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The wear-free sliding of layers or flakes of graphene-like 2D materials, important in many experimental systems, may occur either smoothly or through stick-slip, depending on driving conditions, corrugation, twist angles, as well as edges and defects. No single parameter has been so far identified to discriminate a priori between the two sliding regimes. Such a parameter, $\eta$, does exist in the ideal (Prandtl-Tomlinson) problem of a point particle sliding across a 1D periodic lattice potential. In that case $\eta >1$ implies mechanical instability, generally leading to stick-slip, with $\eta = \frac{2\pi^2 U_0}{K_\mathrm{p} a^2}$, where $U_0$ is the potential magnitude, $a$ the lattice spacing, and $K_\mathrm{p}$ the pulling spring constant. Here we show, supported by a repertoire of graphene flake/graphene sliding simulations, that a similar stick-slip predictor $\eta_\mathrm{eff}$ can be defined with the same form but suitably defined $U_\mathrm{eff}$, $a_\mathrm{eff}$ and $K_\mathrm{eff}$. Remarkably, simulations show that $a_\mathrm{eff} = a$ of the substrate remains an excellent approximation, while $K_\mathrm{eff}$ is an effective stiffness parameter, combining equipment and internal elasticity. Only the effective energy barrier $U_\mathrm{eff}$ needs to be estimated in order to predict whether stick-slip sliding of a 2D island or extended layer is expected or not. In a misaligned defect-free circular graphene sliding island of contact area $A$, we show that $U_\mathrm{eff}$, whose magnitude for a micrometer size diameter is of order 1 eV, scales as $A^{1/4}$, thus increasing very gently with size. The PT-like parameter $\eta_\mathrm{eff}$ is therefore proposed as a valuable tool in 2D layer sliding., Comment: submitted to Physical Review B

The way metal interfaces evolve during frictional sliding, and how that evolution can be externally influenced under external drivers are important questions, hard to investigate experimentally because the contacts themselves are generally difficult to access. Here we focus on an elementary constituent of a general metal-metal interface, namely an ultra-thin individual nanocontact, where recent rheological studies of crystalline gold nanocontacts [Nature 569, 393 (2019)] showed a dramatic and unexpected mechanical softening as a result of external oscillatory tensile stress. The question which we address through realistic nonequilibrium molecular dynamics simulations is to what extent such mechanical softening might influence the shearing habit of gold nanocontacts at room temperature. It is found that the shearing evolution, which occurs through a series of discrete slips, is indeed rheologically softened, even though not completely, by the oscillations. Differences also emerge for different types of external oscillation, tensile or rotational. The relevance of these results for future experiments will be discussed., Comment: submitted to Physical Review Materials

Alex, the main discoverer of high Tc superconductivity, was also a dear friend. Here I offer a few frank anecdotes, possibly inaccurate in some details but heartfelt and accurate in the substance, as a personal tribute to our friendship., Comment: To appear on Physica C Superconductivity -- K. Alex M\"uller memorial issue

Graphene is a powerful membrane prototype for both applications and fundamental research. Rheological phenomena including indentation, twisting, and wrinkling in deposited and suspended graphene are actively investigated to unravel the mechanical laws at the nanoscale. Most studies focused on isotropic set-ups, while realistic graphene membranes are often subject to strongly anisotropic constraints, with important consequences for the rheology, strain, indentation, and friction in engineering conditions.

A plethora of two-dimensional (2D) materials entered the physics and engineering scene in the last two decades. Their robust, membrane-like sheet permit -- mostly require -- deposition, giving rise to solid-solid dry interfaces whose bodily mobility, pinning, and general tribological properties under shear stress are currently being understood and controlled, experimentally and theoretically. In this Colloquium we use simulation case studies of twisted graphene system as a prototype workhorse tool to demonstrate and discuss the general picture of 2D material interface sliding. First, we highlight the crucial mechanical difference, often overlooked, between small and large incommensurabilities, corresponding e.g., to small and large twist angles in graphene interfaces. In both cases, focusing on flat, structurally lubric, "superlubric" geometries, we elucidate and review the generally separate scaling with area of static friction in pinned states and of kinetic friction during sliding, tangled as they are with the effects of velocity, temperature, load, and defects. Including the role of island boundaries and of elasticity, and corroborating when possible the existing case-by-case results in literature beyond graphene, the overall picture proposed is meant for general 2D material interfaces, that are of importance for the physics and technology of existing and future bilayer and multilayer systems., Comment: Submitted to Reviews of Modern Physics

The ultra-low kinetic friction F_k of 2D structurally superlubric interfaces, connected with the fast motion of the incommensurate moir\'e pattern, is often invoked for its linear increase with velocity v_0 and area A, but never seriously addressed and calculated so far. Here we do that, exemplifying with a twisted graphene layer sliding on top of bulk graphite -- a demonstration case that could easily be generalized to other systems. Neglecting quantum effects and assuming a classical Langevin dynamics, we derive friction expressions valid in two temperature regimes. At low temperatures the nonzero sliding friction velocity derivative dF_k/dv_0 is shown by Adelman-Doll-Kantorovich type approximations to be equivalent to that of a bilayer whose substrate is affected by an analytically derived effective damping parameter, replacing the semi-infinite substrate. At high temperatures, friction grows proportional to temperature as analytically required by fluctuation-dissipation. The theory is validated by non-equilibrium molecular dynamics simulations with different contact areas, velocities, twist angles and temperatures. Using 6^{\circ}-twisted graphene on Bernal graphite as a prototype we find a shear stress of measurable magnitude, from 25 kPa at low temperature to 260 kPa at room temperature, yet only at high sliding velocities such as 100 m/s. However, it will linearly drop many orders of magnitude below measurable values at common experimental velocities such as 1 {\mu}m/s, a factor 10^{-8} lower. The low but not ultra-low "engineering superlubric" friction measured in existing experiments should therefore be attributed to defects and/or edges, whose contribution surpasses by far the negligible moir\'e contribution., Comment: submitted to Journal of the Mechanics and Physics of Solids

The freestanding twisted bilayer graphene (TBG) is unstable, below a critical twist angle {\theta}_c~3.7 degrees, against a moire (2 \times 1) buckling distortion at T=0. Realistic simulations reveal the concurrent unexpected collapse of the bending rigidity, an unrelated macroscopic mechanical parameter. An analytical model connects bending and buckling anomalies at T=0, but as temperature rises the former fades, while buckling persists further. The (2 \times 1) electronic properties are also surprising. The magic twist angle narrow bands, now eight in number, fail to show zone boundary splittings despite the new periodicity. Symmetry shows how this is dictated by an effective single valley physics. These structural, critical, and electronic predictions promise to make the freestanding state of TBG especially interesting.

