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Low-buckled silicene, germanene, and stanene are group$-IV$ graphene allotropes. They form a honeycomb lattice out of two interpenetrating ($A$ and $B$) triangular sublattices that are vertically separated by a small distance $\Delta_z$. The atomic numbers $Z$ of silicon, germanium, and tin are larger to carbon's ($Z_C=6$), making them the first experimentally viable two-dimensional topological insulators. Those materials have a twice-energy-degenerate atomistic structure characterized by the buckling direction of the $B$ sublattice with respect to the $A$ sublattice [whereby the $B-$atom either protrudes {\em above} ($\Delta_z>0$) or {\em below} ($\Delta_z, Comment: 16 pages, 21 figures. Originally submitted on December 5, 2022

Two-dimensional (2D) materials are being explored as a novel multiferroic platform. One of the most studied magnetoelectric multiferroic 2D materials are antiferromagnetically-coupled (AFM) CrI$_3$ bilayers. Neglecting magnetism, those bilayers possess a crystalline point of inversion, which is only removed by the antiparallel spin configuration among its two constituent monolayers. The resultant intrinsic electric dipole on those bilayers has a magnitude no larger than 0.04 pC/m, it points out-of-plane, and it reverts direction when the--Ising-like--cromium spins are flipped (toward opposite layers {\em versus} away from opposite layers). The combined presence of antiferromagnetism and a weak intrinsic electric dipole makes this material a two-dimensional magnetoelectric multiferroic. Here, we remove the crystalline center of inversion of the bilayer by a relative $60^{\circ}$ rotation of its constituent monolayers. This process {\em enhances} the out-of-plane intrinsic electric dipole tenfold with respect to its magnitude in the non-rotated AFM bilayer and also creates an even stronger and switchable in-plane intrinsic electric dipole. The ability to create a three-dimensional electric dipole is important, because it enhances the magnetoelectric coupling on this experimentally accessible 2D material, which is explicitly calculated here as well., Comment: Accepted at PRB on May 1, 2023

Traditional ferroelectrics undergo thermally-induced phase transitions whereby their structural symmetry increases. The associated higher-symmetry structure is dubbed {\em paraelectric}. Ferroelectric transition metal dichalcogenide bilayers have been recently shown to become paraelectric, but not much has been said of the atomistic configuration of such a phase. As discovered through numerical calculations that include molecular dynamics here, their paraelectricity can only be ascribed to a time average of ferroelectric phases with opposing intrinsic polarizations, whose switching requires macroscopically large areas to slip in unison., Comment: Accepted in Nano Letters as of 9/28/2022

A two-dimensional topological crystalline insulator (TCI) with a single unit cell (u.c.) thickness is demonstrated here. To that end, one first shows that tetragonal ($C_4$ in-plane) symmetry is not a necessary condition for the creation of zero-energy metallic surface states on TCI slabs of finite-thicknesses, because zero-energy states persist even as all the in-plane rotational symmetries--furnishing topological protection--are completely removed. In other words, zero-energy levels on the model are not due to (nor are they protected by) topology. Furthermore, effective twofold energy degeneracies taking place at few discrete $k-$points away from zero energy in the bulk Hamiltonian--that are topologically protected--persist at the u.c.~thickness limit. The chiral nature of the bulk TCI Hamiltonian permits creating a $2\times 2$ square Hamiltonian, whose topological properties remarkably hold invariant at both the bulk and at the single u.c.~thickness limits. The identical topological characterization for bulk and u.c.-thick phases is further guaranteed by a calculation involving Pfaffians. This way, a two-atom-thick TCI is deployed hereby, in a demonstration of a topological phase that holds both in the bulk, and in two dimensions., Comment: 14 pages, 8 figures, accepted at Journal of Physics: Condensed Matter on 11/7/2022

The ZrSiS family of compounds hosts various exotic quantum phenomena due to the presence of both topological nonsymmorphic Dirac fermions and nodal-line fermions. In this material family, the LnSbTe (Ln= lanthanide) compounds are particularly interesting owing to the intrinsic magnetism from magnetic Ln which leads to new properties and quantum states. In this work, the authors focus on the previously unexplored compound SmSbTe. The studies reveal a rare combination of a few functional properties in this material, including antiferromagnetism with possible magnetic frustration, electron correlation enhancement, and Dirac nodal-line fermions. These properties enable SmSbTe as a unique platform to explore exotic quantum phenomena and advanced functionalities arising from the interplay between magnetism, topology, and electronic correlations., 23 pages, 5 figures

Heterostructures formed from interfaces between materials with complementary properties often display unconventional physics. Of especial interest are heterostructures formed with ferroelectric materials. These are mostly formed by combining thin layers in vertical stacks. Here the first in situ molecular beam epitaxial growth and scanning tunneling microscopy characterization of atomically sharp lateral heterostructures between a ferroelectric SnTe monolayer and a paraelectric PbTe monolayer are reported. The bias voltage dependence of the apparent heights of SnTe and PbTe monolayers, which are closely related to the type-II band alignment of the heterostructure, is investigated. Remarkably, it is discovered that the ferroelectric domains in the SnTe surrounding a PbTe core form either clockwise or counterclockwise vortex-oriented quadrant configurations. In addition, when there is a finite angle between the polarization and the interface, the perpendicular component of the polarization always points from SnTe to PbTe. Supported by first-principles calculation, the mechanism of vortex formation and preferred polarization direction is identified in the interaction between the polarization, the space charge, and the strain effect at the horizontal heterointerface. The studies bring the application of 2D group-IV monochalcogenides on in-plane ferroelectric heterostructures a step closer.

