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Exciton-phonon coupling (ExPC) is crucial for energy relaxation in semiconductors, yet the first-principles calculation of such coupling remains challenging, especially for two-dimensional (2D) systems. Here, an accurate method for calculating ExPC is developed and applied in exciton relaxation problems in monolayer WSe 2 . Considering the interplay between the exciton wave functions and electron-phonon coupling (EPC) matrix elements, we find that ExPC shows selection rules distinct from the ones of EPC. By employing the Wannier exciton model, we generalize these selection rules, which state that the angular quantum numbers of the exciton must match the winding numbers of the EPC matrix elements for the ExPC to be allowed. To verify our theory and method, we calculate intervalley exciton relaxation pathways, which agree well with a recent experiment.

Low-dimensional water transport can be drastically enhanced under atomic-scale confinement. However, its microscopic origin is still under debate. In this work, we directly imaged the atomic structure and transport of two-dimensional water islands on graphene and hexagonal boron nitride surfaces using qPlus-based atomic force microscopy. The lattice of the water island was incommensurate with the graphene surface but commensurate with the boron nitride surface owing to different surface electrostatics. The area-normalized static friction on the graphene diminished as the island area was increased by a power of ~-0.58, suggesting superlubricity behavior. By contrast, the friction on the boron nitride appeared insensitive to the area. Molecular dynamic simulations further showed that the friction coefficient of the water islands on the graphene could reduce to <0.01.

Ice surfaces are closely relevant to many physical and chemical properties, such as melting, freezing, friction, gas uptake and atmospheric reaction 1-8 . Despite extensive experimental and theoretical investigations 9-17 , the exact atomic structures of ice interfaces remain elusive owing to the vulnerable hydrogen-bonding network and the complicated premelting process. Here we realize atomic-resolution imaging of the basal (0001) surface structure of hexagonal water ice (ice Ih) by using qPlus-based cryogenic atomic force microscopy with a carbon monoxide-functionalized tip. We find that the crystalline ice-Ih surface consists of mixed Ih- and cubic (Ic)-stacking nanodomains, forming 19 × 19 periodic superstructures. Density functional theory reveals that this reconstructed surface is stabilized over the ideal ice surface mainly by minimizing the electrostatic repulsion between dangling OH bonds. Moreover, we observe that the ice surface gradually becomes disordered with increasing temperature (above 120 Kelvin), indicating the onset of the premelting process. The surface premelting occurs from the defective boundaries between the Ih and Ic domains and can be promoted by the formation of a planar local structure. These results put an end to the longstanding debate on ice surface structures and shed light on the molecular origin of ice premelting, which may lead to a paradigm shift in the understanding of ice physics and chemistry., (© 2024. The Author(s), under exclusive licence to Springer Nature Limited.)

The permeability and selectivity of biological and artificial ion channels correlate with the specific hydration structure of single ions. However, fundamental understanding of the effect of ion-ion interaction remains elusive. Here, via non-contact atomic force microscopy measurements, we demonstrate that hydrated alkali metal cations (Na + and K + ) at charged surfaces could come into close contact with each other through partial dehydration and water rearrangement processes, forming one-dimensional chain structures. We prove that the interplay at the nanoscale between the water-ion and water-water interaction can lead to an effective ion-ion attraction overcoming the ionic Coulomb repulsion. The tendency for different ions to become closely packed follows the sequence K +  > Na +  > Li + , which is attributed to their different dehydration energies and charge densities. This work highlights the key role of water molecules in prompting close packing and concerted movement of ions at charged surfaces, which may provide new insights into the mechanism of ion transport under atomic confinement., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

Condensation and arrangement of ions at water-solid interfaces are of great importance in the formation of electrical double layers (EDL) and the transport of ions under a confined geometry. So far, the microscopic understanding of interfacial ion configurations is still far from complete, especially when the local ion concentration is high and ion-ion interactions become prominent. In this study, we directly visualized alkali metal cations within the hydrogen-bonding network of water on graphite and Cu(111)-supported graphene surfaces, using qPlus-based noncontact atomic force microscopy (NC-AFM). We found that the codeposition of the alkali cations and water molecules on the hydrophobic graphite surface leads to the formation of an ion-doped bilayer hexagonal ice (BHI) structure, where the ions are repelled from each other and scattered in a disordered distribution. In contrast, the hydrated alkali cations aggregate in one dimension on the more hydrophilic graphene/Cu(111) surface, forming a nematic state with a long-range order. Such a nematic state arises from the delicate interplay between water-ion and water-water interactions under surface confinement. These results reveal the high sensitivity of ion-ion interactions and ionic ordering to the surface hydrophobicity and hydrophilicity.