The understanding of friction at nano-scales, ruled by the regular arrangement of atoms, is surprisingly incomplete. Here we provide a unified understanding by studying the interlocking potential energy of two infinite contacting surfaces with arbitrary lattice symmetries, and extending it to finite contacts. We categorize, based purely on geometrical features, all possible contacts into three different types: a structurally lubric contact where the monolayer can move isotropically without friction, a corrugated and strongly interlocked contact, and a newly discovered directionally structurally lubric contact where the layer can move frictionlessly along one specific direction and retains finite friction along all other directions. This novel category is energetically stable against rotational perturbations and provides extreme friction anisotropy. The finite-size analysis shows that our categorization applies to a wide range of technologically relevant materials in contact, from adsorbates on crystal surfaces to layered two-dimensional materials and colloidal monolayers.

Nanotubes show great promise for miniaturizing advanced technologies. Their exceptional physical properties are intimately related to their morphological and crystal structure. Circumferential faceting of multiwalled nanotubes reinforces their mechanical strength and alters their tribological and electronic properties. Here, the nature of this important phenomenon is fully rationalized in terms of interlayer registry patterns. Regardless of the nanotube identity (that is, diameter, chirality, chemical composition), faceting requires the matching of the chiral angles of adjacent layers. Above a critical diameter that corresponds well with experimental results, achiral multiwalled nanotubes display evenly spaced extended axial facets whose number equals the interlayer difference in circumferential unit cells. Elongated helical facets, commonly observed in experiment, appear in nanotubes that exhibit small interlayer chiral angle mismatch. When the wall chiralities are uncorrelated, faceting is suppressed and outer layer corrugation, which is induced by the moir\'e superlattice, is obtained in agreement with experiments. Finally, we offer an explanation for the higher incidence of faceting in multiwalled boron nitride nanotubes with respect to their carbon-based counterparts.

We identify a new material phenomenon, where minute mechanical manipulations induce pronounced global structural reconfigurations in faceted multi-walled nanotubes. This behavior has strong implications on the tribological properties of these systems and may be the key to understand the enhanced inter-wall friction recently measured for boron-nitride nanotubes with respect to their carbon counterparts. Notably, the fast rotation of helical facets in these systems upon coaxial sliding may serve as a nanoscale Archimedean screw for directional transport of physisorbed molecules.

The cyclic sudden switching of a magnetic impurity from Kondo to a non-Kondo state and back was recently shown to involve an important dissipation of the order of several $k_BT_K$ per cycle. The possibility to reveal this and other electronic processes through nanomechanical dissipation by e.g., ultrasensitive Atomic Force Microscope (AFM) tools currently represents an unusual and interesting form of spectroscopy. Here we explore the dependence on the switching time of the expected dissipation, a quantity whose magnitude is physically expected to drop from maximum to zero between sudden and slow switching, respectively. By applying a recently established matrix-product-state based time-dependent variational algorithm to the magnetic field-induced Kondo switching in an Anderson model of the magnetic impurity, we find that dissipation requires switching within the Kondo time scale $\hbar(k_B T_K)^{-1}$ or faster. While such a fast switching seems problematic for current AFM setups, the challenge is open for future means to detect this dissipation by time-dependent magnetic fields, electrostatic impurity level shift, or hybridization switching.

The peeling of an immobile adsorbed membrane is a well known problem in engineering and macroscopic tribology. In the classic setup, picking up at one extreme and pulling off results in a peeling force that is a decreasing function of the pickup angle. As one end is lifted, the detachment front retracts to meet the immobile tail. At the nanoscale, interesting situations arise with the peeling of graphene nanoribbons (GNRs) on gold, as realized, e.g., by atomic force microscopy. The nanosized system shows a constant-force steady peeling regime, where the tip lifting h produces no retraction of the ribbon detachment point, and just an advancement h of the free tail end. This is opposite to the classic case, where the detachment point retracts and the tail end stands still. Here we characterise, by analytical modeling and numerical simulations, a third, experimentally relevant, setup where the nanoribbon, albeit structurally lubric, does not have a freely moving tail end, which is instead elastically tethered. Surprisingly, novel nontrivial scaling exponents appear that regulate the peeling evolution. As the detachment front retracts and the tethered tail is stretched, power laws of h characterize the shrinking of the adhered length the growth of peeling force and the peeling angle. These exponents precede the final total detachment as a critical point, where the entire ribbon eventually hangs suspended between the tip and tethering spring. These analytical predictions are confirmed by realistic MD simulations, retaining the full atomistic description, also confirming their survival at finite experimental temperatures.

The sliding motion of objects is typically governed by their friction with the underlying surface. Compared to translational friction, however, rotational friction has received much less attention. Here, we experimentally and theoretically study the rotational depinning and orientational dynamics of two-dimensional colloidal crystalline clusters on periodically corrugated surfaces in the presence of magnetically exerted torques. We demonstrate that the traversing of locally commensurate areas of the moir\'e pattern through the edges of clusters, which is hindered by potential barriers during cluster rotation, controls its rotational depinning. The experimentally measured depinning thresholds as a function of cluster size strikingly collapse onto a universal theoretical curve which predicts the possibility of a superlow-static-torque state for large clusters. We further reveal a cluster-size-independent rotation-translation depinning transition when lattice-matched clusters are driven jointly by a torque and a force. Our work provides guidelines to the design of nanomechanical devices that involve rotational motions on atomic surfaces.

