be extended to incorporate multi-terminal junctions or shaped graphene. The structures discussed here enable the access to electron-optics experiments in ballistic graphene

Edge channel confinement in a bilayer graphene nn-pp-nn quantum dot

We combine electrostatic and magnetic confinement to define a quantum dot in bilayer graphene. The employed geometry couples $n$-doped reservoirs to a $p$-doped dot. At magnetic field values around $B = 2~$T, Coulomb blockade is observed. This demonstrates that the coupling of the co-propagating modes at the $p$-$n$ interface is weak enough to form a tunnel barrier, facilitating transport of single charge carriers onto the dot. This result may be of use for quantum Hall interferometry experiments

Snake Trajectories in Ultraclean Graphene p-n Junctions

Snake states are trajectories of charge carriers curving back and forth along an interface. There are two types of snake states, formed by either inverting the magnetic field direction or the charge carrier type at an interface. Whereas the former has been demonstrated in GaAs-AlGaAs heterostructures, the latter has become conceivable only with the advance of ballistic graphene where a gapless p-n interface governed by Klein tunneling can be formed. Such snake states were hidden in previous experiments due to limited sample quality. Here we report on magneto-conductance oscillations due to snake states in a ballistic suspended graphene p-n-junction which occur already at a very small magnetic field of 20mT. The visibility of 30% is enabled by Klein collimation. Our finding is firmly supported by quantum transport simulations. We demonstrate the high tunability of the device and operate it in different magnetic field regimesComment: Accepted for publication in Nature Communication

Excited states in bilayer graphene quantum dots

We report on ground- and excited state transport through an electrostatically defined few-hole quantum dot in bilayer graphene in both parallel and perpendicular applied magnetic fields. A remarkably clear level scheme for the two-particle spectra is found by analyzing finite bias spectroscopy data within a two-particle model including spin and valley degrees of freedom. We identify the two-hole ground-state to be a spin-triplet and valley-singlet state. This spin alignment can be seen as Hund's rule for a valley-degenerate system, which is fundamentally different to quantum dots in carbon nano tubes and GaAs-based quantum dots. The spin-singlet excited states are found to be valley-triplet states by tilting the magnetic field with respect to the sample plane. We quantify the exchange energy to be 0.35meV and measure a valley and spin g-factor of 36 and 2, respectively

Signatures of single quantum dots in graphene nanoribbons within the quantum Hall regime

We report on the observation of periodic conductance oscillations near quantum Hall plateaus in suspended graphene nanoribbons. They are attributed to single quantum dots that are formed in the narrowest part of the ribbon, in the valleys and hills of a disorder potential. In a wide flake with two gates, a double-dot system`s signature has been observed. Electrostatic confinement is enabled in single-layer graphene due to the gaps that are formed between the Landau levels, suggesting a way to create gate-defined quantum dots that can be accessed with quantum Hall edge states

Finding Joy in Science

This piece discusses the importance of sustainable education within the framework of the UN’s 2030 Agenda for Sustainable Development. We emphasize the need to foster a lifelong love for learning by instilling curiosity, emotional bonds, and joy in students. We suggest simplifying teaching methods to maximize depth of understanding, integrating wonder and emotion into scientific education, promoting vertical exploration rather than just covering knowledge horizontally, and fostering resilience and independence through experiential learning. We also advocate for collaborative learning environments and incorporating real-world projects into education. Ultimately, the goal is to create spaces where students can explore, experience joy, and develop a lasting passion for learning

Coupled quantum dots in bilayer graphene

Electrostatic confinement of charge carriers in bilayer graphene provides a unique platform for carbon-based spin, charge or exchange qubits. By exploiting the possibility to induce a band gap with electrostatic gating, we form a versatile and widely tunable multi-quantum dot system. We demonstrate the formation of single, double and triple quantum dots that are free of any sign of disorder. In bilayer graphene we have the possibility to form tunnel barriers using different mechanisms. We can exploit the ambipolar nature of bilayer graphene where pn-junctions form natural tunnel barriers. Alternatively, we can use gates to form tunnel barriers, where we can vary the tunnel coupling by more than two orders of magnitude tuning between a deeply Coulomb blockaded system and a Fabry-P\'erot-like cavity. Demonstrating such tunability is an important step towards graphene-based quantum computation.Comment: 8 pages, 5 figure

Spin-Delocalization in a Helical Open-Shell Hydrocarbon

Neutral open-shell molecules, in which spin density is delocalized through a helical conjugated backbone, hold promise as models for investigating phenomena arising from the interplay of magnetism and chirality. Apart from a handful of examples, however, the chemistry of these compounds remains largely unexplored. Here, we examine the prospect of extending spin-delocalization over a helical backbone in a model compound naphtho[3,2,1- no ]tetraphene, the first helically chiral open-shell hydrocarbon, in which one benzene ring is fused to [5]helicene, forming a phenalenyl subunit. The unpaired electron in this molecule is delocalized over the entire helical core composed of six rings, albeit in a nonuniform fashion, unlike in phenalenyl. In the case of a monosubstituted derivative, the uneven spin-distribution results in a selective σ-dimer formation in solution, as confirmed by 2D NMR spectroscopy. In contrast, the dimerization process is suppressed entirely when four substituents are installed to sterically hinder all reactive positions. The persistent nature of the tetrasubstituted derivative allowed its characterization by EPR, UV–vis, and CD spectroscopies, validating spin-delocalization through a chiral backbone, in accord with DFT calculations. The nonuniform spin-distribution, which dictates the selectivity of the σ-dimer formation, is rationalized by evaluating the aromaticity of the resonance structures that contribute to spin-delocalization