We survey the state-of-the-art knowledge of ferroelectric and ferroelastic group-IV monochalcogenide monolayers. These semiconductors feature remarkable structural and mechanical properties, such as a switchable in-plane spontaneous polarization, soft elastic constants, structural degeneracies, and thermally-driven two-dimensional structural transformations. Additionally, these 2D materials also display selective valley excitations, valley Hall effects, and persistent spin helix behavior. After a description of their Raman spectra, a discussion of optical properties arising from their lack of centrosymmetry---such as an unusually strong second-harmonic intensity, large bulk photovoltaic effects, photostriction, and tunable exciton binding energies---is provided as well. The physical properties observed in these materials originate from (correlate with) their intrinsic and switchable electric polarization, and the physical behavior hereby reviewed could be of use in non-volatile memory, valleytronic, spintronic, and optoelectronic devices: these 2D multiferroics enrich and diversify the 2D materials toolbox., Comment: Accepted for publication at Reviews of Modern Physics on September 9, 2020

Twelve two-dimensional group-IV monochalcogenide monolayers (SiS, SiSe, SiTe, GeS, GeSe, GeTe, SnS, SnSe, SnTe, PbS, PbSe, and PbTe) with a buckled honeycomb atomistic structure--belonging to symmetry group P3m1--and an out-of-plane intrinsic electric polarization are shown to be metastable by three independendent methods. First, we uncover a coordination-preserving structural transformation from the low-buckled honeycomb structure onto the lower-energy Pnm2$_1$ (or Pmmn for PbS, PbSe, and PbTe) phase to estimate {\em energy barriers} $E_B$ that must be overcome during such structural transformation. Using the curvature of the local minima and $E_B$ as inputs to Kramers escape formula, large escape times are found, implying the structural metastability of the buckled honeycomb phase (nevertheless, and with the exception of PbS and PbSe, these phases display escape times ranging from 700 years to multiple times the age of the universe, and can be considered "stable" for practical purposes only in that relative sense). The second demonstration is provided by phonon dispersion relations that include the effect of long-range Coulomb forces and display no negative vibrational modes. The third and final demonstration of structural metastability is furnished by room-temperature {\em ab initio} molecular dynamics for selected compounds. The magnitude of the electronic band gap evolves with chemical composition. Different from other binary two-dimensional compounds such as transition metal dichalcogenide monolayers and hexagonal boron nitride monolayers which only develop an in-plane piezoelectric response, the twelve group-IV monochalcogenide monolayers with a buckled honeycomb structure also display out-of-plane piezoelectric properties., Comment: Accepted at Physical Review B on 1/14/21

The thermoelectric figure of merit $ZT$ comprises electronic and vibrational contributions that drastically change across phase transitions, and the most common theoretical ab initio approach to thermoelectricity fails to describe the evolution of $ZT$ across finite-temperature structural transitions in its entirety. Furthermore, while the thermoelectric behavior of bulk SnSe has been extensively studied, SnSe monolayers have been experimentally realized only recently, and the existent prediction of thermoelectricity on this two-dimensional material is unreliable because it misses its structural transition altogether. SnSe monolayers (and similar GeS, GeSe, GeTe, SnS, and SnTe monolayers) experience a temperature-induced two-dimensional $Pnm{2}_{1}\ensuremath{\rightarrow}P4/nmm$ structural transition precipitated by the softening of vibrational modes, and we describe their thermoelectric properties across the phase transition, using molecular dynamics data to inform both electronic and vibrational coefficients directly and within the same footing. Similar to recent experimental observations pointing to an overestimated $ZT$ past the transition temperature in bulk SnSe, we find a smaller $ZT$ on SnSe monolayers when compared to its value predicted by the standard paradigm, due to the dramatic changes in the electrical conductivity and lattice thermal conductivity as the structural transition ensues. The process described here lends a strong focus to both the vibrational and electronic evolutions throughout the structural transition, and it applies to thermoelectric materials undergoing thermally driven solid-to-solid structural phase transitions in one, two, and three dimensions.

One account of two-dimensional (2D) structural transformations in 2D ferroelectrics predicts an evolution from a structure with ${\mathrm{Pnm}2}_{1}$ symmetry into a structure with square P4/nmm symmetry and is consistent with experimental evidence, while another argues for a transformation into a structure with rectangular Pnmm symmetry. An analysis of the assumptions made in these models is provided here, and six fundamental results concerning these transformations are contributed as follows: (i) Softened phonon modes produce rotational modes in these materials. (ii) The transformation to a structure with P4/nmm symmetry occurs at the lowest critical temperature ${T}_{c}$. (iii) The hypothesis that one unidirectional optical vibrational mode underpins the 2D transformation is unwarranted. (iv) Being successively more constrained, a succession of critical temperatures $({T}_{c}l{T}_{c}^{\ensuremath{'}}l{T}_{c}^{\ensuremath{''}})$ occurs in going from molecular dynamics calculations with the NPT and NVT ensembles onto models with unidirectional oscillations. (v) The choice of exchange-correlation functional impacts the estimate of the critical temperature. (vi) Crucially, the correct physical picture of these transformations is one in which rotational modes confer a topological character to the 2D transformation via the proliferation of vortices.