Metal atomic chains have been reported to change their electronic or magnetic properties by slight mechanical stimulus. However, the mechanical response has been veiled because of lack of information on the bond nature. Here, we clarify the bond nature in platinum (Pt) monatomic chains by our developed in-situ transmission electron microscope method. The stiffness is measured with sub N/m precision by quartz length-extension resonator. The bond stiffnesses at the middle of the chain and at the connecting to the base are estimated to be 25 and 23 N/m, respectively, which are higher than the bulk counterpart. Interestingly, the bond length of 0.25 nm is found to be elastically stretched to 0.31 nm, corresponding to 24% in strain. Such peculiar bond nature could be explained by a novel concept of "string tension". This study is a milestone that will significantly change the way we think about atomic bonds in one-dimensional substance., Comment: 20pages, 4 figures

Chevrel ternary superconductors show an intriguing coexistence of molecular aspects, large electron-phonon and electron-electron correlations, which to some extent still impedes their quantitative understanding. We present a first principles study on the prototypical Chevrel compound PbMo$_{6}$S$_{8}$, including electronic, structural and vibrational properties at zero and high pressure. We confirm the presence of an extremely strong electron-phonon coupling, linked to the proximity to a R$\overline{3}$-P$\overline{1}$ structural phase transition, which weakens as the system, upon applied pressures, is driven away from the phase boundary. A detailed description of the superconducting state is obtained by means of fully \textit{ab initio} superconducting density functional theory (SCDFT). SCDFT accounts for the role of phase instability, electron-phonon coupling with different intra- and inter-molecular phonon modes, and without any empirical parameter, and accurately reproduces the experimental critical temperature and gap. This study provides the conclusive confirmation that Chevrel phases are phonon driven superconductors mitigated, however, by an uncommonly strong Coulomb repulsion. The latter is generated by the combined effect of repulsive Mo states at the Fermi energy and a band gap in close proximity to the Fermi level. This is crucial to rationalize why Chevrel phases, in spite of their extreme electron-phonon coupling, have critical temperatures below 15~K. In addition, we predict the evolution of the superconducting critical temperature as a function of the external pressure, showing an excellent agreement with available experimental data.

Understanding the drift motion and dynamical locking of crystalline clusters on patterned substrates is important for the diffusion and manipulation of nano- and micro-scale objects on surfaces. In a previous work, we studied the orientational and directional locking of colloidal two-dimensional clusters with triangular structure driven across a triangular substrate lattice. Here we show with experiments and simulations that such locking features arise for clusters with arbitrary lattice structure sliding across arbitrary regular substrates. Similar to triangular-triangular contacts, orientational and directional locking are strongly correlated via the real- and reciprocal-space moir\'e patterns of the contacting surfaces. Due to the different symmetries of the surfaces in contact, however the relation between the locking orientation and the locking direction becomes more complicated compared to interfaces composed of identical lattice symmetries. We provide a generalized formalism which describes the relation between the locking orientation and locking direction with arbitrary lattice symmetries., Comment: Published in Physical Review E. 17 pages and 10 figures including supplementary information

Atomic scale friction, an indispensable element of nanotechnology, requires a direct access to, under actual growing shear stress, its successive live phases: from static pinning, to depinning and transient evolution, eventually ushering in steady state kinetic friction. Standard tip-based atomic force microscopy generally addresses the steady state, but the prior intermediate steps are much less explored. Here we present an experimental and simulation approach, where an oscillatory shear force of increasing amplitude leads to a one-shot investigation of all these successive aspects. Demonstration with controlled gold nanocontacts sliding on graphite uncovers phenomena that bridge the gap between initial depinning and large speed sliding, of potential relevance for atomic scale time and magnitude dependent rheology.

Ordinary ice has a proton-disordered phase which is kinetically metastable, unable to reach, spontaneously, the ferroelectric (FE) ground state at low temperature where a residual Pauling entropy persists. Upon light doping with KOH at low temperature, the transition to FE ice takes place, but its microscopic mechanism still needs clarification. We introduce a lattice model based on dipolar interactions plus a competing, frustrating term that enforces the ice rule (IR). In the absence of IR-breaking defects, standard Monte Carlo (MC) simulation leaves this ice model stuck in a state of disordered proton ring configurations with the correct Pauling entropy. A replica exchange accelerated MC sampling strategy succeeds, without open path moves, interfaces, or off-lattice configurations, in equilibrating this defect-free ice, reaching its low-temperature FE order through a well-defined first-order phase transition. When proton vacancies mimicking the KOH impurities are planted into the IR-conserving lattice, they enable standard MC simulation to work, revealing the kinetics of evolution of ice from proton disorder to partial FE order below the transition temperature. Replacing ordinary nucleation, each impurity opens up a proton ring generating a linear string, an actual FE hydrogen bond wire that expands with time. Reminiscent of those described for spin ice, these impurity-induced strings are proposed to exist in doped water ice too, where IRs are even stronger. The emerging mechanism yields a dependence of the long-time FE order fraction upon dopant concentration, and upon quenching temperature, that compares favorably with that known in real-life KOH doped ice., Comment: 11 pages, 4 figures

