Nanoscale mechanical oscillators exhibit a plethora of nonlinear phenomena with promising applications for the sensing and clocking of processes down to atomic length scales. Oscillator dynamics are typically probed by electrical or optical means, providing only limited access to the spatial profile of the oscillator motion. Here, we introduce event-based convergent beam electron diffraction for the spatio-temporal mapping of nanoscale mechanical resonators in ultrafast transmission electron microscopy. Employing an optically driven silicon membrane resonator at various driving strengths, we gain access to nonlinear processes with increasing complexity, ranging from a simple Duffing behavior to nonlinear multimode coupling and period-doubling bifurcations. The time-resolved diffraction probing approach supports a spatial resolution down to a few nanometers and a temporal resolution of 5 ns and provides quantitative information on the local membrane bending. Because the diffraction signal responds to local displacement gradients, which become more pronounced as resonators shrink, this approach offers a route toward probing nonlinear nanomechanics at the atomic scale.

When charge flows through a molecular circuit, it induces a magnetic field that allows the circuit to behave as a nanoscale electromagnet. However, in single-molecule circuits this magnetic field is usually weak. Here we show that radially π-conjugated carbon structures can support amplified circulating currents that generate local magnetic fields. Within tight-binding and density functional theory (DFT) frameworks, we first study cycloparaphenylene (CPP) junctions where both electrodes are attached to the same phenylene unit on the nanohoop. We observe an energy-dependent ring current component that traverses the whole macrocycle by mapping the local current density. Importantly, we find that destructive interference near degenerate resonances can reverse the ring current direction and amplify it strongly relative to the source-drain current. We show that this interference-driven design principle is general, and also carries over to C60 junctions. In fullerene, lower-lying degenerate resonances are more easily accessible through electrostatic gating, reaching a magnetic field of 14.2 mT under a 100 mV source-drain bias. This work thus provides new insights into ring currents in radially π-conjugated carbon structures and highlights their potential as design platforms for single-molecule electromagnets.

Theory predicts the superconductor-to-insulator transition (SIT) to emerge from the competition between Anderson localization, which tends to localize single-particle wavefunctions, and superconductivity, which establishes long-range correlations in the superconducting order parameter. In two-dimensional (2D) superconducting films, the transition temperature T_c at which resistance vanishes, R_(T_BKT)=0, is set by the Berezinskii-Kosterlitz-Thouless (BKT) mechanism and satisfies T_BKT< T_c0, where T_c0 is the mean-field transition temperature. In weakly disordered samples T_BKT≲ T_c0, whereas increasing disorder drives T_BKT≪ T_c0 near the SIT. Whether the finite-temperature transition retains its BKT character throughout this crossover remains an open question. Here, we investigate the evolution of both sheet resistance R_(T) and superfluid stiffness J_s(T) over a wide range of disorder strength W. We establish that even near the SIT, the finite-temperature transition from the superconducting to the resistive state remains of BKT type. However, as disorder approaches the critical value, the zero temperature superfluid phase stiffness, J_s(0), is found to vanish rapidly while T_c0 remains finite, which we attribute to quantum phase fluctuations as the drive for the zero-temperature transition. Three decades after its experimental discovery by Haviland, Liu, and Goldman, our measurements clarify the origin of the SIT in 2D films.

The generation of unidirectional motion has been a long-standing challenge in engineering of molecular motors. Here, a mechanism driving the rotation is presented based on electron current through helical orbitals on a n-bonded carbon chain. Such electron current through helical orbitals has been shown to be circulating around the carbon chain. It is natural to expect that the associated electronic angular momentum drives a rotation when the current is turned on. As intuitive as this relation might seem, it is also incomplete because a formal definition of helicality in terms of a physical observable has not yet been given. Such a definition is proposed here. Based on this definition, we show how helicality determines the motor's sense of rotation. We exemplify the relation between helicality and angular momentum in H & uuml;ckel models of linear carbon chains (cumulenes and oligoynes). We attribute the previously reported opposite helicality sense of frontier orbitals (highest occupied molecular orbital and lowest unoccupied molecular orbital) to the approximate sublattice symmetry. For oligoynes, this symmetry is hidden in the sense that it does not reduce to a mere labeling of atoms. Sublattice symmetry, combined with time-reversal invariance, allows us to derive Onsager-type reciprocal relations of various linear response coefficients, dictating, e.g., an odd energy dependence of angular momentum response to voltage bias. We propose an observable consequence of the approximate sublattice symmetry: If the carbon chain is employed as an axle of a molecular rotor, the sense of rotation is independent on the direction of the current.