Low-symmetry 2D materials---such as ReS$_2$ and ReSe$_2$ monolayers, black phosphorus monolayers, group-IV monochalcogenide monolayers, borophene, among others---have more complex atomistic structures than the honeycomb lattices of graphene, hexagonal boron nitride, and transition metal dichalcogenides. The reduced symmetries of these emerging materials give rise to inhomogeneous electron, optical, valley, and spin responses, as well as entirely new properties such as ferroelasticity, ferroelectricity, magnetism, spin-wave phenomena, large nonlinear optical properties, photogalvanic effects, and superconductivity. Novel electronic topological properties, nonlinear elastic properties, and structural phase transformations can also take place due to low symmetry. The "Beyond Graphene: Low-Symmetry and Anisotropic 2D Materials" Special Topic was assembled to highlight recent experimental and theoretical research on these emerging materials., Comment: Guest Editorial for the Special Issue entitled "Beyond Graphene: Low-Symmetry and Anisotropic 2D Materials" at Journal of Applied Physics

We performed density functional theory calculations with self-consistent van der Waals corrected exchange-correlation (XC) functionals to capture the structure of black phosphorus and twelve monochalcogenide monolayers and find the following results: (a) The in-plane unit cell changes its area in going from the bulk to a monolayer. The change of in-plane distances implies that bonds weaker than covalent or ionic ones are at work within the monolayers themselves. This observation is relevant for the prediction of the critical temperature $T_c$. (b) There is a hierarchy of independent parameters that uniquely define a ground state ferroelectric unit cell (and square and rectangular paraelectric unit cells as well): only 5 optimizable parameters are needed to establish the unit cell vectors and the four basis vectors of the ferroelectric ground state unit cell, while square and rectangular paraelectric structures are defined by only 3 or 2 independent optimizable variables, respectively. (c) The reduced number of independent structural variables correlates with larger elastic energy barriers on a rectangular paraelectric unit cell when compared to the elastic energy barrier of a square paraelectric structure. This implies that $T_c$ obtained on a structure that keeps the lattice parameters fixed (for example, using an NVT ensemble) should be larger than the transition temperature on a structure that is allowed to change in-plane lattice vectors (for example, using the NPT ensemble). (d) The dissociation energy (bulk cleavage energy) of these materials is similar to the energy required to exfoliate graphite and MoS$_2$. (e) There exists a linear relation among the square paraelectric unit cell lattice parameter and the lattice parameters of the rectangular ferroelectric ground state unit cell. These results highlight the subtle atomistic structure of these novel 2D ferroelectrics., Comment: Submitted on September 17, 2019

Group-IV monochalcogenides are emerging as a new class of layered materials beyond graphene, transition metal dichalcogenides (TMDCs), and black phosphorus (BP). In this paper, we report experimental and theoretical investigations of the band structure and transport properties of GeSe and its heterostructures. We find that GeSe exhibits a markedly anisotropic electronic transport, with maximum conductance along the armchair direction. Density functional theory calculations reveal that the effective mass is 2.7 times larger along the zigzag direction than the armchair direction; this mass anisotropy explains the observed anisotropic conductance. The crystallographic orientation of GeSe is confirmed by angleresolved polarized Raman measurements, which are further supported by calculated Raman tensors for the orthorhombic structure. Novel GeSe/MoS2 p-n heterojunctions are fabricated, combining the natural p-type doping in GeSe and n-type doping in MoS2. The temperature dependence of the measured junction current reveals that GeSe and MoS2 have a type-II band alignment with a conduction band offset of ~0.234 eV. The anisotropic conductance of GeSe may enable the development of new electronic and optoelectronic devices, such as high-efficiency thermoelectric devices and plasmonic devices with resonance frequency continuously tunable through light polarization direction. The unique GeSe/MoS2 p-n junctions with type-II alignment may become essential building blocks of vertical tunneling field-effect transistors for low-power applications. The novel p-type layered material GeSe can also be combined with n-type TMDCs to form heterogeneous complementary metal oxide semiconductor (CMOS) circuits., Comment: Nano Research; published version. 15 pages and 5 figures

Two-dimensional (2D) quasiparticle standing waves originate from the interference of coherent quantum states and are usually created by the scattering off edges, atomic steps, or adatoms that induce large potential barriers. We report standing waves close to the valence band maximum (EV), confined by electrically neutral domain walls of newly discovered ferroelectric SnTe monolayers, as revealed by spatially resolved scanning tunneling spectroscopy. Ab initio calculations show that this novel confinement arises from the polarization lifted hole valley degeneracy and a ∼90° rotation of the Brillouin zones that render holes’ momentum mismatched across neighboring domains. These results show a potential for polarization-tuned valleytronics in 2D ferroelectrics.