The lifting, peeling and exfoliation of physisorbed ribbons (or flakes) of 2D material such as graphene off a solid surface are common and important manoeuvres in nanoscience. The feature that makes this case peculiar is the structural lubricity generally realized by stiff 2D material contacts. We model theoretically the mechanical peeling of a nanoribbon of graphene as realized by the tip-forced lifting of one of its extremes off a flat crystal surface. The evolution of shape, energy, local curvature and body advancement are ideally expected to follow a succession of regimes: (A) initial prying, (B) peeling with stretching but without sliding (stripping), (C) peeling with sliding, (D) liftoff. In the case where in addition the substrate surface corrugation is small or negligible, then (B) disappears, and we find that the (A)-(C) transition becomes universal, analytical and sharp, determined by the interplay between bending rigidity and adsorption energy. This general two-stage peeling transition is identified as a sharp crossover in published data of graphene nanoribbons pulled off an atomic-scale Au(111) substrate., Comment: 10 pages, 5 figures

Bodies in relative motion separated by a gap of a few nanometers can experience a tiny friction force. This non-contact dissipation can have various origins and can be successfully measured by a sensitive pendulum atomic force microscope tip oscillating laterally above the surface. Here, we report on the observation of dissipation peaks at selected voltage-dependent tip-surface distances for oxygen-deficient strontium titanate (SrTiO_3) surface at low temperatures (T = 5K). The observed dissipation peaks are attributed to tip-induced charge and spin state transitions in quantum-dot-like entities formed by single oxygen vacancies (and clusters thereof, possibly through a collective mechanism) at the SrTiO_3 surface, which in view of technological and fundamental research relevance of the material opens important avenues for further studies and applications.

We discuss and qualify a previously unnoticed connection between two different phenomena in the physics of nanoscale friction, general in nature and also met in experiments including sliding emu- lations in optical lattices, and protein force spectroscopy. The first is thermolubricity, designating the condition in which a dry nanosized slider can at sufficiently high temperature and low velocity exhibit very small viscous friction f ~ v despite strong corrugations that would commonly imply hard mechanical stick-slip f ~ log(v). The second, apparently unrelated phenomenon present in externally forced nanosystems, is the occurrence of negative work tails ("free lunches") in the work probabilty distribution, tails whose presence is necessary to fulfil the celebrated Jarzynski equality of non-equilibrium statistical mechanics. Here we prove analytically and demonstrate numerically in the prototypical classical overdamped one-dimensional point slider (Prandtl-Tomlinson) model that the presence or absence of thermolubricity is exactly equivalent to satisfaction or violation of the Jarzynski equality. The divide between the two regimes, satisfaction of Jarzynski with ther- molubricity, and violation of both, simply coincides with the total frictional work per cycle falling below or above kT respectively. This concept can, with due caution, be extended to more complex sliders, thus inviting crosscheck experiments, such as searching for free lunches in cold ion sliding as well as in forced protein unwinding, and alternatively checking for a thermolubric regime in dragged colloid monolayers. As an important byproduct, we derive a parameter-free formula expressing the linear velocity coefficient of frictional dissipated power in the thermolubric viscous regime, correcting previous empirically parametrized expressions.

Using both a resonant level model and the time-dependent Gutzwiller approximation, we study the power dissipation of a localized impurity hybridized with a conduction band when the hybridization is periodically switched on and off. The total dissipated energy is proportional to the Kondo temperature, with a non-trivial frequency dependence. At low frequencies it can be well approximated by the one of a single quench, and is obtainable analitically; at intermediate frequencies it undergoes oscillations; at high frequencies, after reaching its maximum, it quickly drops to zero. This frequency-dependent energy dissipation could be relevant to systems such as irradiated quantum dots, where Kondo can be switched at very high frequencies.

The phase diagram of isotropically expanded graphene cannot be correctly predicted by ignoring either electron correlations, or mobile carbons, or the effect of applied stress, as was done so far. We calculate the ground state enthalpy (not just energy) of strained graphene by an accurate off-lattice Quantum Monte Carlo (QMC) correlated ansatz of great variational flexibility. Following undistorted semimetallic graphene (SEM) at low strain, multi-determinant Heitler-London correlations stabilize between $\simeq$8.5% and $\simeq$15% strain an insulating Kekule-like dimerized (DIM) state. Closer to a crystallized resonating-valence bond than to a Peierls state, the DIM state prevails over the competing antiferromagnetic insulating (AFI) state favored by density-functional calculations which we conduct in parallel. The DIM stressed graphene insulator, whose gap is predicted to grow in excess of 1 eV before failure near 15% strain, is topological in nature, implying under certain conditions 1D metallic interface states lying in the bulk energy gap., Comment: 10 pages, 7 figures

Recent model simulations discovered unexpected non-monotonic features in the wear-free dry phononic friction as a function of the sliding speed. Here we demonstrate that a rather straight- forward application of linear-response theory, appropriate in a regime of weak slider-substrate in- teraction, predicts frictional one-phonon singularities which imply a non-trivial dependence of the dynamical friction force on the slider speed and/or coupling to the substrate. The explicit formula which we derive reproduces very accurately the classical atomistic simulations when available. By modifying the slider-substrate interaction the analytical understanding obtained provides a practical means to tailor and control the speed dependence of friction with substantial freedom.

Graphene nanoribbons (GNRs) physisorbed on a Au(111) surface can be picked up, lifted at one end, and made slide by means of the tip of an atomic-force microscope. The dynamical transition from smooth sliding to multiple stick-slip regimes, the pushing/pulling force asymmetry, the presence of pinning, and its origin are real frictional processes in a nutshell, in need of a theoretical description. To this purpose, we conduct classical simulations of frictional manipulations for GNRs up to 30 nm in length, one end of which is pushed or pulled horizontally while held at different heights above the Au surface. These simulations allow us to clarify theoretically the emergence of stick-slip originating from the short 1D edges rather than the 2D "bulk", the role of adhesion, of lifting, and of graphene bending elasticity in determining the GNR sliding friction. The understanding obtained in this simple context is of additional value for more general cases.