Light confinement in nanostructures produces an enhanced light-matter interaction that enables a vast range of applications including single-photon sources, nanolasers and nanosensors. In particular, nanocavity-confined polaritons display a strongly enhanced light-matter interaction in the infrared regime. This interaction could be further boosted if polaritonic modes were moulded to form whispering-gallery modes; but scattering losses within nanocavities have so far prevented their observation. Here, we show that hexagonal BN nanotubes act as an atomically smooth nanocavity that can sustain phonon-polariton whispering-gallery modes, owing to their intrinsic hyperbolic dispersion and low scattering losses. Hyperbolic whispering-gallery phonon polaritons on BN nanotubes of ～4 nm radius (sidewall of six atomic layers) are characterized by an ultrasmall nanocavity mode volume (V m  ≈ 10 -10 λ 0 3 at an optical wavelength λ 0  ≈ 6.4 μm) and a Purcell factor (Q/V m ) as high as 10 12 . We posit that BN nanotubes could become an important material platform for the realization of one-dimensional, ultrastrong light-matter interactions, with exciting implications for compact photonic devices., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

Isotopic mixtures result in distinct properties of materials such as thermal conductivity and nuclear process. However, the knowledge of isotopic interface remains largely unexplored mainly due to the challenges in atomic-scale isotopic identification. Here, using electron energy-loss spectroscopy in a scanning transmission electron microscope, we reveal momentum-transfer-dependent phonon behavior at the h- 10 BN/h- 11 BN isotope heterostructure with sub-unit-cell resolution. We find the phonons' energy changes gradually across the interface, featuring a wide transition regime. Phonons near the Brillouin zone center have a transition regime of ~3.34 nm, whereas phonons at the Brillouin zone boundary have a transition regime of ~1.66 nm. We propose that the isotope-induced charge effect at the interface accounts for the distinct delocalization behavior. Moreover, the variation of phonon energy between atom layers near the interface depends on both of momentum transfer and mass change. This study provides new insights into the isotopic effects in natural materials., (© 2023. The Author(s).)

We applied the harmonic inversion technique to extract vibrational eigenvalues from the semiclassical initial value representation (SC-IVR) propagator of molecular systems described by explicit potential surfaces. The cross-correlation filter-diagonalization (CCFD) method is used for the inversion problem instead of the Fourier transformation, which allows much shorter propagation time and is thus capable of avoiding numerical divergence issues while getting rid of approximations like the separable one to the pre-exponential factor. We also used the "Divide-and-Conquer" technique to control the total dimensions under consideration, which helps to further enhance the numerical behavior of SC-IVR calculations and the stability of harmonic inversion methods. The technique is tested on small molecules and water trimer to justify its applicability and reliability. Results show that the CCFD method can effectively extract the vibrational eigenvalues from short trajectories and reproduce the original spectra conventionally obtained from long-time ones, with no loss on accuracy while the numerical behavior is much better. This work demonstrates the possibility to apply the combined method of CCFD and SC-IVR to real molecular potential surfaces, which might be a new way to overcome the numerical instabilities caused by the increase of dimensions.

The nature of hydrated proton on solid surfaces is of vital importance in electrochemistry, proton channels, and hydrogen fuel cells but remains unclear because of the lack of atomic-scale characterization. We directly visualized Eigen- and Zundel-type hydrated protons within the hydrogen bonding water network on Au(111) and Pt(111) surfaces, using cryogenic qPlus-based atomic force microscopy under ultrahigh vacuum. We found that the Eigen cations self-assembled into monolayer structures with local order, and the Zundel cations formed long-range ordered structures stabilized by nuclear quantum effects. Two Eigen cations could combine into one Zundel cation accompanied with a simultaneous proton transfer to the surface. Moreover, we revealed that the Zundel configuration was preferred over the Eigen on Pt(111), and such a preference was absent on Au(111).