We use a classical analytical and separable elastic energy landscape describing SnO monolayers to estimate the softening of elastic moduli through a mechanical instability occurring at finite temperature in this material. Although not strictly applicable to this material due to its low energy barrier $J$ that leads to a quantum paraelastic phase, the present exercise is relevant as it establishes a conceptual procedure to estimate such moduli straight from a two-dimensional elastic energy landscape. As additional support for the existence of a quantum paraelastic phase, we carry a qualitative WKB analysis to estimate escape times from an individual well on the landscape; escape times increase exponentially with the height of the barrier $J$. We also provide arguments against an additional transformation onto a planar lattice due to its high energy cost. These results continue to establish a case for the usefulness of soft matter concepts in two-dimensional materials, and of the potential lurking of quantum effects into soft matter., Accepted at PRB on 3/12/2019

SnTe hosts ferroelectricity that competes with its weak nontrivial band topology: in the high-symmetry rocksalt structure - in which its intrinsic electric dipole is quenched - this material develops metallic surface bands, but in its rhombic ground-state configuration - which hosts a nonzero spontaneous electric dipole - the crystalline symmetry is lowered, and the presence of surface electronic bands is not guaranteed. Here, the type of ferroelectric coupling and the atomistic and electronic structure of SnTe films ranging from 2 to 40 atomic layers (ALs) are examined on freestanding samples, to which atomic layers were gradually added. Four-AL SnTe films are antiferroelectrically coupled, while thicker freestanding SnTe films are ferroelectrically coupled. The electronic band gap reduces its magnitude in going from 2 to 40 ALs, but it does not close due to the rhombic nature of the structure. These results bridge the structure of SnTe films from the monolayer to the bulk.

We study the elastic energy landscape of two-dimensional tin oxide (SnO) monolayers and demonstrate a transition temperature of $T_c=8.5\pm 1.8$ K using ab-initio molecular dynamics (MD), that is close to the value of the elastic energy barrier $J$ derived from $T=0$ K density functional theory calculations. The power spectra of the velocity autocorrelation throughout the MD evolution permits identifying soft phonon modes likely responsible for the structural transformation. The mean atomic displacements obtained from a Bose-Einstein occupation of the phonon modes suggest the existence of a quantum paraelastic phase that could be tuned with charge doping: SnO monolayers could be 2D quantum paraelastic materials with a charge-tunable quantum phase transition., Accepted at the Physical Review Letters on 12/12/18

Structural degeneracies underpin the ferroic behavior of next-generation two-dimensional materials, and lead to peculiar two-dimensional structural transformations under external fields, charge doping and/or temperature. The most direct indicator of the ease of these transformations is an {\em elastic energy barrier}, defined as the energy difference between the (degenerate) structural ground state unit cell, and a unit cell with an increased structural symmetry. Proximity of a two-dimensional material to a bulk substrate can affect the magnitude of the critical fields and/or temperature at which these transformations occur, with the first effect being a relative charge transfer, which could trigger a structural quantum phase transition. With this physical picture in mind, we report the effect of modest charge doping (within $-0.2$ and $+0.2$ electrons per unit cell) on the elastic energy barrier of ferroelastic black phosphorene and nine ferroelectric monochalcogenide monolayers. The elastic energy barrier $J_s$ is the energy needed to create a $Pnm2_1\to P4/nmm$ two-dimensional structural transformation. Similar to the effect on the elastic energy barrier of ferroelastic SnO monolayers, group-IV monochalcogenide monolayers show a tunable elastic energy barrier for similar amounts of doping: a decrease (increase) of $J_s$ can be engineered under a modest hole (electron) doping of no more than one tenth of an electron or a hole per atom., Submitted to Journal of Applied Physics

We study the injection current response tensor (also known as circular photogalvanic effect or ballistic current) in ferrolectric monolayer GeS, GeSe, SnS, and SnSe. We find that the injection current is perpendicular to the spontaneous in-plane polarization and could reach peak (bulk) values of the order of $10^{10}$A/V$^{2}$s in the visible spectrum. The magnitude of the injection current is the largest reported in the literature to date for a two dimensional material. To rationalize the large injection current, we correlate the injection current spectrum with the joint density of states, electric polarization, strain, etc. We find that various factors such as anisotropy, in-plane polarization and wave function delocalization are important in determining the injection current tensor in these materials. We also find that compression along the polar axis can increase the injection current (or change its sign), and hence strain can be an effective control knob for their nonlinear optical response. Conversely, the injection current can be a sensitive probe of the crystal structure., 11 pages, 10 figures, typos fixed, published version

2D SnTe films with a thickness of as little as 2 atomic layers (ALs) have recently been shown to be ferroelectric with in-plane polarization. Remarkably, they exhibit transition temperatures (Tc ) much higher than that of bulk SnTe. Here, combining molecular beam epitaxy, variable temperature scanning tunneling microscopy, and ab initio calculations, the underlying mechanism of the Tc enhancement is unveiled, which relies on the formation of γ-SnTe, a van der Waals orthorhombic phase with antipolar inter-layer coupling in few-AL thick SnTe films. In this phase, 4n - 2 AL (n = 1, 2, 3…) thick films are found to possess finite in-plane polarization (space group Pmn21), while 4n AL thick films have zero total polarization (space group Pnma). Above 8 AL, the γ-SnTe phase becomes metastable, and can convert irreversibly to the bulk rock salt phase as the temperature is increased. This finding unambiguously bridges experiments on ultrathin SnTe films with predictions of robust ferroelectricity in GeS-type monochalcogenide monolayers. The observed high transition temperature, together with the strong spin-orbit coupling and van der Waals structure, underlines the potential of atomically thin γ-SnTe films for the development of novel spontaneous polarization-based devices.