Atomically thin graphene exhibits fascinating mechanical properties, although its hardness and transverse stiffness are inferior to those of diamond. To date, there hasn't been any practical demonstration of the transformation of multi-layer graphene into diamond-like ultra-hard structures. Here we show that at room temperature and after nano-indentation, two-layer graphene on SiC(0001) exhibits a transverse stiffness and hardness comparable to diamond, resisting to perforation with a diamond indenter, and showing a reversible drop in electrical conductivity upon indentation. Density functional theory calculations suggest that upon compression, the two-layer graphene film transforms into a diamond-like film, producing both elastic deformations and sp2-to-sp3 chemical changes. Experiments and calculations show that this reversible phase change is not observed for a single buffer layer on SiC or graphene films thicker than 3 to 5 layers. Indeed, calculations show that whereas in two-layer graphene layer-stacking configuration controls the conformation of the diamond-like film, in a multilayer film it hinders the phase transformation., Comment: Published online on Nature Nanotechnology on December 18, 2017

Thermal ripples of graphene are well understood at room temperature, but their quantum counterparts at low temperatures are still in need of a realistic quantitative description. Here we present atomistic path-integral Monte Carlo simulations of freestanding graphene, which show upon cooling a striking classical-quantum evolution of height and angular fluctuations. The crossover takes place at ever-decreasing temperatures for ever-increasing wavelengths so that a completely quantum regime is never attained. Zero-temperature quantum graphene is flatter and smoother than classical at large scales, yet rougher at short scales. The angular fluctuation distribution of the normals can be quantitatively described by coexistence of two Gaussians, one classical strongly T-dependent and one quantum about $2^{\circ}$ wide, of zero-point character. The quantum evolution of ripple-induced height and angular spread should be observable in electron diffraction in graphene and other two-dimensional materials like MoS$_2$, bilayer graphene, boron nitride, etc., Comment: 6 pages, 6 figures, paper is accompanied by supplementary material available in Ancillary files or inside the directory anc/ included in the source of this manuscript

Revealing phase transitions of solids through mechanical anomalies in the friction of nanotips sliding on their surfaces is an unconventional and instructive tool for continuous transitions, unexplored for first-order ones. Owing to slow nucleation, first-order structural transformations generally do not occur at the precise crossing of free energies, but hysteretically, near the spinodal temperatures where, below and above the thermodynamic transition temperature, one or the other metastable free energy branches terminates. The spinodal transformation, a collective one-shot event with no heat capacity anomaly, is easy to trigger by a weak external perturbations. Here we propose that even the gossamer mechanical action of an AFM tip may locally act as a surface trigger, narrowly preempting the spontaneous spinodal transformation, and making it observable as a nanofrictional anomaly. Confirming this expectation, the CCDW-NCCDW first-order transition of the important layer compound 1T-TaS$_2$ is shown to provide a demonstration of this effect., Comment: 8 pages, 5 figures

The textbook thermophoretic force which acts on a body in a fluid is proportional to the local temperature gradient. The same is expected to hold for the macroscopic drift behavior of a diffusive cluster or molecule physisorbed on a solid surface. The question we explore here is whether that is still valid on a 2D membrane such as graphene at short sheet length. By means of a non-equilibrium molecular dynamics study of a test system -- a gold nanocluster adsorbed on free-standing graphene clamped between two temperatures $\Delta T$ apart -- we find a phoretic force which for submicron sheet lengths is parallel to, but basically independent of, the local gradient magnitude. This identifies a thermophoretic regime that is ballistic rather than diffusive, persisting up to and beyond a hundred nanometer sheet length. Analysis shows that the phoretic force is due to the flexural phonons, whose flow is known to be ballistic and distance-independent up to relatively long mean-free paths. Yet, ordinary harmonic phonons should only carry crystal momentum and, while impinging on the cluster, should not be able to impress real momentum. We show that graphene, and other membrane-like monolayers, support a specific anharmonic connection between the flexural corrugation and longitudinal phonons whose fast escape leaves behind a 2D-projected mass density increase endowing the flexural phonons, as they move with their group velocity, with real momentum, part of which is transmitted to the adsorbate through scattering. The resulting distance-independent ballistic thermophoretic force is not unlikely to possess practical applications.

The quantum motion of nuclei, generally ignored in sliding friction, can become important for an atom, ion, or light molecule sliding in an optical lattice. The density-matrix-calculated evolution of a quantum Prandtl-Tomlinson model, describing the frictional dragging by an external force of a quantum particle, shows that classical predictions can be very wrong. The strongest quantum effect occurs not for weak, but for strong periodic potentials, where barriers are high but energy levels in each well are discrete, and resonant tunnelling to excited states in the nearest well can preempt classical stick-slip with great efficiency. The resulting permeation of otherwise impassable barriers is predicted to cause quantum lubricity

We address the atomistic nature of the longitudinal static friction against sliding of graphene nanoribbons (GNRs) deposited on gold, a system whose structural and mechanical properties have been recently the subject of intense experimental investigation. By means of numerical simulations and modeling we show that the GNR interior is structurally lubric ("superlubric") so that the static friction is dominated by the front/tail regions of the GNR, where the residual uncompensated lateral forces arising from the interaction with the underneath gold surface opposes the free sliding. As a result of this edge pinning the static friction does not grow with the GNR length, but oscillates around a fairly constant mean value. These friction oscillations are explained in terms of the GNR-Au(111) lattice mismatch: at certain GNR lengths close to an integer number of the beat (or moire') length there is good force compensation and superlubric sliding; whereas close to half odd-integer periods there is significant pinning of the edge with larger friction. These results make qualitative contact with recent state-of-the-art atomic force microscopy experiment, as well as with the sliding of other different incommensurate systems., Comment: 11 pages, 5 figures

We discuss, based on first principles calculations, the possibility to tune the magnetism of oxygen vacancies at the (001) surface of strontium titanate $(\mathrm{SrTiO_3}\!)$. The magnetic moment of single and clustered vacancies stemming from Ti-O broken bonds can be both quenched and stabilized controllably by chemical potential adjustment associated with doping the system with electrons or holes. We discuss to what extent this route to magnetization state control is robust against other external influences like chemical doping, mechanical action and electric field. Such control of vacancy state and magnetization can conceivably be achieved experimentally by using local probe tips.

