Since the initial isolation of few-layer graphene, a plethora of two-dimensional atomic crystals has become available, covering almost all known materials types including metals, semiconductors, superconductors, ferro- and antiferromagnets. These advances have augmented the already existing variety of two-dimensional materials that are routinely realized by quantum confinement in bulk-semiconductor heterostructures. This review focuses on the type of material for which two-dimensional realizations are still being actively sought: magnetoelectrics. We present an overview of current theoretical expectation and experimental progress towards fabricating low-dimensional versions of such materials that can be magnetized by electric charges and polarized electrically by an applied magnetic field - unusual electromagnetic properties that could be the basis for various useful applications. The interplay between spatial confinement and magnetoelectricity is illustrated using the paradigmatic example of magnetic-monopole fields generated by electric charges in or near magnetoelectric media. For the purpose of this discussion, the image-charge method familiar from electrostatics is extended to solve the boundary-value problem for a magnetoelectric medium in the finite-width slab geometry using image dyons, i.e., point objects having both electric and magnetic charges. We discuss salient features of the magnetoelectrically induced fields arising in the thin-width limit.
Magnetoelectric (ME) effect, the phenomenon of inducing magnetization by application of an electric field or vice versa, holds great promise for magnetic sensing and switching applications. Studies of the ME effect have so far focused on the control of the electron spin degree of freedom (DOF) in materials such as multiferroics and conventional semiconductors. Here, we report a new form of the ME effect based on the valley DOF in two-dimensional (2D) Dirac materials. By breaking the three-fold rotational symmetry in single-layer MoS2 via a uniaxial stress, we have demonstrated the pure electri…
We propose an intrinsic nonlinear spin magnetoelectric effect in magnetic materials, offering the potential of all-electric control of spin degree of freedom in centrosymmetric magnets, which reside outside of the current paradigm based on linear spin response. We reveal the band geometric origin of this effect in the momentum and magnetization space Berry connection polarizabilities, and clarify its symmetry characters. As an intrinsic effect, it is determined solely by the material's band structure and represents a material characteristic. Combining our theory with first-principles calculati…
Multiferroics are those materials with more than one ferroic order, and magnetoelectricity refers to the mutual coupling between magnetism and electricity. The discipline of multiferroicity has never been so highly active as that in the first decade of the twenty-first century, and it has become one of the hottest disciplines of condensed matter physics and materials science. A series of milestones and steady progress in the past decade have enabled our understanding of multiferroic physics substantially comprehensive and profound, which is further pushing forward the research frontier of this…
The relationship between magnetoelectricity and electromagnetism is a subject of a strong interest and numerous discussions in microwave and optical wave physics and material sciences. The definition of the energy and momentum of the electromagnetic (EM) field in a magnetoelectric (ME) medium is not a trivial problem. The question of whether electromagnetism and magnetoelectricity can coexist without an extension of Maxwell theory arises when we study the effects of EM energy propagation and consider group velocity of the waves in a ME medium. The energy balance equation reveals unusual topolo…
Nowadays, designing and searching for materials with multiple functional characteristics are the key to achieving high-performance electronic devices. Among many candidates, two-dimensional multiferroic materials have great potential to be applied in highly-integrated magnetoelectric devices, such as high-density non-volatile memories. Here, we predict a two-dimensional material VOF2 monolayer to possess intrinsic ferroelectric and ferromagnetic properties. The VOF$_2$ monolayer own the largest in-plane ferroelectric polarization ($332$ pC/m) in the family of VO$X_2$ ($X$: halogen) oxyhalides.…
Achieving multiferroic two-dimensional (2D) materials should enable numerous functionalities in nanoscale devices. Until now, however, predicted 2D multiferroics are very few and with coexisting yet only loosely coupled (type-I) ferroelectricity and magnetism. Here, a type-II multiferroic MXene Hf$_{2}$VC$_{2}$F$_{2}$ monolayer is identified, where ferroelectricity originates directly from its magnetism. The noncollinear Y-type spin order generates a polarization perpendicular to the spin helical plane. Remarkably, the multiferroic transition is estimated to occur above room temperature. Our i…
Although several multiferroic materials/heterostructures have been extensively studied, finding strong magnetoelectric couplings for the electric field control of the magnetization remains challenging. Here, a novel interfacial magnetoelectric coupling based on three components (ferroelectric dipole, magnetic moment, and antiferromagnetic order) is analytically formulated. As an extension of carrier-mediated magnetoelectricity, the new coupling is shown to induce an electric-magnetic hysteresis loop. Realizations employing BiFeO$_3$ bilayers grown along the [$111$] axis are proposed. Without i…
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 d…
We develop a theory for optical Faraday rotation noise in two-dimensional Dirac materials. In contrast to spin noise in conventional semiconductors, we find that the Faraday rotation fluctuations are influenced not only by spins but also the valley degrees of freedom attributed to intervalley scattering processes. We illustrate our theory with two-dimensional transition metal dichalcogenides and discuss signatures of spin and valley noise in the Faraday noise power spectrum. We propose optical Faraday noise spectroscopy as a technique for probing both spin and valley relaxation dynamics in two…