The dissipation of heat is an inevitable byproduct of all processes─physical, chemical, biological, and computational─putting fundamental limits on the energy required. For quantum machines, these limits have heretofore appeared to be prohibitively stringent due to the large entropy produced in processes at low absolute temperatures. However, we show that the conventional formulas used to compute heat and entropy in quantum processes are incomplete as they omit a term involving the flow of free energy that becomes increasingly important at low temperatures. We analyze steady-state and transient flows of heat and entropy in three representative driven quantum systems and show that inclusion of the new term is needed to obey the third law of thermodynamics. Importantly, the correct results for heat dissipated in quantum processes are orders of magnitude lower than that predicted by the conventional formula. The crossover to the macroscopic limit, where the conventional formula is recovered, is demonstrated.

Light-matter interactions are governed by conservation laws of energy and momentum. For harmonic generation in crystalline solids, energy conservation imposes that m incoming photons with energy ħ ω_0 are combined to form one photon at energy mħ ω_0. Linear momentum conservation governs phase matching, whereas angular momentum conservation connects the angular momentum carried by photons to the discrete rotational symmetry of the crystal lattice. As a consequence, circular harmonic generation exerts a torque on the lattice and, conversely, a macroscopic rotation of the crystal induces a nonlinear rotational Doppler shift. These cornerstone laws of nonlinear optics rely on macroscopic symmetry arguments, and therefore provide little insight into the microscopic origin of angular momentum transfer. Here we uncover a direct connection between angular momentum conservation in nonlinear optics and the electronic quantum geometry, by proving that the transferred angular momentum from light to the crystal is proportional to the local Berry curvature at one optical resonance. This relation is encoded in the nonlinear harmonic circular dichroism, which we measure experimentally in an atomically thin semiconductor. With this, we extend our understanding of nonlinear optics, and we establish a method for the all-optical control and read-out of the local Berry curvature.

The generation of unidirectional motion has been a long-standing challenge in engineering of molecular motors and, more generally, machines. A molecular motor is characterized by a set of low energy states that differ in their configuration, i.e. position or rotation. In biology and Feringa-type motors, unidirectional motion is driven by excitation of the molecule into a high-energy transitional state followed by a directional relaxation back to a low-energy state. Directionality is created by a steric hindrance for movement along one of the directions on the path from the excited state back to a low energy state. Here, we showcase a principle mechanism for the generation of unidirectional rotation of a molecule without the need of steric hindrance and transitional excited states. The chemical design of the molecule consisting of a platform, upright axle and chiral rotor moiety enables a rotation mechanism that relies on the transfer of orbital angular momentum from the driving current to the rotor. The transfer is mediated via orbital currents that are carried by helical orbitals in the axle.

Hilbert space fragmentation, as it is currently investigated, primarily originates from specific kinematic constraints or emergent conservation laws in many-body systems with translation invariance. It leads to non-ergodic dynamics and possible breakdown of the eigenstate thermalization hypothesis. Here, we demonstrate that also in disordered systems, such as the XXZ model with random on-site fields, fragmentation appears as a natural concept offering fresh perspectives, for example, on many-body delocalization (MBdL). Specifically, we split the Fock-space into subspaces, potential-energy shells, which contain the accessible phase space for the relaxation of a quenched initial state. In this construction, dynamical observables reflect properties of the shell geometry, e.g., the drastic sample-to-sample fluctuations observed in the weak disorder regime, $WW_c$, the potential-energy shell decays into fragments; we argue that, unlike percolation, fragmentation is a strong-coupling scenario with turn-around flow: $W_c(L)$ diverges with increasing system size. We conjecture that the slowing down of the relaxation dynamics reported in traditional MBdL studies is (essentially) a manifestation of Fock-space fragmentation introduced here.

Metal-metal contacts, though not yet widely realized, may provide exciting opportunities to serve as tunable and functional interfaces in single-molecule devices. One of the simplest components which might facilitate such binding interactions is the ferrocene group. Notably, direct bonds between the ferrocene iron center and metals such as Pd or Co have been demonstrated in molecular complexes comprising coordinating ligands attached to the cyclopentadienyl rings. Here, we demonstrate that ferrocene-based single-molecule devices with Fe-Au interfacial contact geometries form at room temperature in the absence of supporting coordinating ligands. Applying a photoredox reaction, we propose that ferrocene only functions effectively as a contact group when oxidized, binding to gold through a formal Fe 3+ center. This observation is further supported by a series of control measurements and density functional theory calculations. Our findings extend the scope of junction contact chemistries beyond those involving main group elements, lay the foundation for light switchable ferrocene-based single-molecule devices, and highlight new potential mechanistic function(s) of unsubstituted ferrocenium groups in synthetic processes.