The contact strength, adhesion and friction, between graphene and an incommensurate crystalline substrate such as {\it h}-BN depends on their relative alignment angle $\theta$. The well established Novaco-McTague (NM) theory predicts for a monolayer graphene on a hard bulk {\it h}-BN crystal face a small spontaneous misalignment, here $\theta_{NM}$\,$\simeq$\,0.45 degrees which if realized would be relevant to a host of electronic properties besides the mechanical ones. Because experimental equilibrium is hard to achieve, we inquire theoretically about alignment or misalignment by simulations based on dependable state-of-the-art interatomic force fields. Surprisingly at first, we find compelling evidence for $\theta = 0$, i.e., full energy-driven alignment in the equilibrium state of graphene on {\it h}-BN. Two factors drive this deviation from NM theory. First, graphene is not flat, developing on {\it h}-BN a long-wavelength out-of-plane corrugation. Second, {\it h}-BN is not hard, releasing its contact stress by planar contractions/expansions that accompany the interface moir\'e structure. Repeated simulations by artificially forcing graphene to keep flat, and {\it h}-BN to keep rigid, indeed yield an equilibrium misalignment similar to $\theta_{NM}$ as expected. Subsequent sliding simulations show that friction of graphene on {\it h}-BN, small and essentially independent of misalignments in the artificial frozen state, strongly increases in the more realistic corrugated, strain-modulated, aligned state.

The Aubry unpinned--pinned transition in the sliding of two incommensurate lattices occurs for increasing mutual interaction strength in one dimension ($1D$) and is of second order at $T=0$, turning into a crossover at nonzero temperatures. Yet, real incommensurate lattices come into contact in two dimensions ($2D$), at finite temperature, generally developing a mutual Novaco-McTague misalignment, conditions in which the existence of a sharp transition is not clear. Using a model inspired by colloid monolayers in an optical lattice as a test $2D$ case, simulations show a sharp Aubry transition between an unpinned and a pinned phase as a function of corrugation. Unlike $1D$, the $2D$ transition is now of first order, and, importantly, remains well defined at $T>0$. It is heavily structural, with a local rotation of moir\'e pattern domains from the nonzero initial Novaco-McTague equilibrium angle to nearly zero. In the temperature ($T$) -- corrugation strength ($W_0$) plane, the thermodynamical coexistence line between the unpinned and the pinned phases is strongly oblique, showing that the former has the largest entropy. This first-order Aubry line terminates with a novel critical point $T=T_c$, marked by a susceptibility peak. The expected static sliding friction upswing between the unpinned and the pinned phase decreases and disappears upon heating from $T=0$ to $T=T_c$. The experimental pursuit of this novel scenario is proposed., Comment: 9 pages, 9 figures

A new organic superconductor, possibly with formula $K_3$ p-terphenyl, has been discovered by Wang, Gao, Huang and Chen, reaching a very high $T_c$ of about 120~K. Besides a clear diamagnetic signal, most other details such as stoichiometry and structure are yet unknown. However, pristine p-terphenyl has a familiar $P2_1/a$ staggered bimolecular structure, and it can be reasonably assumed that a similar bimolecular structure could be retained by hypothetical $K_3$ p-terphenyl. We point out that the resulting 2-narrow band metal would support the same $s_{\pm}$ superconductivity recently proposed for doped polycyclic aromatic hydrocarbons such as La-phenanthrene or $K_3$-picene. In that model, narrow bands, a large Hubbard $U$ and the neighbourhood of a Mott transition enhance superconductivity rather than damaging it.

Long after its discovery superconductivity in alkali fullerides A$_3$C$_{60}$ still challenges conventional wisdom. The freshest inroad in such ever-surprising physics is the behaviour under intense infrared (IR) excitation. Signatures attributable to a transient superconducting state extending up to temperatures ten times higher than the equilibrium $T_c\sim$ 20 K have been discovered in K$_3$C$_{60}$ after ultra-short pulsed IR irradiation -- an effect which still appears as remarkable as mysterious. Motivated by the observation that the phenomenon is observed in a broad pumping frequency range that coincides with the mid-infrared electronic absorption peak still of unclear origin, rather than to TO phonons as has been proposed, we advance here a radically new mechanism. First, we argue that this broad absorption peak represents a "super-exciton" involving the promotion of one electron from the $t_{1u}$ half-filled state to a higher-energy empty $t_{1g}$ state, dramatically lowered in energy by the large dipole-dipole interaction acting in conjunction with Jahn Teller effect within the enormously degenerate manifold of $\big(t_{1u}\big)^2\big(t_{1g}\big)^1$ states. Both long-lived and entropy-rich because they are triplets, the IR-induced excitons act as a sort of cooling mechanism that permits transient superconductive signals to persist up to much larger temperatures., Comment: 16 pages article and 19 pages supplementary notes

BaBiO$_3$ is a mixed-valence perovskite which escapes the metallic state through a Bi valence (and Bi-O bond) disproportionation or CDW distortion, resulting in a semiconductor with a gap of 0.8 eV at zero pressure. The evolution of structural and electronic properties at high pressure is, however, largely unknown. Pressure, one might have hoped, could reduce the disproportionation, making the two Bi ions equivalent and bringing the system closer to metallicity or even to superconductivity, such as is attained at ambient pressure upon metal doping. We address the high-pressure phase diagram of pristine BaBiO$_3$ by ab initio DFT calculations based on GGA and hybrid functionals in combination with crystal structure prediction methods based on evolutionary algorithms, molecular dynamics and metadynamics. The calculated phase diagram from 0 to 50 GPa indicates that pristine BaBiO$_3$ resists metallization under pressure, undergoing instead at room temperature structural phase transitions from monoclinic \textit{I2/m} to nearly tetragonal \textit{P-1} at 7 GPa, possibly to monoclinic \textit{C2/m} at 27 GPa, and to triclinic \textit{P1} at 43 GPa. Remarkably, all these phases sustain and in fact increase the inequivalence of two Bi neighboring sites and of their Bi-O bonds and, in all cases except semimetallic \textit{C2/m}, the associated insulating character. We then present high-pressure resistivity data which generally corroborate these results, and show that the insulating character persists at least up to 80 GPa, suggesting that the \textit{C2/m} phase is probably an artifact of the small computational cell., Comment: 8 pages, 10 figures

