Session R12: 2D Materials: Magnetism and Optoelectronics

Relative stability and magnetic ground state of all stacking patterns in bilayer chromium trihalides from first principles

Chromium trihalides, CrX₃ (X = Cl, Br, I), are layered magnetic materials that have recently attracted considerable attention owing to their easy exfoliability. Their monolayers are ferromagnetic, with spins lying in-plane for CrCl₃ and out-of-plane for CrBr₃ and CrI₃. This difference is reflected also in distinct interlayer interactions when layers are stacked into their bulk: antiferromagnetic for CrCl₃, while ferromagnetic for the others. Still, even multilayers of CrI₃ behave as antiferromagnets, whereas CrBr₃ remains ferromagnetic. Here, we address this controversy by studying bilayers of these materials using density functional theory. We enumerate all possible stacking patterns with the smallest unit cell and investigate their relative stability. We show that, depending on the stacking order, the magnetic ground state can be different. In particular, we recover that the bulk stacking is indeed the most stable and it is correctly ferromagnetic for CrI₃ and CrBr₃, although there exist other low-lying metastable configurations that are antiferromagnetic. Based on our findings, we speculate on how the apparent controversy could be resolved.   

C1 vacancy in pentagraphene

Pentagraphene (PG), a two-dimensional allotrope of carbon with only five-membered rings, was recently predicted to exhibit exciting electronic and thermal properties with possible implications in nanoelectronics. However, its potential properties arising from defects have not been explored yet. Here, we explore the C1 vacancy in PG using first-principles density functional calculations. This defect introduces four midgap levels indicating the possibility of studying the charge states. The charged defect is amphoteric with deep donor and deep acceptor levels. Introducing the vacancy in the sheet renders it inherently ferromagnetic (FM) with a magnetic moment of 4 μ_B. Upon further investigating spin polarization in PG, three possible unique magnetic configurations are found to exist: FM, anti-ferromagnetic (AFM)−dominant, and quenched-AFM. The energy differences between the FM and the AFM states are on an average ~2 meV/atom, indicating that reversible spin manipulation through thermal energy is possible.   

Magnon-assisted tunnelling in van der Waals heterostructures based on CrBr 3

Recently, the family of two-dimensional materials has been expanded to include ferromagnets. It was shown that CrI₃ exhibits ferromagnetism down to thicknesses of a single monolayer [Huang, B. et al. Nature 546, 270 (2017)]. CrI₃ is part of a group of materials known as the chromium trihalides, CrX₃ (where X=Cl, Br or I). I will report on a few layers of exfoliated CrBr₃ (2-6 layers) that are also ferromagnetic by fabricating and characterising functional tunnelling devices where the CrBr₃ layer is sandwiched in between two graphene electrodes. I will also report a new type of tunnelling mechanism in van der Waals heterostructures by demonstrating that electrons in our device tunnel between the graphene layers via the emission (and, at high temperature, absorption) of magnons in the CrBr₃ barrier.
  

Spin texture of a quasi-two-dimensional ferromagnetic kagome metal

The discovery of low dimensional, long range magnetic order and the study on accurate control of such order have led to the revolution of magnetic storage devices that reformed our daily lives. Two dimensional systems with underlying kagome symmetry is found to be one of the most convenient platforms for the creation and manipulation of various magnetic structures. For example, planar ferromagnetism and non-colinear antiferromagnetism are present in kagome metals Fe₃Sn₂ and Mn₃Sn, respectively, both of which are also recently found to be topologically nontrivial. In this talk, we report our study on the spin texture of Fe₃Sn₂, using both spin-resolved ARPES and DFT calculations. Our results show that the topological Dirac bands at the K points of Fe₃Sn₂ originates from inner layers of the crystal, and are highly spin-polarized along a single spatial direction, realizing in-plane ferromagnetism. This study reveals the low-lying spin texture of a two dimensional topological metal, serving as guidence for spintronic applications on systems alike.   

Bulk electronic and local magnetic properties of semiconducting 2H-MoTe2

Layered transition metal dichalcogenides are currently intensively investigated due to their opto-electronic, superconducting and topological properties as well as their potential usage as mono-layer building blocks. However, despite their layered nature they often exhibit three dimensional (3D) properties in the bulk. Surprisingly, in semiconducting 2H-MoTe₂ long-range magnetic order of unknown origin has recently been observed at low temperature [1]. Here we present the full 3D band structure of 2H-MoTe₂, determined with soft X-ray ARPES. We find a pronounced k_z dispersion in most bands, consistent with ab-inito calculations, proving the three dimensional character of this material.
Furthermore, we present results of beta detected ⁸Li NMR measurements and show that the spin-lattice relaxation of the implanted Li ions is inconsistent with long range magnetic order, but supports the presence of magnetic fluctuations. We also find signatures of Li diffusion below room temperature, indicating a potential application in Li battery materials.