Lattice {\em Kirigami}, ultra-light metamaterials, poly-disperse aggregates, ceramic nano-lattices, and two-dimensional (2-D) atomic materials share an inherent structural discreteness, and their material properties evolve with their shape. To exemplify the intimate relation among material properties and the local geometry, we explore the properties of phosphorene --a new 2-D atomic material-- in a conical structure, and document a decrease of the semiconducting gap that is directly linked to its non-planar shape. This geometrical effect occurs regardless of phosphorene allotrope considered, and it provides a unique optical vehicle to single out local structural defects on this 2-D material. We also classify other 2-D atomic materials in terms of their crystalline unit cells, and propose means to obtain the local geometry directly from their diverse two-dimensional structures while bypassing common descriptions of shape that are based from a parametric continuum., Comment: Published at PNAS (accepted on 3/31/2015, and online free of charge at www.pnas.org as of 4/27/2015.)

Under a Creative Commons license.-- et al., Pseudopotential-based Density-Functional Theory (DFT) permits the calculation of material properties with a modest computational effort, besides an acknowledged tradeoff of generating and testing pseudopotentials that reproduce established benchmark structural and electronic properties. To facilitate the needed benchmarking process, here we present a pragmatic method to optimize pseudopotentials for arbitrary materials directly from eigenvalue sets consistent with all-electron results. This method thus represents a much needed pragmatic route for the creation and assessment of sensitive pseudopotentials for DFT calculations that has been exemplified within the context of the SIESTA code. Comprehensive optimized pseudopotentials, basis sets, and lattice parameters are provided for twenty chemical elements in the bulk, and for both LDA and GGA exchange–correlation potentials. This method helps addressing the following issues: (i) the electronic dispersion and structural properties for Ge, Pd, Pt, Au, Ag, and Ta better agree with respect to all-electron results now, (ii) we provide the expected metallic behavior of Sn in the bulk – which comes out semiconducting when using available pseudopotentials, (iii) we create a validated pseudopotential for LDA-tungsten, and (iv) we create the first Bi pseudopotential for SIESTA that reproduces well-known electron and hole pockets at the L and T points. We investigated the transferability of these pseudopotentials and basis sets, and predict a new phase for two-dimensional tin as well., P.R. and S.B.L. acknowledge partial support from the Arkansas Biosciences Institute. V.M.G.S. and J.F. acknowledge funding from the Spanish MICINN, Grant FIS2012-34858, and European Commission FP7 ITN “MOLESCO” (Grant No. 606728). V.M.G.S. thanks the Spanish Ministerio de Economía y Competitividad for a Ramón y Cajal fellowship (RYC-2010-06053), Y.Y. and L.B. thank ONR (Grants N00014-11-1-0384 and N00014-12-1-1034), and K.P. acknowledges funding from the National Science Foundation (DMR-1206354).

Effects that are not captured by the generalized-gradient density-functional theory play a prominent effect on the structural binding, and on the electronic and optical properties of reduced-dimensional and weakly-bound materials. Here, we report the exfoliation energy of selenium and tellurium atomic chains with non-empirical van der Waals corrections, and their electronic and optical properties with the GW and Bethe-Salpeter formalisms. The exfoliation energy is found to be within 0.547 to 0.719 eV/u.c. for the selenium atomic chain, and 0.737 to 0.926 eV/u.c. for the tellurium atomic chain (u.c. stands for unit cell), depending on the approximation for the van der Waals interaction and the numerical tool chosen. The GW electronic bandgap turned out to be 5.22--5.47 (4.44--4.59) eV for the Se (Te) atomic chains, with the lowest bound obtained with the Godby-Needs (GB), and the upper bound to the Hybertsen-Louie (HL) plasmon-pole models (PPMs). The binding energy of the ground-state excitonic state ranges between 2.69 to 2.72 eV for selenium chains within the HL and GB PPM, respectively, and turned out to be 2.35 eV for tellurium chains with both approximations. The ground state excitonic wave function is localized within 50 \AA{} along the axis for both types of atomic chains, and its energy lies within the visible spectrum: blue [2.50(GN)--2.78(HL) eV] for selenium, and yellow--green [2.09(GN)--2.28(HL) eV] for tellurium, which could be useful for LED applications in the visible spectrum., Comment: 8 pages, 7 figures. Accepted at PRB on 7/2/2018

This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schr\"odinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family., Comment: Review article, 66 pages, 65 figures. V2: accepted in Reports on Progress in Physics, with significant changes respect to the previous version

Photostriction is predicted for SnS and SnSe monolayers, two-dimensional ferroelectrics with rectangular unit cells (the lattice vector $\mathbf{a}_1$ is larger than $\mathbf{a}_2$) and an intrinsic dipole moment parallel to $\mathbf{a}_1$. Photostriction in these two-dimensional materials is found to be induced by a screened electric polarization in the photoexcited electronic state (i.e., a converse piezoelectric effect) that leads to a compression of $a_1$ and a comparatively smaller increase of $a_2$ for a reduced unit cell area. The structural change documented here is ten times larger than that observed in BiFeO$_3$, making monochalcogenide monolayers an ultimate platform for this effect. This structural modification should be observable under experimentally feasible densities of photexcited carriers on samples that have been grown already, having a potential usefulness for light-induced, remote mechano-opto-electronic applications., 5 pages, 4 figures, one Table