The onset or demise of Kondo effect in a magnetic impurity on a metal surface can be triggered, as often observed, by the simple mechanical nudging of a tip. This mechanically-driven quantum phase transition must reflect in a corresponding mechanical dissipation peak; yet, this kind of effect has not been focused upon so far. Aiming at the simplest theoretical modeling, we initially treat the impurity as a non-interacting resonant level turned cyclically on and off, and obtain a dissipation per cycle which is proportional to the hybridization $\Gamma$, with a characteristic temperature dependent resonant peak value. A better treatment is obtained next by solving an Anderson impurity model by numerical renormalization group. Here, many body effects yield a dissipation whose peak value is now proportional to $T_K |\log T|$ so long as $T\sim T_K$, followed for $T\sim \Gamma$ by a second high temperature regime where dissipation is proportional to $\Gamma|\log T|$. The detectability of Kondo mechanical dissipation in atomic force microscopy is discussed., Comment: Revised version

The quantum physics of ions and electrons behind low-energy spectra of strongly correlated {\it molecular} conductors, superconductors and Mott insulators is poorly known, yet fascinating especially in orbitally degenerate cases. The fulleride insulator Cs$_{3}$C$_{60}$ (A15), one such system, exhibits infrared (IR) spectra with low temperature peak features and splittings suggestive of static Jahn-Teller distortions with breakdown of orbital symmetry in the molecular site. That is puzzling, for there is no detectable static distortion, and because the features and splittings disappear upon modest heating, which they should not. Taking advantage of the Mott-induced collapse of electronic wavefunctions from lattice-extended to nanoscale localized inside a caged molecular site, we show that unbroken spin and orbital symmetry of the ion multiplets explains the IR spectrum without adjustable parameters. This demonstrates the importance of a fully quantum treatment of nuclear positions and orbital momenta in the Mott insulator sites, dynamically but not statically distorted. The observed demise of these features with temperature is explained by the thermal population of a multiplet term whose nuclear positions are essentially undistorted, but whose energy is very low-lying. That term is in facts a scaled-down orbital excitation analogous to that of other Mott insulators, with the same spin $1/2$ as the ground state, but with a larger orbital moment of two instead of one., Comment: 6 pages, 3 figures

Old and novel layered structures are attracting increasing attention for their physical, electronic, and frictional properties. SiS$_2$, isoelectronic to SiO$_2$, CO$_2$ and CS$_2$, is a material whose phases known experimentally up to 6 GPa exhibit 1D chain-like, 2D layered and 3D tetrahedral structures. We present highly predictive $ab$ $initio$ calculations combined with evolutionary structure search and molecular dynamics simulations of the structural and electronic evolution of SiS$_2$ up to 100 GPa. A highly stable CdI$_2$-type layered structure, which is octahedrally coordinated with space group $P\bar{3}m1$ surprisingly appears between 4 and up to at least 100 GPa. The tetrahedral-octahedral switch is naturally expected upon compression, unlike the layered character realized here by edge-sharing SiS$_6$ octahedral units connecting within but not among sheets. The predicted phase is semiconducting with an indirect band gap of about 2 eV at 10 GPa, decreasing under pressure until metallization around 40 GPa. The robustness of the layered phase suggests possible recovery at ambient pressure, where calculated phonon spectra indicate dynamical stability. Even a single monolayer is found to be dynamically stable in isolation, suggesting that it could possibly be sheared or exfoliated from bulk $P\bar{3}m1$-SiS$_2$., Comment: 12 pages, 9 Figures

Scanning tunnelling microscopy and break-junction experiments realize metallic and molecular nanocontacts that act as ideal one-dimensional channels between macroscopic electrodes. Emergent nanoscale phenomena typical of these systems encompass structural, mechanical, electronic, transport, and magnetic properties. This Review focuses on the theoretical explanation of some of these properties obtained with the help of first-principles methods. By tracing parallel theoretical and experimental developments from the discovery of nanowire formation and conductance quantization in gold nanowires to recent observations of emergent magnetism and Kondo correlations, we exemplify the main concepts and ingredients needed to bring together ab initio calculations and physical observations. It can be anticipated that diode, sensor, spin-valve and spin-filter functionalities relevant for spintronics and molecular electronics applications will benefit from the physical understanding thus obtained.

Layered molybdenum dichalchogenides are semiconductors whose gap is controlled by delicate interlayer interactions. The gap tends to drop together with the interlayer distance, suggesting collapse and metallization under pressure. We predict, based on first principles calculations, that layered semiconductors 2H$_c$-MoSe$_2$ and 2H$_c$-MoTe$_2$ should undergo metallization at pressures between 28 and 40 GPa (MoSe$_2$) and 13 and 19 GPa (MoTe$_2$). Unlike MoS$_2$ where a 2H$_c$ $\to$ 2H$_a$ layer sliding transition is known to take place, these two materials appear to preserve the original 2H$_c$ layered structure at least up to 100 GPa and to increasingly resist lubric layer sliding under pressure. Similar to metallized MoS$_2$ they are predicted to exhibit a low density of states at the Fermi level, and presumably very modest superconducting temperatures if any. We also study the $\beta$-MoTe$_2$ structure, metastable with a higher enthalpy than 2H$_c$-MoTe$_2$. Despite its ready semimetallic and (weakly) superconducting character already at zero pressure, metallicity is not expected to increase dramatically with pressure.