The breakdown of translational symmetry at heterointerfaces leads to the emergence of new phonon modes localized at the interface 1 . These modes have an essential role in thermal and electrical transport properties in devices, especially in miniature ones wherein the interface may dominate the entire response of the device 2 . Although related theoretical work began decades ago 1,3-5 , experimental research is totally absent owing to challenges in achieving the combined spatial, momentum and spectral resolutions required to probe localized modes. Here, using the four-dimensional electron energy-loss spectroscopy technique, we directly measure both the local vibrational spectra and the interface phonon dispersion relation for an epitaxial cubic boron nitride/diamond heterointerface. In addition to bulk phonon modes, we observe modes localized at the interface and modes isolated from the interface. These features appear only within approximately one nanometre around the interface. The localized modes observed here are predicted to substantially affect the interface thermal conductance and electron mobility. Our findings provide insights into lattice dynamics at heterointerfaces, and the demonstrated experimental technique should be useful in thermal management, electrical engineering and topological phononics., (© 2021. The Author(s), under exclusive licence to Springer Nature Limited.)

Phonon polaritons enable light confinement at deep subwavelength scales, with potential technological applications, such as subdiffraction imaging, sensing and engineering of spontaneous emission. However, the trade-off between the degree of confinement and the excitation efficiency of phonon polaritons prevents direct observation of these modes in monolayer hexagonal boron nitride (h-BN), where they are expected to reach ultrahigh confinement. Here, we use monochromatic electron energy-loss spectroscopy (about 7.5 meV energy resolution) in a scanning transmission electron microscope to measure phonon polaritons in monolayer h-BN, directly demonstrating the existence of these modes as the phonon Reststrahlen band (RS) disappears. We find phonon polaritons in monolayer h-BN to exhibit high confinement (>487 times smaller wavelength than that of light in free space) and ultraslow group velocity down to about 10 -5 c. The large momentum compensation provided by electron beams additionally allows us to excite phonon polaritons over nearly the entire RS band of multilayer h-BN. These results open up a broad range of opportunities for the engineering of metasurfaces and strongly enhanced light-matter interactions.

The hydrogen-bonding networks of water have strong intra- and intermolecular vibrational coupling which influences the energy dissipation and proton transfer in water. Disentangling and quantitative characterization of different coupling effects in water at a single-molecular level still remains a great challenge. Using tip-enhanced inelastic electron tunneling spectroscopy (IETS) based on low-temperature scanning tunneling microscopy, we report the direct quantitative assessment of the intermolecular coupling constants of the OH-stretch vibrational bands of an isolated water tetramer adsorbed on a Au(111)-supported NaCl(001) bilayer film. This is achieved by distinguishing various coupled modes of the H-bonded O-H stretching vibrations through tip-height dependent IET spectra. In contrast, such vibrational coupling is negligible in the half-deuterated water tetramer owing to the large energy mismatch between the OH and OD stretching modes. Not only do these findings advance our understanding on the effects of local environment on the intermolecular vibrational coupling in water, but also open up a new route for vibrational spectroscopic studies of extended H-bonded network at the single-molecular level.

The formation and growth of water-ice layers on surfaces and of low-dimensional ice under confinement are frequent occurrences 1-4 . This is exemplified by the extensive reporting of two-dimensional (2D) ice on metals 5-11 , insulating surfaces 12-16 , graphite and graphene 17,18 and under strong confinement 14,19-22 . Although structured water adlayers and 2D ice have been imaged, capturing the metastable or intermediate edge structures involved in the 2D ice growth, which could reveal the underlying growth mechanisms, is extremely challenging, owing to the fragility and short lifetime of those edge structures. Here we show that noncontact atomic-force microscopy with a CO-terminated tip (used previously to image interfacial water with minimal perturbation) 12 , enables real-space imaging of the edge structures of 2D bilayer hexagonal ice grown on a Au(111) surface. We find that armchair-type edges coexist with the zigzag edges usually observed in 2D hexagonal crystals, and freeze these samples during growth to identify the intermediate edge structures. Combined with simulations, these experiments enable us to reconstruct the growth processes that, in the case of the zigzag edge, involve the addition of water molecules to the existing edge and a collective bridging mechanism. Armchair edge growth, by contrast, involves local seeding and edge reconstruction and thus contrasts with conventional views regarding the growth of bilayer hexagonal ices and 2D hexagonal matter in general.