GeSe and SnSe monochalcogenide monolayers and bilayers undergo a two-dimensional phase transition from a rectangular unit cell to a square unit cell at a critical temperature Tc well below the melting point. Its consequences on material properties are studied within the framework of Car-Parrinello molecular dynamics and density-functional theory. No in-gap states develop as the structural transition takes place, so that these phase-change materials remain semiconducting below and above Tc. As the in-plane lattice transforms from a rectangle into a square at Tc, the electronic, spin, optical, and piezoelectric properties dramatically depart from earlier predictions. Indeed, the Y and X points in the Brillouin zone become effectively equivalent at Tc, leading to a symmetric electronic structure. The spin polarization at the conduction valley edge vanishes, and the hole conductivity must display an anomalous thermal increase at Tc. The linear optical absorption band edge must change its polarization as well, making this structural and electronic evolution verifiable by optical means. Much excitement is drawn by theoretical predictions of giant piezoelectricity and ferroelectricity in these materials, and we estimate a pyroelectric response of about 3×10−12 C/Km here. These results uncover the fundamental role of temperature as a control knob for the physical properties of few-layer group-IV monochalcogenides., M. M. and S. B.-L. are funded by an Early Career Grant from the U.S. DOE (Grant No. SC0016139). Y. Y. and L. B. were funded by ONR Grant No. N00014-12-1-1034, and B. M. F. by NSF Grant No. DMR-1206515 and CONACyT (Mexico). J. F. acknowledges funding from the Spanish MICINN, Grant No. FIS2012-34858, and European Commission FP7 ITN MOLESCO (Grant No. 606728). Calculations were performed on Trestles at the Arkansas High Performance Computing Center, which is funded through multiple National Science Foundation grants and the Arkansas Economic Development Commission.

In this article we highlight recent work in which we computed the spin unpolarized coherent electron transport through two terminal nanoscale graphene/metal junctions using equilibrium Green's functions coupled to Density functional theory, capturing in detail the important electronic effects created at metal/graphene interfaces. In those calculations the metal contacts may or may not bind covalently to graphene. Along the way, connections to other models for coherent transport on graphene junctions with metal contacts are given as well. As it may be known, the computation of the electronic dispersion at the interface between graphene and binding metals in a transport setup is extremely time-consuming, and it is perhaps for this reason that effects of metals are neglected or are captured only qualitatively in the theoretical and computational modeling of graphene devices. It thus seems to us that a methodology to go past this stumbling block may be well-received. We outline an approach to obtain tight-binding parameters describing the electronic dispersion at interfaces between titanium leads and graphene. The deployment of those tight-binding parameters is new, and it constitutes the main contribution on the present paper.

Mechanical strain creates strong gauge fields in graphene, offering the possibility of controlling its electronic properties. We developed a gauge field theory on a honeycomb lattice valid beyond first-order continuum elasticity. Along the way, we resolve a recent controversy on the theory of strain engineering in graphene: there are no K-point dependent gauge fields.

Ultrahigh vacuum scanning tunneling microscopy and first-principles calculations have been carried out to study monolayer graphene nanomembranes deposited in situ onto UHV-cleaved GaAs(110) and InAs(110) surfaces. A bias-dependent semitransparency effect is observed in which the substrate atomic structure is clearly visible through the graphene monolayer. Statistical data analysis and density functional theory calculations suggest that this semitransparency phenomenon is due to the scanning tunneling microscope tip pushing the graphene membrane away from its equilibrium location and closer to the substrate surface, causing their electronic states to intermix.

Layered titanate nanostructures are uniquely suited to large-scale application in energy science due to their inexpensive processing, ease of synthesis, and their versatility to be ion-exchanged with specific elements. The quantity and scope of experimental literature that exists for these porous, ion-exchangeable nanostructures is not matched in the computational studies available; we have expanded the boundaries of both by combining the experiment and the computation to answer questions about how dopant atoms are integrated into the layered titanate nanofiber crystal lattice during synthesis. We simulated doped hydrogen trititanate (H2Ti3O7) with and without magnetic substitutional doping for a variety of dopant sites. Predicted structural energies, band structure, charge distribution, and magnetic properties were examined. Simulated XRD patterns are comparable to experimental results from synthesized doped nanofibers. Finally, EDX scans confirmed the presence of dopants in the titanates. We found that this combined computational/experimental collaboration provided strong evidence for one interpretation of the dopant integration, and we expect to generalize this work on different dopants.

