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This survey concerns regular graphs that are extremal with respect to the number of independent sets and, more generally, graph homomorphisms. More precisely, in the family of of d-regular graphs, which graph G maximizes/minimizes the quantity i(G) 1/v(G) , the number of independent sets in G normalized exponentially by the size of G? What if i(G) is replaced by some other graph parameter? We review existing techniques, highlight some exciting recent developments, and discuss open problems and conjectures for future research.

HighlightsThe electrochemical principles/mechanism of Li–S batteries and origin of the shuttle effect have been discussed.The efficient strategies have been summarized to inhibit the shuttle effect.The recent advances of inhibition of shuttle effect in Li–S batteries for all components from anode to cathode.Lithium–sulfur (Li–S) batteries are supposed to be one of the most potential next-generation batteries owing to their high theoretical capacity and low cost. Nevertheless, the shuttle effect of firm multi-step two-electron reaction between sulfur and lithium in liquid electrolyte makes the capacity much smaller than the theoretical value. Many methods were proposed for inhibiting the shuttle effect of polysulfide, improving corresponding redox kinetics and enhancing the integral performance of Li–S batteries. Here, we will comprehensively and systematically summarize the strategies for inhibiting the shuttle effect from all components of Li–S batteries. First, the electrochemical principles/mechanism and origin of the shuttle effect are described in detail. Moreover, the efficient strategies, including boosting the sulfur conversion rate of sulfur, confining sulfur or lithium polysulfides (LPS) within cathode host, confining LPS in the shield layer, and preventing LPS from contacting the anode, will be discussed to suppress the shuttle effect. Then, recent advances in inhibition of shuttle effect in cathode, electrolyte, separator, and anode with the aforementioned strategies have been summarized to direct the further design of efficient materials for Li–S batteries. Finally, we present prospects for inhibition of the LPS shuttle and potential development directions in Li–S batteries.

Chirality-induced spin selectivity (CISS) generates giant spin polarization in transport through chiral molecules, paving the way for novel spintronic devices and enantiomer separation. Unlike conventional transport, CISS magnetoresistance (MR) violates Onsager’s reciprocal relation, exhibiting significant resistance changes when reversing electrode magnetization at zero bias. However, its underlying mechanism remains unresolved. In this work, we propose that CISS MR originates from charge trapping that modifies the electron tunneling barrier and circumvents Onsager’s relation, distinct from previous spin polarization-based models. Charge trapping is governed by the non-Hermitian skin effect, where dissipation leads to exponential wavefunction localization at the ferromagnet-chiral molecule interface. Reversing magnetization or chirality alters the localization direction, changing the occupation of impurity/defect states in the molecule ( i.e ., charge trapping) – a phenomenon we term magnetochiral charge pumping. Our theory explains why CISS MR can far exceed the ferromagnet spin polarization and why chiral molecules violate the reciprocal relation but chiral metals do not. Furthermore, it predicts exotic phenomena beyond the conventional CISS framework, including asymmetric MR induced by magnetic fields alone (without ferromagnetic electrodes), as confirmed by recent experiments. This work offers a deeper understanding of CISS and opens avenues for controlling electrostatic interactions in chemical and biological systems through the magnetochiral charge pumping. Some chiral molecules can produce a giant spin polarization, a feature termed chirality-induced spin selectivity. The origin of this has been hotly debated. In this theory work, Zhao, Zhang and coauthors propose that the origin of the effect lies in charge trapping induced barrier modification, termed magnetochiral charge pumping.

The topological surface states of magnetic topological systems, such as Weyl semimetals and axion insulators, are associated with unconventional transport properties such as nonzero or half-quantized surface anomalous Hall effect. Here we study the surface anomalous Hall effect and its spectral signatures in different magnetic topological phases using both model Hamiltonian and first-principles calculations. We demonstrate that by tailoring the magnetization and interlayer electron hopping, a rich three-dimensional topological phase diagram can be established, including three types of topologically distinct insulating phases bridged by Weyl semimetals, and can be directly mapped to realistic materials such as MnBi 2 Te 4 /(Bi 2 Te 3 ) n systems. Among them, we find that the surface anomalous Hall conductivity in the axion-insulator phase is a well-localized quantity either saturated at or oscillating around e 2 /2 h , depending on the magnetic homogeneity. We also discuss the resultant chiral hinge modes embedded inside the side surface bands as the potential experimental signatures for transport measurements. Our study is a significant step forward towards the direct realization of the long-sought axion insulators in realistic material systems. Experimentally detectable signature of an axion insulator remains elusive. Here, the authors predict a topological phase diagram of MnBi 2 Te 4 /(Bi 2 Te 3 ) n heterostructure, where the chiral hinge mode induced by the surface anomalous Hall conductivity is identified as a signature of an axion insulator state.