Accessing, controlling and understanding nanoscale friction and dissipation is a crucial issue in nanotechnology, where moving elements are central. Recently, ultra-sensitive noncontact pendulum Atomic Force Microscope (AFM) succeeded in detecting the electronic friction drop caused by the onset of superconductivity in Nb, raising hopes that a wider variety of mechanisms of mechanical dissipation arising from electron organization into different collective phenomena will become accessible through this unconventional surface probe. Among them, the driven phase dynamics of charge-density-waves (CDWs) represents an outstanding challenge as a source of dissipation. Here we report a striking multiplet of AFM dissipation peaks arising at nanometer distances above the surface of NbSe$_2$ - a layered compound exhibiting an incommensurate CDW. Each peak appears at a well defined tip-surface interaction force of the order of a nN, and persists until T=70K where CDW short-range order is known to disappear. A theoretical model is presented showing that the peaks are connected to tip-induced local 2$\pi$ CDW phase slips. Under the attractive potential of the approaching tip, the local CDW surface phase landscape deforms continuously until a series of 2$\pi$ jumps occur between different values of the local phase. As the tip oscillates to and fro, each slip gives rise to a hysteresis cycle, appearing at a selected distance, the dissipation corresponding to "pumping" in and out a local slip in the surface CDW phase of NbSe$_2$., Comment: 9 pages, 8 figures

The sliding of three-dimensional clusters and two-dimensional islands adsorbed on crystal surfaces represent an important test case to understand friction. Even for the same material, monoatomic islands and thick clusters will not as a rule exhibit the same friction, but specific differences have not been explored. Through realistic molecular dynamics simulations of the static friction gold on graphite, an experimentally relevant system, we uncover as a function of gold thickness a progressive drop of static friction from monolayer islands, that are easily pinned, towards clusters, that slide more readily. The main ingredient contributing to this thickness-induced lubricity appears to be the increased effective rigidity of the atomic contact, acting to reduce the cluster interdigitation with the substrate. A second element which plays a role is lateral contact size, which can accommodate the solitons typical of the incommensurate interface only above a critical contact diameter, which is larger for monolayer islands than for thick clusters. The two effects concur to make clusters more lubric than islands, and large sizes more lubric than smaller ones. These conclusions are expected to be of broader applicability in diverse nanotribological systems, where the role played by static, and dynamic, friction is generally quite important., Comment: Nanoscale, 2016

Cold ions sliding across periodic potential patterns formed by lasers elucidate the physics of dry friction between crystals. Experiments with no more than six ions suffice to explore a vast domain of frictional forces., Comment: 2 pages, 1 Figure

We consider non-equilibrium phenomena in a very simple model that displays a zero-temperature first-order phase transition. The quantum Ising model with a four-spin exchange is adopted as a general representative of first-order quantum phase transitions that belong to the Ising universality class, such as for instance the order-disorder ferroelectric transitions, and possibly first-order T = 0 Mott transitions. In particular, we address quantum quenches in the exactly solvable limit of infinite connectivity and show that, within the coexistence region around the transition, the system can remain trapped in a metastable phase, as long as it is spatially homogeneous so that nucleation can be ignored. Motivated by the physics of nucleation, we then study in the same model static but inhomogeneous phenomena that take place at surfaces and interfaces. The first order nature implies that both phases remain locally stable across the transition, and with that the possibility of a metastable wetting layer showing up at the surface of the stable phase, even at T=0. We use mean-field theory plus quantum fluctuations in the harmonic approximation to study quantum surface wetting.

We investigate theoretically the possibility to observe dynamical mode locking, in the form of Shapiro steps, when a time-periodic potential or force modulation is applied to a two-dimensional (2D) lattice of colloidal particles that are dragged by an external force over an optically generated periodic potential. Here we present realistic molecular dynamics simulations of a 2D experimental setup, where the colloid sliding is realized through the motion of soliton lines between locally commensurate patches or domains, and where the Shapiro steps are predicted and analyzed. Interestingly, the jump between one step and the next is seen to correspond to a fixed number of colloids jumping from one patch to the next, across the soliton line boundary, during each AC cycle. In addition to ordinary "integer" steps, coinciding here with the synchronous rigid advancement of the whole colloid monolayer, our main prediction is the existence of additional smaller "subharmonic" steps due to localized solitonic regions of incommensurate layers executing synchronized slips, while the majority of the colloids remains pinned to a potential minimum. The current availability and wide parameter tunability of colloid monolayers makes these predictions potentially easy to access in an experimentally rich 2D geometrical configuration.

Recent measurements suggest the possibility to exploit ionic liquids (ILs) as smart lubricants for nano-contacts, tuning their tribological and rheological properties by charging the sliding interfaces. Following our earlier theoretical study of charging effects on nanoscale confinement and squeezout of a model IL, we present here molecular dynamics simulations of the frictional and lubrication properties of that model under charging conditions.First we describe the case when two equally charged plates slide while being held together to a confinement distance of a few molecular layers.The shear sliding stress is found to rise as the number of IL layers decreases stepwise. However the shear stress shows, within each given number of layers, only a weak dependence upon the precise value of the normal load, a result in agreement with data extracted from recent experiments.We subsequently describe the case of opposite charging of the sliding plates, and follow the shear stress when the charging is slowly and adiabatically reversed in the course of time, under fixed load. Despite the fixed load, the number and structure of the confined IL layers changes with changing charge, and that in turn drives strong friction variations. The latter involve first of all charging-induced freezing of the IL film, followed by a discharging-induced melting, both made possible by the nanoscale confinement. Another mechanism for charging-induced frictional changes is a shift of the plane of maximum shear from mid-film to the plate-film interface, and viceversa. While these occurrences and results invariably depend upon the parameters of the model IL and upon its specific interaction with the plates, the present study helps identifying a variety of possible behavior, obtained under very simple assumptions, while connecting it to an underlying equilibrium thermodynamics picture., Comment: 11 pages, 13 figures