Experimental indications have been reported suggesting that laser pulses shining on materials with relativistic dispersion can produce currents that survive long after the illumination has died out. Such residual currents, i.e., remnant currents, have applications in petahertz logical gates. The remnant currents' strength strongly depends on the pulse shape. We develop an analytical formula that allows one to optimize the pulse shape for remnant current production; we predict remnant currents exceeding the values observed so far by up to five orders of magnitude. This can be achieved by using single-cycle pulses instead of the previously employed multicycle pulses. In fact, remnant currents can be almost as strong as the peak current under irradiation.

Single-molecule junctions - nanoscale systems where a molecule is connected to metallic electrodes - offer a unique platform for studying charge, spin and energy transport in non-equilibrium many-body quantum systems, with few parallels in other areas of condensed matter physics. Over the past decades, these systems have revealed a wide range of remarkable quantum phenomena, including quantum interference, non-equilibrium spin-crossover, diode-like behavior, or chiral-induced spin selectivity, among many others. To develop a detailed understanding, it turned out essential to have available ab initio-based tools for accurately describing quantum transport in such systems. They need to be capable of capturing the intricate electronic structure of molecules, sometimes in the presence of electron-electron or electron-phonon interactions, in out-of-equilibrium environments. Such tools are indispensable also for experimentally observed phenomena explained in terms of parametrized tight-binding models for the quantum transport problem. While FHI-aims also offers specialized transport routines, e.g. for chemically functionalized nanotubes or nanotube networks, our focus in this section is on the AITRANSS package designed for simulations of single-molecule transport. AITRANSS is an independent post-processing tool that combined with FHI-aims enables the calculation of electronic transport properties, as well as atom-projected density of states, spin properties and the simulation of scanning tunneling microscope images in molecular junctions. Pilot versions of the code extend some of these capabilities to non-linear transport in the applied bias, with plans to include these features in future releases of the package.

Motivated by experimental reports on chirality induced spin selectivity, we investigate a minimal model that allows us to calculate the charge and spin conductances through helical molecules analytically. The spin-orbit interaction is assumed to be non-vanishing on the molecule and negligible in the reservoirs (leads). The band structure of the molecule features four helical modes with spin-momentum locking that are analogous of edge-currents in the quantum spin Hall effect. While charge is conserved and therefore the charge current is independent of where it is measured-reservoirs or molecule-our detailed calculations reveal that the spin currents in the left and right leads are equal in magnitudes but with opposite signs (in linear response). We predict that transport currents flowing through helical molecules are accompanied by a spin accumulation in the contact region with the same magnetization direction for source and drain. Furthermore, we predict that the spin-conductance can be extracted directly from measuring the (quasi-static) spin accumulation-rather than the spin current itself, which is very challenging to obtain experimentally.

The use of electric fields applied across magnetic heterojunctions that lack spatial inversion symmetry has been previously proposed as a non-magnetic mean of controlling localized magnetic moments through spin-orbit torques (SOT). The implementation of this concept at the single-molecule level has remained a challenge, however. Here, we present first-principle calculations of SOT in a single-molecule junction under bias and beyond linear response. Employing a self-consistency scheme invoking density functional theory and non-equilibrium Green's function theory, we compute the current-induced SOT. Responding to this torque, a localized magnetic moment can tilt. Within the linear regime our quantitative estimates for the SOT in single-molecule junctions yield values similar to those known for magnetic interfaces. Our findings contribute to an improved microscopic understanding of SOT in single molecules.

High-harmonic generation (HHG) is a versatile technique for probing ultrafast electron dynamics. While HHG is sensitive to the electronic properties of the target, HHG also depends on the waveform of the laser pulse. As is well known, (peak) positions, omega, in the high-harmonic spectrum can shift when the carrier envelope phase (CEP), phi, is varied. We derive formula describing the corresponding parametric dependencies of CEP shifts; in particular, we have a transparent result for the (peak) shift, d omega/d phi = -2 f over bar omega/omega 0, where omega(0) describes the fundamental frequency and f over bar ; characterizes the chirp of the driving laser pulse. We compare the analytical formula to full-fledged numerical simulations finding only 17% average relative absolute deviation in d omega/d phi. Our analytical result is fully consistent with experimental observations.

