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<jats:title>Abstract</jats:title> <jats:p>We have screened 71 two-dimensional (2D) materials with <jats:italic>C</jats:italic> <jats:sub>3</jats:sub> symmetry for non-trivial second order topological order and find that 28 compounds exhibit an obstructed atomic limit (OAL). In the case of <jats:italic>C</jats:italic> <jats:sub>3</jats:sub> symmetry, the second order topology can be calculated from bulk symmetry indicator invariants, which predict the value of fractional corner charges in symmetry conserving nanoflakes. The procedure is exemplified by MoS<jats:sub>2</jats:sub> in the H-phase, which constitutes a generic example of a 2D OAL material and the predicted fractional corner charges is verified by direct calculations of nanoflakes with armchair edges. We also determine the bulk topological polarization, which always lead to gapless states at zigzag edges and thus deteriorates the concept of fractional corner charges in nanoflakes with zigzag edges that are typically more stable that armchair flakes. We then consider the case of TiCl<jats:sub>2</jats:sub>, which has vanishing polarization as well as an OAL and we verify that the edge states of nanoflakes with zigzag edges may indeed by passivated such that the edges remain insulating and the corner charges are well defined. For the 28 OAL materials we find that 16 have vanishing polarization and these materials thus constitute a promising starting point for experimental verification of second order topology in a 2D material.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>V<jats:sub>2</jats:sub>CT<jats:italic> <jats:sub>x</jats:sub> </jats:italic> shows a low ion diffusion barrier, while the multiple oxidation states of vanadium allow V<jats:sub>2</jats:sub>CT<jats:italic> <jats:sub>x</jats:sub> </jats:italic> to participate in multi-electron redox reactions, which demonstrates a greater potential for electrochemical energy storage applications. However, the lateral arrangement of V<jats:sub>2</jats:sub>CT<jats:italic> <jats:sub>x</jats:sub> </jats:italic> lamellae tends to cause the accumulation and collapse of the structure. Herein, the two-dimensional layered V<jats:sub>2</jats:sub>CT<jats:italic> <jats:sub>x</jats:sub> </jats:italic> is modified with Ag<jats:sup>+</jats:sup> and Cu<jats:sup>2+</jats:sup>, the V<jats:sub>2</jats:sub>CT<jats:italic> <jats:sub>x</jats:sub> </jats:italic>/Ag/Cu composite is successfully prepared. The Ag nanoparticles (NPs) and Cu NPs grown between the layers of V<jats:sub>2</jats:sub>CT<jats:italic> <jats:sub>x</jats:sub> </jats:italic> can effectively suppress the accumulation of the lamellae and ensure the smooth transfer of electrolyte ions and electrons between the layers. Meanwhile, the doping of Ag NPs and Cu NPs can enlarge the interlayer spacing of V<jats:sub>2</jats:sub>CT<jats:italic> <jats:sub>x</jats:sub> </jats:italic>, which can expose more active contact sites for electrolyte ions, shorten the diffusion path of electrolyte ions, and effectively improve the electrochemical performance of V<jats:sub>2</jats:sub>CT<jats:italic> <jats:sub>x</jats:sub> </jats:italic>. The Ag NPs and Cu NPs agglomerate in the delamination of V<jats:sub>2</jats:sub>CT<jats:italic> <jats:sub>x</jats:sub> </jats:italic> to form a conductive channel covering multiple layers, which facilitates cross-layer electron transfer and reduces the internal resistance of the V<jats:sub>2</jats:sub>CT<jats:italic> <jats:sub>x</jats:sub> </jats:italic>/Ag/Cu composite. Basis on the above reasonable structural designs, the internal resistance of the V<jats:sub>2</jats:sub>CT<jats:italic> <jats:sub>x</jats:sub> </jats:italic>/Ag/Cu composite is only 0.72 Ω, showing excellent diffusion ability of K<jats:sup>+</jats:sup>. The result represents a new step forward in exploring the electrochemical properties of two dimensional materials of V<jats:sub>2</jats:sub>CT<jats:italic> <jats:sub>x</jats:sub> </jats:italic>.