Ridged, orthorhombic two-dimensional atomic crystals with a bulk {\em Pnma} structure such as black phosphorus and monochalcogenide monolayers are an exciting and novel material platform for a host of applications. Key to their crystallinity, monolayers of these materials have a four-fold degenerate structural ground state, and a single energy scale $E_C$ (representing the elastic energy required to switch the longer lattice vector along the $x-$ or $y-$direction) determines how disordered these monolayers are at finite temperature. Disorder arises when nearest neighboring atoms become gently reassigned as the system is thermally excited beyond a critical temperature $T_c$ that is proportional to $E_C/k_B$. $E_C$ is tunable by chemical composition and it leads to a classification of these materials into two categories: (i) Those for which $E_C\ge k_BT_m$, and (ii) those having $k_BT_m>E_C\ge 0$, where $T_m$ is a given material's melting temperature. Black phosphorus and SiS monolayers belong to category (i): these materials do not display an intermediate order-disorder transition and melt directly. All other monochalcogenide monolayers with $E_C>0$ belonging to class (ii) will undergo a two-dimensional transition prior to melting. $E_C/k_B$ is slightly larger than room temperature for GeS and GeSe, and smaller than 300 K for SnS and SnSe monolayers, so that these materials transition near room temperature. The onset of this generic atomistic phenomena is captured by a planar Potts model up to the order-disorder transition. The order-disorder phase transition in two dimensions described here is at the origin of the {\em Cmcm} phase being discussed within the context of bulk layered SnSe., Accepted on 01/11/2016. This document is the Submitted Manuscript version of a Published Work that appeared in final form in Nano Letters, copyright [2016]

This work investigates the significance of the number of periods in two-dimensional photonic crystals. Models have been developed to study various photonic crystal properties (Reflection, Photonic crystal band gap). The numbers of photonic crystal periods, length of periods, and material properties have been investigated to determine their effect on the losses in the waveguide. The model focuses on a square period and has been designed to study transmission properties and the effects of period length. A finite difference frequency domain (FDFD) model has also been created to calculate the photonic band structure. Additionally, a simplified study focuses on the transmission of light through photonic crystal layers.

Black phosphorus is a monoatomic semiconducting layered material that degrades exothermically in the presence of light and ambient contaminants. Its degradation dynamics remain largely unknown. Even before degradation, local-probe studies indicate non-negligible local curvature --through a non-constant height distribution-- due to the unavoidable presence of intrinsic defects. We establish that these intrinsic defects are photo-oxidation sites because they lower the chemisorption barrier of ideal black phosphorus (> 10 eV and out of visible-range light excitations) right into the visible and ultra-violet range (1.6 to 6.8 eV), thus enabling photo-induced oxidation and dissociation of oxygen dimers. A full characterization of the material's shape and of its electronic properties at the early stages of the oxidation process is presented as well. This study thus provides fundamental insights into the degradation dynamics of this novel layered material., Accepted on 07/31/2015. This document is the Submitted Manuscript version of a Published Work that appeared in final form in ACS Central Science, copyright [2015]

Two-dimensional materials were first isolated no longer than ten years ago, and a comprehensive understanding of their properties under non-planar shapes is still being developed. Strictly speaking, the theoretical study of the properties of graphene and other two-dimensional materials is the most complete for planar structures and for structures with small deformations from planarity. The opposite limit of large deformations is yet to be studied comprehensively but that limit is extremely relevant because it determines material properties near the point of failure. We are exploring uses for discrete differential geometry within the context of graphene and other two-dimensional materials, and these concepts appear promising in linking materials properties to shape regardless of how large a given material deformation is. A brief account of additional contributions arising from our group to two-dimensional materials that include graphene, stanene and phosphorene is provided towards the end of this manuscript., Submitted on December 30, 2014 as an invited contribution to an upcoming issue on Advances in Graphene Science and Engineering. Editors: Jeanie Lau (UC-Riverside), Roland Kawakami (Ohio State) and Arthur Epstein (Ohio State). Accepted version of the manuscript, with small changes with respect to the previously posted one

Using a combination of x-ray absorption spectroscopy (XAS) experiments and first-principles calculations, we demonstrate that insulating ${\mathrm{KCuO}}_{2}$ contains Cu in an unusually high formal 3+ valence state, and the ligand-to-metal (O-to-Cu) charge-transfer energy is intriguingly negative ($\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}\ensuremath{-}1.5$ eV) and has a dominant ($\ensuremath{\sim}60%$) ligand-hole character in the ground state akin to the high ${T}_{c}$ cuprate Zhang-Rice state. Unlike most other formal ${\mathrm{Cu}}^{3+}$ compounds, the Cu $2p$ XAS spectra of ${\mathrm{KCuO}}_{2}$ exhibit pronounced $3{d}^{8}$ (${\mathrm{Cu}}^{3+}$) multiplet structures, which account for $\ensuremath{\sim}40%$ of its ground state wave function. Ab initio calculations elucidate the origin of the band gap in ${\mathrm{KCuO}}_{2}$ as arising primarily from strong intracluster Cu $3d$-O $2p$ hybridizations (${t}_{\mathrm{pd}}$); the value of the band gap decreases with a reduced value of ${t}_{\mathrm{pd}}$. Further, unlike conventional negative-charge-transfer insulators, the band gap in ${\mathrm{KCuO}}_{2}$ persists even for vanishing values of Coulomb repulsion $U$, underscoring the importance of single-particle band-structure effects connected to the one-dimensional nature of the compound.