After a decade of many claims to the opposite, there now is a growing consensus that generic disordered quantum wires, e.g. the XXZ-Heisenberg chain, do not exhibit many-body localization (MBL) - at least not in a strict sense within a reasonable window of disorder values $W$. Specifically, computational studies of short wires exhibit an extremely slow but unmistakable flow of physical observables with increasing time and system size (``creep") that is consistently directed away from (strict) localization. Our work sheds fresh light on delocalization physics: Strong sample-to-sample fluctuations indicate the absence of a generic time scale, i.e. of a naive ``clock rate"; however, the concept of an ``internal clock" survives, at least in an ensemble sense. Specifically, we investigate the relaxation of the imbalance $\mathcal{I}(t)$ and its temporal fluctuations $\mathcal{F}(t)$, the entanglement and Renyi entropies, $\mathcal{S}_{\mathrm{e}}(t)$ and $ \mathcal{S}_2(t)$, in a 1D system of interacting disordered fermions. We observe that adopting $\mathcal{S}_{\mathrm{e}}(t), \mathcal{S}_2(t)$ as a measure for the internal time per sample reduces the sample-to-sample fluctuations but does not eliminate them. However, a (nearly) perfect collapse of the average $\overline{\mathcal{I}}(t)$ and $\overline{\mathcal{F}}(t)$ for different $W$ is obtained when plotted against $\overline{\mathcal{S}}_{\mathrm{e}}(t)$ or $\overline{\mathcal{S}}_2(t)$, indicating that the average entropy appropriately models the ensemble-averaged internal clock. We take the tendency for faster-than-logarithmic growth of $\overline{\mathcal{S}}_{\mathrm{e}}(t)$ together with smooth dependency on $W$ of all our observables within the entire simulation window as support for the cross-over scenario, discouraging an MBL transition within the traditional parametric window of computational studies.

Chirality-induced spin selectivity has been reported in many experiments, but a generally accepted theoretical explanation has not yet been proposed. Here, we introduce a simple model system of a straight cylindrical free-electron wire containing a helical string of atomic scattering centers with spin-orbit interaction. The advantage of this simple model is that it allows deriving analytical expressions for the spin scattering rates, such that the origin of the effect can be easily followed. We find that spin-selective scattering can be viewed as resulting from the constructive interference of partial waves scattered by the spin-orbit terms. We demonstrate that forward scattering rates are independent of spin, while back scattering is spin dependent over wide windows of energy. Although the model does not represent the full details of electron transmission through chiral molecules, it clearly reveals a mechanism that could operate in chiral systems.

There has been great endeavor to engineer molecular rotors operated by an electrical current. A frequently met operation principle is the transfer of angular momentum taken from the incident flux. In this paper, we present an alternative driving agent that works also in situations where angular momentum of the incoming flux is conserved. This situation arises typically with molecular rotors that exhibit an easy axis of rotation. For quantitative analysis we investigate here a classical model where molecule and wires are represented by a rigid curved path. We demonstrate that in the presence of chirality, the rotor generically undergoes a directed motion, provided that the incident current exceeds a threshold value. Above this threshold, the corresponding rotation frequency (per incoming particle current) for helical geometries turns out to be 2πm/M1, where m/M1 is the ratio of the mass of an incident charge carrier and the mass of the helix per winding number.

A critical overview of the theory of the chirality-induced spin selectivity (CISS) effect, that is, phenomena in which the chirality of molecular species imparts significant spin selectivity to various electron processes, is provided. Based on discussions in a recently held workshop, and further work published since, the status of CISS effects-in electron transmission, electron transport, and chemical reactions-is reviewed. For each, a detailed discussion of the state-of-the-art in theoretical understanding is provided and remaining challenges and research opportunities are identified.

Single-molecule topological insulators are promising candidates as conducting wires over nanometre length scales. A key advantage is their ability to exhibit quasi-metallic transport, in contrast to conjugated molecular wires which typically exhibit a low conductance that decays as the wire length increases. Here, we study a family of oligophenylene-bridged bis(triarylamines) with tunable and stable mono- or di-radicaloid character. These wires can undergo one- and two-electron chemical oxidations to the corresponding mono-cation and di-cation, respectively. We show that the oxidized wires exhibit reversed conductance decay with increasing length, consistent with the expectation for Su-Schrieffer-Heeger-type one-dimensional topological insulators. The 2.6-nm-long di-cation reported here displays a conductance greater than 0.1G(0), where G(0) is the conductance quantum, a factor of 5,400 greater than the neutral form. The observed conductance-length relationship is similar between the mono-cation and di-cation series. Density functional theory calculations elucidate how the frontier orbitals and delocalization of radicals facilitate the observed non-classical quasi-metallic behaviour.