Symmetry breaking in two-dimensional layered materials plays a significant role in their macroscopic electrical, optical, magnetic and topological properties, including but not limited to spin-polarization effects, valley-contrasting physics, nonlinear Hall effects, nematic order, ferroelectricity, Bose-Einstein condensation and unconventional superconductivity. Engineering symmetry breaking of two-dimensional layered materials not only offers extraordinary opportunities to tune their physical properties, but also provides unprecedented possibilities to introduce completely new physics and tec…
Unlike conventional two-dimensional (2D) semiconductor superlattices, moiré patterns in 2D materials are flexible and their electronic, magnetic, optical, and mechanical properties depend on their topography. Within a continuous+atomistic theory treating 2D materials as crystalline elastic membranes, we abandon the flat-membrane scenario usually assumed for these materials and address out-of-plane deformations. We confront our predictions to experimental analyses on model systems, epitaxial graphene, and MoS$_2$ on metals and reveal that compression/expansion and bending energies stored in the…
We present details of our effective computational methods based on the real-space finite-difference formalism to elucidate electronic and magnetic properties of the two-dimensional (2D) materials within the framework of the density functional theory. The real-space finite-difference formalism enables us to treat truly 2D computational models by imposing individual boundary condition on each direction. The formulae for practical computations under the boundary conditions specific to the 2D materials are derived and the electronic band structures of 2D materials are demonstrated using the propos…
Two-dimensional materials and their mechanical properties are known to be profoundly affected by rippling deformations. However, although ripples are fairly well understood, less is known about their origin and controlled modification. Here, motivated by recent reports of laser-controlled creation of line defects in graphene, we investigate how line defects could be used to control rippling in graphene and other two-dimensional materials. By sequential multi-scale coupling of density-functional tight-binding and continuum elasticity simulations, we quantify the amount of rippling when the numb…
The emerging two-dimensional (2D) materials exhibit a wide range of electronic properties, ranging from insulating hexagonal boron nitride, semiconducting transition metal dichalcogenides such as molybdenum disulfide, to semi-metallic graphene. Here, we first review the optical properties and applications of a variety of 2D materials, followed by two different approaches to enhance their interactions with light: through their integration with external photonic structures and through their intrinsic polaritonic resonances. Finally, we cover a narrow bandgap layered material, black phosphorus, w…
The electronic band structures of two-dimensional materials are significantly different from those of their bulk counterparts, due to quantum confinement and strong modifications of electronic screening. An accurate determination of electronic states is a prerequisite to design electronic or optoelectronic applications of two-dimensional materials, however, most of the theoretical methods we have available to compute band gaps are either inaccurate, computationally expensive, or only applicable to bulk systems. Here we show that reliable band structures of nanostructured systems can now be eff…
The flexibility of two-dimensional (2D) materials enables static and dynamic ripples that are known to cause lateral contraction, shrinking of the material boundary. However, the limits of 2D materials' \emph{lateral expansion} are unknown. Therefore, here we discuss the limits of intrinsic lateral expansion of 2D materials that are modified by compressive line defects. Using thin sheet elasticity theory and sequential multiscale modeling, we find that the lateral expansion is inevitably limited by the onset of rippling. The maximum lateral expansion $χ_{max}\approx 2.1\cdot t^2σ_d$, governed …
In the presence of an external magnetic field, the optical response of two-dimensional materials, whose charge carriers behave as massless Dirac fermions with arbitrary anisotropic Fermi velocity, is investigated. Using Kubo formalism, we obtain the magneto-optical conductivity tensor for these materials, which allows to address the magneto-optical response of anisotropic Dirac fermions from the well known magneto-optical conductivity of isotropic Dirac fermions. As an application, we analyse the combined effects of strain-induced anisotropy and magnetic field on the transmittance, as well as …
Based on density functional theory calculations, we investigated the two-dimensional in-plane ordered MXene (i-MXenes), focusing particularly on the magnetic properties. It is observed that robust two-dimensional magnetism can be achieved by alloying nonmagnetic MXene with magnetic transition metal atoms. Moreover, both the magnetic ground states and the magnetocrystalline anisotropy energy of the i-MXenes can be effectively manipulated by strain, indicating strong piezomagnetic effect. Further studies on the transport properties reveal that i-MXenes provide an interesting playground to realiz…
We present a two-color Kerr microscopy system based on two electronically synchronized erbium-fiber laser oscillators with independently tunable emission energies spanning most of the visible spectrum. Combining a spatial resolution below 2 $μ$m and sub-ps time resolution with high sensitivity and cryogenic sample temperatures, it is ideally suited for studying spin and valley dynamics in a wide range of two-dimensional materials. We illustrate its capabilities by studying a monolayer of the common semiconducting transition metal disulfide MoS$_2$.