In this study, we describe a new experimental approach based on constant-current scanning tunneling spectroscopy to controllably and reversibly pull freestanding graphene membranes up to 35 nm from their equilibrium height. In addition, we present scanning tunneling microscopy (STM) images of freestanding graphene membranes with atomic resolution. Atomic-scale corrugation amplitudes 20 times larger than the STM electronic corrugation for graphene on a substrate were observed. The freestanding graphene membrane responds to a local attractive force created at the STM tip as a highly-conductive yet flexible grounding plane with an elastic restoring force. We indicate possible applications of our method in the controlled creation of pseudo-magnetic fields by strain on single-layer graphene., Comment: 16 pages, 3 figures

We employ room-temperature ultrahigh vacuum scanning tunneling microscopy (UHV STM) and {\em ab-initio} calculations to study graphene flakes that were adsorbed onto the Si(111)$-$7$\times$7 surface. The characteristic 7$\times$7 reconstruction of this semiconductor substrate can be resolved through graphene at all scanning biases, thus indicating that the atomistic configuration of the semiconducting substrate is not altered upon graphene adsorption. Large-scale {\em ab-initio} calculations confirm these experimental observations and point to a lack of chemical bonding among interfacial graphene and silicon atoms. Our work provides insight into atomic-scale chemistry between graphene and highly-reactive surfaces, directing future passivation and chemical interaction work in graphene-based heterostructures., Comment: Accepted at Applied Physics Letters on 8/9/15

We present in this article a pseudopotential (PP) database for DFT calculations in the context of the SIESTA code [1], [2] and [3]. Comprehensive optimized PPs in two formats (psf files and input files for ATM program) are provided for 20 chemical elements for LDA and GGA exchange-correlation potentials. Our data represents a validated database of PPs for SIESTA DFT calculations. Extensive transferability tests guarantee the usefulness of these PPs., Spanish MICINN, Grant FIS2012-34858, and European Commission FP7 ITN “MOLESCO” (Grant no. 606728). V.M.G.S. thanks the Spanish Ministerio de Economía y Competitividad for a Ramón y Cajal fellowship (RYC-2010-06053), Y.Y..., Rivero, P., Manuel García-Suárez, V., Pereñiguez, D., Utt, K., Yang, Y., Bellaiche, L., Park, K., Ferrer, J., Barraza-Lopez, S.

Low-buckled silicene is a prototypical quantum spin Hall insulator with the topological quantum phase transition controlled by an out-of-plane electric field. We show that this field-induced electronic transition can be further tuned by an in-plane hydrostatic biaxial strain $\varepsilon$, owing to the curvature-dependent spin-orbit coupling (SOC): There is a $Z_2$ = 1 topological insulator phase for biaxial strain $|\varepsilon|$ smaller than 0.07, and the band gap can be tuned from 0.7 meV for $\varepsilon = +0.07$ up to a fourfold 3.0 meV for $\varepsilon = -0.07$. First-principles calculations also show that the critical field strength $E_c$ can be tuned by more than 113\%, with the absolute values nearly 10 times stronger than the theoretical predictions based on a tight-binding model. The buckling structure of the honeycomb lattice thus enhances the tunability of both the quantum phase transition and the SOC-induced band gap, which are crucial for the design of topological field-effect transistors based on two-dimensional materials., Comment: 5 pages, 4 figures

Elemental phosphorous is believed to have several stable allotropes that are energetically nearly degenerate, but chemically reactive. To prevent chemical degradation under ambient conditions, these structures may be capped by monolayers of hexagonal boron nitride ({\em h}-BN) or graphene. We perform {\em ab initio} density functional calculations to simulate scanning tunneling microscopy (STM) images of different layered allotropes of phosphorus and study the effect of capping layers on these images. We find that protective monolayers of insulating {\em h}-BN allow to distinguish between the different structural phases of phosphorus underneath, even though the images are filtered through only nitrogen atoms that appear transparent. No such distinction is possible for phosphorus films capped by semimetallic graphene that masks the underlying structure. Our results suggest that the real-space imaging capability of STM is not hindered by selected capping layers that protect phosphorus surfaces., Published version, replaces previous one

In realizing practical non-trivial topological electronic phases stable structures need to be determined first. Tin and lead do stabilize an optimal two-dimensional high-buckled phase --a hexagonal-close packed bilayer structure with nine-fold atomic coordination-- and they do not stabilize topological fullerenes, as demonstrated by energetics, phonon dispersion curves, and the structural optimization of finite-size samples. The high-buckled phases are metallic due to their high atomic coordination. The optimal structure of fluorinated tin lacks three-fold symmetry and it stabilizes small samples too. It develops two oblate conical valleys on the first Brillouin zone coupling valley, sublattice, and spin degrees of freedom with a novel $\tau_z\sigma_xs_x$ term, thus making it a new 2D platform for valleytronics., Comment: Submitted on 07/27/14. Accepted as a Rapid Communication on 11/20/14

We address the fundamental issue of growth of perovskite ultra-thin films under the condition of a strong polar mismatch at the heterointerface exemplified by the growth of a correlated metal LaNiO$_3$ on the band insulator SrTiO$_3$ along the pseudo cubic [111] direction. While in general the metallic LaNiO$_3$ film can effectively screen this polarity mismatch, we establish that in the ultra-thin limit, films are insulating in nature and require additional chemical and structural reconstruction to compensate for such mismatch. A combination of in-situ reflection high-energy electron diffraction recorded during the growth, X-ray diffraction, and synchrotron based resonant X-ray spectroscopy reveal the formation of a chemical phase La$_2$Ni$_2$O$_5$ (Ni$^{2+}$) for a few unit-cell thick films. First-principles layer-resolved calculations of the potential energy across the nominal LaNiO$_3$/SrTiO$_3$ interface confirm that the oxygen vacancies can efficiently reduce the electric field at the interface.