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Equilateral triangle-shaped graphene nanoislands with a lateral dimension of <jats:italic>n</jats:italic> benzene rings are known as <jats:inline-formula> <jats:tex-math><?CDATA $[n]$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>[n]</mml:mtext> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tdmaca4e2ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>triangulenes. Individual <jats:inline-formula> <jats:tex-math><?CDATA $[n]$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>[n]</mml:mtext> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tdmaca4e2ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>triangulenes are open-shell molecules, with single-particle electronic spectra that host <jats:italic>n</jats:italic> − 1 half-filled zero modes and a many-body ground state with spin <jats:inline-formula> <jats:tex-math><?CDATA $S = (n-1)/2$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>S</mml:mi> <mml:mo>=</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tdmaca4e2ieqn3.gif" xlink:type="simple" /> </jats:inline-formula>. The on-surface synthesis of triangulenes has been demonstrated for <jats:inline-formula> <jats:tex-math><?CDATA $n = 3,4,5,7$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>7</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tdmaca4e2ieqn4.gif" xlink:type="simple" /> </jats:inline-formula> and the observation of a Haldane symmetry-protected topological phase has been reported in chains of [3]triangulenes. Here, we provide a unified theory for the electronic properties of a family of two-dimensional honeycomb lattices whose unit cell contains a pair of triangulenes with dimensions <jats:inline-formula> <jats:tex-math><?CDATA $n_a,n_b$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tdmaca4e2ieqn5.gif" xlink:type="simple" /> </jats:inline-formula>. Combining density functional theory and tight-binding calculations, we find a wealth of half-filled narrow bands, including a graphene-like spectrum (for <jats:inline-formula> <jats:tex-math><?CDATA $n_a = n_b = 2$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tdmaca4e2ieqn6.gif" xlink:type="simple" /> </jats:inline-formula>), spin-1 Dirac electrons (for <jats:inline-formula> <jats:tex-math><?CDATA $n_a = 2,n_b = 3$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tdmaca4e2ieqn7.gif" xlink:type="simple" /> </jats:inline-formula>), <jats:inline-formula> <jats:tex-math><?CDATA $p_{x,y}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tdmaca4e2ieqn8.gif" xlink:type="simple" /> </jats:inline-formula>-orbital physics (for <jats:inline-formula> <jats:tex-math><?CDATA $n_a = n_b = 3$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tdmaca4e2ieqn9.gif" xlink:type="simple" /> </jats:inline-formula>), as well as a gapped system with flat valence and conduction bands (for <jats:inline-formula> <jats:tex-math><?CDATA $n_a = n_b = 4$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tdmaca4e2ieqn10.gif" xlink:type="simple" /> </jats:inline-formula>). All these results are rationalized with a class of effective Hamiltonians acting on the subspace of the zero-energy states that generalize the graphene honeycomb model to the case of fermions with an internal pseudospin degree of freedom with <jats:italic>C</jats:italic> <jats:sub>3</jats:sub> symmetry.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Two-dimensional <jats:italic>Ferrovalley</jats:italic> materials with intrinsic valley polarization are rare but highly promising for valley-based nonvolatile random access memory and valley filter devices. These ferromagnetic materials exhibit valleys at or near the Fermi level with intrinsic magnetism. The strong coupling between magnetism and spin–orbit coupling induces intrinsic valley polarization. Using Kinetically Limited Minimization, an unconstrained crystal structure prediction algorithm, and prototype sampling based on first-principles calculations, we have discovered new <jats:italic>Ferrovalley</jats:italic> materials, rare-earth iodides RI<jats:sub>2</jats:sub>, where R is a rare-earth element belonging to Sc, Y, or La-Lu, and I is Iodine. The rare-earth iodides are layered and demonstrate either 2H, 1T, or 1T<jats:sub> <jats:italic>d</jats:italic> </jats:sub> phase as the ground state in bulk, analogous to transition metal dichalcogenides (TMDCs). The calculated exfoliation energy of monolayers (MLs) is comparable to that of graphene and TMDCs, suggesting possible experimental synthesis. The MLs in the 2H phase exhibit ferromagnetism due to unpaired electrons in <jats:italic>d</jats:italic> and <jats:italic>f</jats:italic> orbitals. Throughout the rare-earth series, <jats:italic>d</jats:italic> bands have valley polarization at <jats:italic>K</jats:italic> and <jats:inline-formula> <jats:tex-math><?CDATA $\overline{K}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover> <mml:mi>K</mml:mi> <mml:mo accent="false">‾</mml:mo> </mml:mover> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tdmacab72ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> points in the Brillouin zone in the vicinity of the Fermi level. Large intrinsic valley polarization in the range of 15–143 meV without external stimuli is observed in these <jats:italic>Ferrovalley</jats:italic> materials, which can be enhanced further by applying an in-plane bi-axial strain. These valleys can selectively be probed and manipulated for information storage and processing, potentially offering superior performance beyond conventional electronics and spintronics. We further show that the 2H ferromagnetic phase of RI<jats:sub>2</jats:sub> MLs possesses non-zero Berry curvature and exhibits anomalous valley Hall effect with considerable anomalous Hall conductivity. Our work will incite exploratory synthesis of the predicted Ferrovalley materials and their application in valleytronics and beyond.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The magnetoresistance (MR) of spin values usually displays a symmetric dependence on the magnetic field. An antisymmetric MR phenomenon has been discovered recently that breaks the field symmetry and has the potential to realize multi-bit memory. In this work, we report a controllable switch between the antisymmetric and symmetric MRs and propose a multi-bit memory performance in Fe3GeTe2 (FGT)/graphite/FGT trilayer with modified vertical geometry. Via investigating the evolution of the antisymmetric MR depending on the spatial distribution, current direction, and magnetization configuration, we demonstrate that the antisymmetric MR results from the local nonequilibrium current through the trilayer. Furthermore, an exchange bias effect is induced which modifies the antisymmetric MR. A stable multi-bit memory is presented in the heterostructure. Such architecture for multi-state memory provides insights into other spin-valve structures to improve storage density. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Graphene oxide (GO) sheet structures are highly variable and depend on preparation conditions. The use of molecular simulation is a complementary strategy to explore how this complexity influences the ion transport properties of GO membranes. However, despite recent advances, computational models of GO typically lack the required complexity as suggested by experiment. The labor required to create such an ensemble of such structural models with the required complexity is impractical without recourse to automated approaches, but no such code currently can meet this challenge. Here, a modular tiling concept is introduced, along with the HierGO suite of code; an automated approach to producing highly complex hierarchically-structured models of GO with a high degree of control in terms of holes and topological defects, and oxygen-group placement, that can produce simulation-ready input files. The benefits of the code are exemplified by modeling and contrasting the properties of three types of GO membrane stack; the widely-modeled Lerf-Klinowski structure, and two types of highly heterogeneous GO sheet reflecting differing processing conditions. The outcomes of this work clearly demonstrate how the introduction of the complexity modeled here leads to new insights into the structure/property relationships of GO with respect to permeation pathways of water, ions and molecular agents that are inaccessible using previously-considered models. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The effect of degeneracy and the impact of free-carrier screening on a low-field mobility and a high-field drift velocity in MoS<jats:sub>2</jats:sub> and WS<jats:sub>2</jats:sub> are explored using an in-house ensemble Monte Carlo simulator. Electron low field mobility increases to 8400 cm<jats:sup>2</jats:sup>/Vs for MoS<jats:sub>2</jats:sub> and to 12040 cm<jats:sup>2</jats:sup>/Vs for WS<jats:sub>2</jats:sub> when temperature decreases to 77 K and carrier concentration is around 5cdot10^12cm^-2. In the case of holes, best mobility values were 9320 cm<jats:sup>2</jats:sup>/Vs and 13290 cm<jats:sup>2</jats:sup>/Vs, reached at 77 K, while at room temperature these fall to 80 