A theory of an optical two-photon breather in a graphene monolayer (or graphene-like two-dimensional material) is constructed. The system of the material equations for two-photon transitions and the wave equation for transverse magnetic polarized modes of the surface plasmon polaritons are shown to reduce to the nonlinear Schrödinger equation with damping. Explicit analytical expressions for a surface small intensity two-photon breather (0$π$ pulse) of self-induced transparency are obtained. It is shown that the optical conductivity of graphene reduces the amplitude of the surface two-photon n…
We study exciton radiative decay in a two-dimensional material, taking into account large thermal population in the non-radiative states, from which excitons are scattered into the radiative states by acoustic phonons. We find an analytical solution of the kinetic equation for the non-equilibrium distribution function of excitons in the radiative states. Our estimates for bright excitons in transition metal dichalcogenides indicate a strong depletion of radiative state population due to insufficient exciton-phonon scattering rate at low temperatures.
We review experimental and theoretical results on thermal transport in semiconductor nanostructures (multilayer thin films, core/shell and segmented nanowires), single- and few-layer graphene, hexagonal boron nitride, molybdenum disulfide and black phosphorus. Different possibilities of phonon engineering for optimization of electrical and heat conductions are discussed. The role of the phonon energy spectra modification on the thermal conductivity in semiconductor nanostructures is revealed. The dependence of thermal conductivity in graphene and related two-dimensional (2D) materials on tempe…
We use a generative neural network model to create thousands of new, one-dimensional materials. The model is trained using 508 stable one-dimensional materials from the Computational 1D Materials Database (C1DB) database. More than 500 of the new materials are shown with density functional theory calculations to be dynamically stable and with heats of formation within 0.2 eV of the convex hull of known materials. Some of the new materials could also have been obtained by chemical element substitution in the training materials, but completely new classes of materials are also produced. The band…
The advent of graphene and other two-dimensional van der Waals materials, with their unique electrical, optical, and thermal properties, has resulted in tremendous progress for fundamental science. Recent developments suggest that taking one more step down in dimensionality - from monolayer, atomic sheets to individual atomic chains - can bring exciting prospects as the ultimate limit in material downscaling is reached while establishing an entirely new field of one-dimensional quantum materials. Here we review this emerging area of one-dimensional van der Waals quantum materials and anticipat…
The emergence of graphene and two-dimensional van der Walls materials renewed interest to investigation of the low-frequency noise in the low-dimensional systems. The layered van der Waals materials offers unique opportunities for studying the low-frequency noise owing to the properties controlled by the thickness of these materials, and tunable carrier concentration. In this review, we describe unusual low-frequency noise phenomena in quasi-2D and quasi-1D van der Waals materials. We also demonstrate that the low-frequency noise spectroscopy is a powerful tool for investigation of the electro…
Using the tight-binding approach, we analyze the effect of a one-dimensional superlattice (1DSL) potential on the electronic structure of black phosphorene and transition metal dichalcogenides. We observe that the 1DSL potential results in a decrease of the energy band gap of the two-dimensional (2D) materials. An analytical model is presented to relate the decrease in the direct-band gap to the different orbital characters between the valence band top and conduction band bottom of the 2D materials. The direct-to-indirect gap transition, which occurs under a 1DSL potential with an unequal barr…
While preserving many of the unusual features of single-layer graphene, few-layer graphene (FLG) provides a richness and flexibility of electronic structure that render this set of materials of great interest for both fundamental studies and applications. Essential for progress, however, is an understanding of the evolution of the electronic structure of these materials with increasing layer number. In this report, the evolution of the electronic structure of FLG, for N = 1 - 8 atomic layers, has been characterized by measurements of the optical conductivity spectra. For each layer thickness N…