The development of bifunctional catalysts for oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) is highly desirable for fuel cells and rechargeable metal-air batteries. Till now, it is still challenging to achieve both efficient activities on a single commercial noble-metal catalyst. Recently, N, P co-doped graphene has shown good bifunctional evidence. However, the atomic-scale understanding of the bifunctional mechanism is still lacking. Here, we show that the N and P atoms prefer to bond with each other, forming embedded N-P clusters in graphene. The catalytic performances of the N-P clusters are sensitive to their geometries, especially the N:P ratios. The N:P ratio of ∼2 is optimal for OER, while ∼3 is optimal for ORR. Through evaluating the ORR/OER potential gaps, we found that the N-P cluster designated as N C 2 P C 1 shows both the high performances of ORR and OER, responsible for the unique bifunctionality in the N, P co-doped graphene.

In this Letter, the links to Supplementary Videos 5, 7, 9 and 10 were incorrect, and there were some formatting errors in the Supplementary Video legends. These errors have been corrected online.

Ion hydration and transport at interfaces are relevant to a wide range of applied fields and natural processes 1-5 . Interfacial effects are particularly profound in confined geometries such as nanometre-sized channels 6-8 , where the mechanisms of ion transport in bulk solutions may not apply 9,10 . To correlate atomic structure with the transport properties of hydrated ions, both the interfacial inhomogeneity and the complex competing interactions among ions, water and surfaces require detailed molecular-level characterization. Here we constructed individual sodium ion (Na + ) hydrates on a NaCl(001) surface by progressively attaching single water molecules (one to five) to the Na + ion using a combined scanning tunnelling microscopy and noncontact atomic force microscopy system. We found that the Na + ion hydrated with three water molecules diffuses orders of magnitude more quickly than other ion hydrates. Ab initio calculations revealed that such high ion mobility arises from the existence of a metastable state, in which the three water molecules around the Na + ion can rotate collectively with a rather small energy barrier. This scenario would apply even at room temperature according to our classical molecular dynamics simulations. Our work suggests that anomalously high diffusion rates for specific hydration numbers of ions are generally determined by the degree of symmetry match between the hydrates and the surface lattice.

Proton tunneling is an elementary process in the dynamics of hydrogen-bonded systems. Collective tunneling is known to exist for a long time. Atomistic investigations of this mechanism in realistic systems, however, are scarce. Using a combination of ab initio theoretical and high-resolution experimental methods, we investigate the role played by the protons on the chirality switching of a water tetramer on NaCl(001). Our scanning tunneling spectroscopies show that partial deuteration of the H 2 O tetramer with only one D 2 O leads to a significant suppression of the chirality switching rate at a cryogenic temperature (T), indicating that the chirality switches by tunneling in a concerted manner. Theoretical simulations, in the meantime, support this picture by presenting a much smaller free-energy barrier for the translational collective proton tunneling mode than other chirality switching modes at low T. During this analysis, the virial energy provides a reasonable estimator for the description of the nuclear quantum effects when a traditional thermodynamic integration method cannot be used, which could be employed in future studies of similar problems. Given the high-dimensional nature of realistic systems and the topology of the hydrogen-bonded network, collective proton tunneling may exist more ubiquitously than expected. Systems of this kind can serve as ideal platforms for studies of this mechanism, easily accessible to high-resolution experimental measurements.

Recent experiments have triggered a debate about the ability of protons to transfer easily through individual layers of graphene and hexagonal boron nitride (h-BN). However, state-of-the-art computer calculations have shown that the barriers to proton penetration can, at >3 eV, be excessively high. Despite considerable interest the origin of this apparent anomaly between experiment and simulation remains unclear. We offer a new perspective on this debate and show on the basis of first-principles calculations that the barrier for proton penetration is significantly reduced, to <1 eV, upon hydrogenation, even in the absence of pinholes in the lattice. Although hydrogenation has not been offered as an explanation before, analysis reveals that the barrier is reduced because hydrogenation destabilizes the initial state (a deep-lying chemisorption state) and expands the honeycomb lattice through which the protons penetrate. This study offers a rationalization of the fast proton transfer observed in experiments and highlights the ability of proton transport through single-layer materials in hydrogen-rich solutions.