cm<jats:sup>2</jats:sup>/Vs and 150 cm<jats:sup>2</jats:sup>/Vs for MoS<jats:sub>2</jats:sub> and WS<jats:sub>2</jats:sub>, respectively. The carrier screening effect plays a major role at low fields, and low and intermediate temperatures, where a combination of large occupancy of primary valleys and carrier-phonon interactions dominated by relatively low energy exchange processes results in an enhanced screening of intrinsic scattering. For electrons, degeneracy yields to transport in secondary valleys, which plays an important role in the decrease of the low field mobility at high concentrations and/or at room temperature. The high-field drift velocity is not much affected by carrier screening because of an increased carrier scattering with surface optical polar phonons, favouring larger phonon wavevector interactions with small dielectric function values.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The nature of superconductivity in monolayer transition metal dichalcogenides is still under debate. It has already been argued that repulsive Coulomb interactions, combined with the disjoint Fermi surfaces around the K, K′ valleys and at the Γ point, can lead to superconducting instabilities in monolayer NbSe2. Here, we demonstrate the two-bands nature of superconductivity in NbSe2. It arises from the competition of repulsive long range intravalley and short range inter-valley interactions together with Ising spin-orbit coupling. The two distinct superconducting gaps, one for each spin-orbit split band, consist of a mixture of s-wave and f-wave components. Their different amplitudes are due to different normal densities of states of the two bands at the Fermi level. Using a microscopic multiband BCS approach, we derive and self-consistently solve the gap equation, demonstrating the stability of nontrivial solutions in a realistic parameter range. We find a universal behavior of the temperature dependence of the gaps and of the critical in-plane field which is consistent with various sets of existing experimental data. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The transport and optical properties of semiconducting transition metal dichalcogenides around room temperature are dictated by electron-phonon scattering mechanisms within a complex, spin-textured and multi-valley electronic landscape. The relative positions of the valleys are critical, yet they are sensitive to external parameters and very difficult to determine directly. We propose a first-principles model as a function of valley positions to calculate carrier mobility and Kerr rotation angles, and apply it to MoS$_2$, WS$_2$, MoSe$_2$, and WSe$_2$. The model brings valuable insights, as well as quantitative predictions of macroscopic properties for a wide range of carrier density. The doping-dependant mobility displays a characteristic peak, the height depending on the position of the valleys. In parallel, the Kerr rotation signal is enhanced when same spin-valleys are aligned, and quenched when opposite spin-valleys are populated. We provide guidelines to optimize and correlate these quantities with respect to experimental parameters, as well as the theoretical support for \emph{in situ} characterization of the valley positions.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We prepare monolayers of tantalum sulfide on Au(111) evaporation of Ta in a reactive background of H<jats:sub>2</jats:sub>S. Under sulfur-rich conditions monolayers of 2H-TaS<jats:sub>2</jats:sub> develop, whereas under sulfur-poor conditions TaS forms a structure that can be derived from 2H-TaS<jats:sub>2</jats:sub> by removal of the bottom layer. We analyse the alignment of the layers with respect to the substrate and the relation with the domains in the Au(111) herringbone reconstruction using scanning tunneling microscopy (STM). With the help of density functional theory (DFT) calculations we can determine the registry of the two phases with the substrate. We develop a growth process that allows preparation of uniquely oriented 2H-TaS<jats:sub>2</jats:sub> on Au(111). 2H-TaS<jats:sub>2</jats:sub> and TaS have a remarkably similar plane lattice structure and we observe the formation of lateral 2H-TaS<jats:sub>2</jats:sub>-TaS heterostructures with atomically well-defined and defect-free boundaries. observe mirror twin boundaries within 2H-TaS2 along the S- and Ta-edge.</jats:p>