The discovery of graphene and other two-dimensional (2-D) materials has stimulated a general interest in low-dimensional (low-D) materials. Whereas long time ago, Peierls and Landau's theoretical work demonstrated that any one- and two-dimensional materials could not exist in any finite temperature environment. Then, two basic issues became a central concern for many researchers: How can stable low-D materials exist? What kind of low-D materials are stable? Here, we establish an energy stability criterion for low-D materials, which seeks to provide a clear answer to these questions. For a cert…
Two dimensional optical materials, such as graphene can be characterized by a surface conductivity. So far, the transformation optics schemes have focused on three dimensional properties such as permittivity $ε$ and permeability $μ$. In this paper, we use a scheme for transforming surface currents to highlight that the surface conductivity transforms in a way different from $ε$ and $μ$. We use this surface conductivity transformation to demonstrate an example problem of reducing scattering of plasmon mode from sharp protrusions in graphene.
We study hydrodynamic phonon heat transport in two-dimensional (2D) materials. Starting from the Peierls-Boltzmann equation within the Callaway model, we derive a 2D Guyer-Krumhansl-like equation describing non-local hydrodynamic phonon transport, taking into account the quadratic dispersion of flexural phonons. In additional to Poiseuille flow, second sound propagation, the equation predicts heat current vortices and negative nonlocal thermal conductance in 2D materials, common in classical fluid but scarcely considered in phonon transport. Our results also illustrate the universal transport …
Low-dimensional materials differ from their bulk counterpart in many respects. In particular, the screening of the Coulomb interaction is strongly reduced, which can have important consequences such as the significant increase of exciton binding energies. In bulk materials the binding energy is used as an indicator in optical spectra to distinguish different kinds of excitons, but this is not possible in low-dimensional materials, where the binding energy is large and comparable in size for excitons of very different localization. Here we demonstrate that the exciton band structure, which can …
Two dimensional (2D) materials, e.g. graphene, transition metal dichalcogenides (TMDs), black phosphorus (BP), have demonstrated fascinating electrical and optical characteristics and exhibited great potential in optoelectronic applications. High performance and multifunctional devices were achieved by employing diverse designs of architectures, such as hybrid systems with nanostructured materials, bulk semiconductors and organics, forming 2D heterostructures. In this review, we mainly discuss the recent progresses of 2D materials in high responsive photodetectors, light-emitting devices and s…
Deterministic transfer of two-dimensional crystals constitutes a crucial step towards the fabrication of heterostructures based on artificial stacking of two-dimensional materials. Moreover, control on the positioning of two-dimensional crystals facilitates their integration in complex devices, which enables the exploration of novel applications and the discovery of new phenomena in these materials. Up to date, deterministic transfer methods rely on the use of sacrificial polymer layers and wet chemistry to some extent. Here, we develop an all-dry transfer method that relies on viscoelastic st…
We investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. We obtain the exact solution of the shifted and truncated Coulomb problems, with the wavefunctions expressed in terms of special functions (namely Whittaker functions), whilst the energy spectrum must be determined via solutions to transcendental equations. Most notably, there are critical bandgaps below which certain low-lying quantum states are missing in a manifestation of atomic collapse.
We derive the explicit analytical form for the charge-dipole and dipole-dipole interactions in 2D configuration space. We demonstrate that the reduction of dimensionality can alter the charge-dipole and dipole-dipole interactions in 2D case. The asymptotics of these interactions at large distances coincide to the charge-dipole and dipole-dipole interactions in 3D configuration space.