Platinum is the most efficient catalyst for hydrogen evolution reaction in acidic conditions, but its widespread use has been impeded by scarcity and high cost. Herein, Pt atomic clusters (Pt ACs) containing Pt-O-Pt units were prepared using Co/N co-doped carbon (CoNC) as support. Pt ACs are anchored to single Co atoms on CoNC by forming strong interactions. Pt-ACs/CoNC exhibits only 24 mV overpotential at 10 mA cm −2 and a high mass activity of 28.6 A mg −1 at 50 mV, which is more than 6 times higher than commercial Pt/C with any Pt loadings. Spectroscopic measurements and computational modeling reveal the enhanced hydrogen generation activity attributes to the charge redistribution between Pt and O atoms in Pt-O-Pt units, making Pt atoms the main active sites and O linkers the assistants, thus optimizing the proton adsorption and hydrogen desorption. This work opens an avenue to fabricate noble-metal-based ACs stabilized by single-atom catalysts with desired properties for electrocatalysis. Modulating single-metal sites at the atomic level can boost the intrinsic catalytic activity. Here, the authors describe the design of Pt atomic clusters containing Pt-O-Pt units supported on Co single atoms and N co-doped carbon for enhanced hydrogen evolution catalysis.

Synthesis of mesoporous graphene materials by soft-template methods remains a great challenge, owing to the poor self-assembly capability of precursors and the severe agglomeration of graphene nanosheets. Herein, a micelle-template strategy to prepare porous graphene materials with controllable mesopores, high specific surface areas and large pore volumes is reported. By fine-tuning the synthesis parameters, the pore sizes of mesoporous graphene can be rationally controlled. Nitrogen heteroatom doping is found to remarkably render electrocatalytic properties towards hydrogen evolution reactions as a highly efficient metal-free catalyst. The synthesis strategy and the demonstration of highly efficient catalytic effect provide benchmarks for preparing well-defined mesoporous graphene materials for energy production applications.

Abstract Aortic dissection is a life-threatening condition for which diagnosis mainly relies on imaging examinations, while reliable biomarkers to detect or monitor are still under investigation. Recent advances in technologies provide an unprecedented opportunity to yield the identification of clinically valuable biomarkers, including proteins, ribonucleic acids (RNAs), and deoxyribonucleic acids (DNAs), for early detection of pathological changes in susceptible patients, rapid diagnosis at the bedside after onset, and a superior therapeutic regimen primarily within the concept of personalized and tailored endovascular therapy for aortic dissection.

Here, resistance of such a dielectric layer changes dramatically upon charge trapping/detrapping (see Fig. 1), insensitive to the bias direction. [...]CISS MR bypasses the constraint of Onsager’s reciprocal relation, different from the electric magnetochiral anisotropy (EMCA). [...]the charge accumulation is induced and maintained by the current. [...]charge trapping is nonvolatile while the charge accumulation is volatile. (ii) Different from accumulated charge, the trapped charge has a long lifetime and does not leak into electrodes because the trapped electron is confined by a potential in the insulator and effectively isolated from metallic reservoirs. Here, the charge trapping state is not in thermodynamic equilibrium but a metastable state, distinct from the charge accumulation case where node and electrodes maintain connection and balance. (iii) Physically, the charge accumulation occurs usually at the interface between the metal and the semiconductor layer while the charge trapping happens at defects or impurities within the insulating layer. [...]Tirion and van Wees’ model cannot describe such a nonvolatile metastable state for charge trapping because it does not include the nonadiabatic dynamics.

Single-atom catalysts offer a pathway to cost-efficient catalysis using the minimal amount of precious metals. However, preparing and keeping them stable during operation remains a challenge. Here we report the synthesis of double transition metal MXene nanosheets—Mo 2 TiC 2 T x , with abundant exposed basal planes and Mo vacancies in the outer layers—by electrochemical exfoliation, enabled by the interaction between protons and the surface functional groups of Mo 2 TiC 2 T x . The as-formed Mo vacancies are used to immobilize single Pt atoms, enhancing the MXene’s catalytic activity for the hydrogen evolution reaction. The developed catalyst exhibits a high catalytic ability with low overpotentials of 30 and 77 mV to achieve 10 and 100 mA cm −2 and a mass activity about 40 times greater than the commercial platinum-on-carbon catalyst. The strong covalent interactions between positively charged Pt single atoms and the MXene contribute to the exceptional catalytic performance and stability. Single-atom catalysts are very attractive due to their ability to maintain high activities at the lowest possible precious metal loading. Here, a double transition metal MXene that effectively anchors single Pt atoms is reported, and exhibits superior performance and stability towards the hydrogen evolution reaction.

Due to the high theoretical specific energy, the lithium–oxygen battery has been heralded as a promising energy storage system for applications such as electric vehicles. However, its large over-potentials during discharge–charge cycling lead to the formation of side-products, and short cycle life. Herein, we report an ionic liquid bearing the redox active 2,2,6,6-tetramethyl-1-piperidinyloxy moiety, which serves multiple functions as redox mediator, oxygen shuttle, lithium anode protector, as well as electrolyte solvent. The additive contributes a 33-fold increase of the discharge capacity in comparison to a pure ether-based electrolyte and lowers the over-potential to an exceptionally low value of 0.9 V. Meanwhile, its molecule facilitates smooth lithium plating/stripping, and promotes the formation of a stable solid electrolyte interface to suppress side-reactions. Moreover, the proportion of ionic liquid in the electrolyte influences the reaction mechanism, and a high proportion leads to the formation of amorphous lithium peroxide and a long cycling life (> 200 cycles). In particular, it enables an outstanding electrochemical performance when operated in air. Li-O 2 batteries are promising candidates for the next generation of rechargeable batteries, but the side reactions and poor cycling stability limit their applications. Here, the authors show a versatile ionic liquid with functional groups that can address both issues for cells operated in oxygen and air.