Although the size effect in ferroelectric thin films has been known for long time, the underlying mechanism is not yet fully understood and whether or not there is a critical thickness below which the ferroelectricity vanishes is still under debate. Here, we directly measure the thickness-dependent polarization in ultrathin PbZr 0.2 Ti 0.8 O 3 films via quantitative annular bright field imaging. We find that the polarization is significantly suppressed for films <10-unit cells thick (∼4 nm). However, approximately the polarization never vanishes. The residual polarization is ∼16 μCcm -2 (∼17%) at 1.5-unit cells (∼0.6 nm) thick film on bare SrTiO 3 and ∼22 μCcm -2 at 2-unit cells thick film on SrTiO 3 with SrRuO 3 electrode. The residual polarization in these ultrathin films is mainly attributed to the robust covalent Pb-O bond. Our atomic study provides new insights into mechanistic understanding of nanoscale ferroelectricity and the size effects.

In the rechargeable lithium ion batteries, the rate capability and energy efficiency are largely governed by the lithium ion transport dynamics and phase transition pathways in electrodes. Real-time and atomic-scale tracking of fully reversible lithium insertion and extraction processes in electrodes, which would ultimately lead to mechanistic understanding of how the electrodes function and why they fail, is highly desirable but very challenging. Here, we track lithium insertion and extraction in the van der Waals interactions dominated SnS2 by in situ high-resolution TEM method. We find that the lithium insertion occurs via a fast two-phase reaction to form expanded and defective LiSnS2, while the lithium extraction initially involves heterogeneous nucleation of intermediate superstructure Li0.5SnS2 domains with a 1-4 nm size. Density functional theory calculations indicate that the Li0.5SnS2 is kinetically favored and structurally stable. The asymmetric reaction pathways may supply enlightening insights into the mechanistic understanding of the underlying electrochemistry in the layered electrode materials and also suggest possible alternatives to the accepted explanation of the origins of voltage hysteresis in the intercalation electrode materials.

At the ferroelectric surface, the broken translational symmetry induced bound charge should significantly alter the local atomic configurations. Experimentally revealing the atomic structure of ferroelectric surface, however, is very challenging due to the strong spatial variety between nano-sized domains, and strong interactions between the polarization and other structural parameters. Here, we study surface structures of Pb(Zr0.2Ti0.8)O3 thin film by using the annular bright-field imaging. We find that six atomic layers with suppressed polarization and a charged 180° domain wall are at negatively poled surfaces, no reconstruction exists at positively poled surfaces, and seven atomic layers with suppressed polarization and a charged 90° domain wall exist at nominally neutral surfaces in ferroelastic domains. Our results provide critical insights into engineering ferroelectric thin films, fine grain ceramics and surface chemistry devices. The state-of-the-art methodology demonstrated here can greatly advance our understanding of surface science for oxides.

We report the quantitative assessment of nuclear quantum effects on the strength of a single hydrogen bond formed at a water-salt interface, using tip-enhanced inelastic electron tunneling spectroscopy based on a scanning tunneling microscope. The inelastic scattering cross section was resonantly enhanced by "gating" the frontier orbitals of water via a chlorine-terminated tip, so the hydrogen-bonding strength can be determined with high accuracy from the red shift in the oxygen-hydrogen stretching frequency of water. Isotopic substitution experiments combined with quantum simulations reveal that the anharmonic quantum fluctuations of hydrogen nuclei weaken the weak hydrogen bonds and strengthen the relatively strong ones. However, this trend can be completely reversed when a hydrogen bond is strongly coupled to the polar atomic sites of the surface., (Copyright © 2016, American Association for the Advancement of Science.)

Water-solid interactions are of broad importance both in nature and technology. The hexagonal bilayer model based on the Bernal-Fowler-Pauling ice rules has been widely adopted to describe water structuring at interfaces. Using a cryogenic scanning tunnelling microscope, here we report a new type of two-dimensional ice-like bilayer structure built from cyclic water tetramers on an insulating NaCl(001) film, which is completely beyond this conventional bilayer picture. A novel bridging mechanism allows the interconnection of water tetramers to form chains, flakes and eventually a two-dimensional extended ice bilayer containing a regular array of Bjerrum D-type defects. Ab initio density functional theory calculations substantiate this bridging growth mode and reveal a striking proton-disordered ice structure. The formation of the periodic Bjerrum defects with unusually high density may have a crucial role as H donor sites in directing multilayer ice growth and in catalysing heterogeneous chemical reactions on water-coated salt surfaces.