Confinement of the electron gas along one of the spatial directions opens an avenue for studying fundamentals of quantum transport along the side of numerous practical electronic applications, with high-electron-mobility transistors being a prominent example. A heterojunction of two materials with dissimilar electronic polarisation can be used for engineering of the conducting channel. Extension of this concept to single-layer materials leads to one-dimensional electron gas (1DEG). MoS2/WS2 lateral heterostructure is used as a prototype for the realisation of 1DEG. The electronic polarisation …
Two-dimensional (2D) topological materials (TMs) have attracted tremendous attention due to the promise of revolutionary devices with non-dissipative electric or spin currents. Unfortunately, the scarcity of 2D TMs holds back the experimental realization of such devices. In this work, based on our recently developed, highly efficient TM discovery algorithm using symmetry indicators, we explore the possible 2D TMs in all non-magnetic compounds in four recently proposed materials databases for possible 2D materials. We identify hundreds of 2D TM candidates, including 205 topological (crystalline…
Controlling extra charge carriers is pivotal in manipulating electronic, optical, and magnetic properties of various two-dimensional (2D) materials. Nonetheless, the ubiquitous hole doping of 2D materials in the air and acids has been controversial in its mechanistic details. Here we show their common origin is an electrochemical reaction driven by redox couples of oxygen and water molecules. Using real-time photoluminescence imaging of WS2 and Raman spectroscopy of graphene, we capture molecular diffusion through the 2D nanoscopic space between 2D materials and hydrophilic substrates, and sho…
Electron supercollimation, in which a wavepacket is guided to move undistorted along a selected direction, is a highly desirable property that has yet been realized experimentally. Disorder in general is expected to inhibit supercollimation. Here, we report a counter-intuitive phenomenon of electron supercollimation by disorder in graphene and related Dirac fermion materials. We show that one can use one-dimensional disorder potentials to control electron wavepacket transport. This is distinct from known systems where an electron wavepacket would be further spread by disorder and hindered in t…
We demonstrate how weak hybridization can lead to apparent heavy doping of 2d materials even in case of physisorptive binding. Combining ab-intio calculations and a generic model we show that strong reshaping of Fermi surfaces and changes in Fermi volumes on the order of several 10$\%$ can arise without actual charge transfer. This pseudodoping mechanism is very generically effective in metallic 2d materials either weakly absored to metallic substrates or embedded in vertical heterostructures. It can explain strong apparent doping of TaS2 on Au (111) observed in recent experiments. Consequence…
We develop a theory of optical transitions in Coulomb impurity-doped two-dimensional transition metal dichalcogenide monolayers and study the transitions from the spin-resolved valence band to the (Coulomb) donor and acceptor impurities under the influence of a synthetic valley-selective magnetic field produced by a mechanical strain. It is shown that the optical properties of the system are determined by the strength of the synthetic magnetic field, which uncovers an experimental tool, which can be used to manipulate the properties of two-dimensional materials in valley magneto-optoelectronic…
There has been a huge increase of interests in two-dimensional van der Waals materials over the past ten years or so with the conspicuous absence of one particular class of materials: magnetic van der Waals systems. In this Viewpoint, we point it out and illustrate how we might be able to benefit from exploring these so-far neglected materials.
In recent years, noncollinear topological textures have long gained increasing research attentions for their high values of both fundamental researches and potential applications. The recent discovery of intrinsic orders in magnetic and polar two-dimensional van der Waals materials provides a new ideal platform for the investigation of noncollinear topological textures. Here, we review the theoretical and experimental progresses on noncollinear topological textures in two-dimensional van der Waals materials in very recent years. During these years, magnetic skyrmions of both Bloch and Néel typ…
Current theoretical description of field-induced electron emission remains mostly bounded by the classic Fowler-Nordheim (FN) framework developed nearly one century ago. For the emerging class of two-dimensional (2D) materials, many basic assumptions of FN model become invalid due to their reduced dimensionality and exotic electronic properties. In this work, we develop analytical and semi-analytical models of field-induced vertical electron emission from the surface of 2D materials by explicitly taking into account the reduced dimensionality, non-parabolic energy spectrum, non-conserving in-p…
We present a comprehensive review of formation and control of single photon sources from two dimensional materials. We critically analyze the creation and control of these quantum emitters both at room and at low temperature. Deterministic formation and position controlled methodology is elaborated and pictorially explained. We enlist major single photon sources from various two dimensional and non two dimensional resources. Plasmonic waveguides and the interfacing of single photon sources with them are critically analyzed and reviewed. Furthermore, we envisize the geometry of plasmonic wavegu…