[1] Z. Guguchia, et. al., arXiv:1711.05392v2 (2017)   

Many-body quantum Monte Carlo study of 2D materials: cohesion and band gap in single-layer phosphorene

Quantum Monte Carlo (QMC) is applied to obtain the fundamental (quasiparticle) electronic band gap, Δ_f, of a semiconducting 2D phosphorene. Similarly to other 2D materials, the electronic structure of phosphorene is strongly influenced by reduced screening, making it challenging to obtain reliable predictions by single-particle density functional or many-body GW methods. Using the recently uncovered universal scaling between the exciton binding energy and Δ_f, we predict the optical gap of about 1.7 eV that can be directly related to experiments. The QMC gaps agree with recent optical absorption and photoluminescence measurements. We also predict the cohesion of phosphorene to be only slightly smaller than that of the bulk crystal. Our investigations not only benchmark GW methods and experiments, but also open the field of 2D electronic structure to computationally intensive but highly predictive QMC methods which include many-body effects such as electronic correlations and van der Waals interactions explicitly.   

Interacting Rydberg Exciton-Polaritons in Two-Dimensional Transition Metal Dichalcogenides

Strong optical nonlinearities play a central role in realizing quantum photonic technologies. In solid state systems, the exciton-polariton which result from the hybridization of material excitations and cavity photons are an attractive candidate to realize such nonlinearities. The interaction arising from the material component, excitons, forms the basis of the polaritonic nonlinearity. Several solid state systems have demonstrated nonlinear interaction of polaritons using the n = 1 excitonic state. However, the nonlinear interaction can be significantly enhanced if excited Rydberg excitonic states can be used instead of the ground state excitons. Recently such excited Rydberg excitonic states have been observed in monolayer transition metal dichalcogenides. Here we demonstrate the formation of Rydberg exciton-polaritons in monolayer WSe2 embedded in a microcavity. Owing to the larger wavefunctions of the Rydberg excitons, these polaritons show greater nonlinear response evidenced through the blue shift of the lower polariton branch under optical excitation. The demonstration of Rydberg exciton-polaritons in two-dimensional semiconductors and their enhanced nonlinear response may facilitate the realization of quantum photonic logic gates and processors.   

Room temperature dynamical control and electroluminescence from microcavity polaritons in monolayer transitional metal dichalcogenides

We demonstrate modulation of exciton-photon interaction in strong coupling regime showing polariton branches at room temperature in monolayer WS₂ field effect transistor embedded inside a microcavity. Transitions from strong to weak coupling happens when WS₂ becomes electron doped under gating due to reduction in oscillator strength of the excitons arising from decreased Coulomb interaction. For polariton electroluminescence from a monolayer WS₂ at room temperature we incorporate a tunnel field effect transistor with graphene-hBN-WS₂-hBN-graphene van der Waal heterostructure inside the microcavity. Injected electrons and holes tunnel through hBN barrier and recombine in the WS₂ resulting in luminescence and shows clear polariton branches. Our findings with these new class of materials pave a novel way to realize low energy optoelectronic switches and possibly room temperature based polariton lasers through electrically controlled polariton luminescence.   

Collective electronic properties of an α-T3 lattice at finite temperatures

Many-body electronic properties, including plasmons, their damping, static screening and transport coefficients have been
calculated based on the finite-temperature polarization function for the α-T₃ model. We have thoroughly
investigated the role of the coupling strength parameter $\alpha$ for the extra atom at the center of the honeycomb lattice, which in our case could be continuously varied from 0 (graphene) to 1 (the dice lattice). Specifically, we obtained and analyzed the dice lattice limit. We have derived several crucial semi-analytical approximations for the static and long
wavelength limits, related to the finite-temperature behavior of the plasmon excitations in α-T₃ materials.   

Probing Moiré Interlayer Exciton States in van der Waals Heterostructures

Moiré superlattices dramatically modify the properties of electrons and excitons in van der Waals heterostructures by introducing a new length and energy scale. The effect can be especially strong for interlayer excitons, where electrons and holes reside in different layers and are sensitive to the local atomic configuration. For example, it was recently predicted that moiré superlattices can host localized interlayer exciton states with distinct optical selection rules due to an emergent moiré angular momentum. In this talk, I will discuss our effort to observe distinct interlayer exciton states and to probe the possible effects of the moiré angular momentum on the interlayer exciton states.   

Controlling Optical Properties of Electron Hole Plasma in Monolayer Transition Metal Dichalcogenides

Recently, monolayer transition metal dichalcogenides (TMDs) have shown the ability to undergo a phase transition between an insulating gas of strongly bound excitons to a conducting electron-hole plasma (EHP). Typically, to reach this phase transition, ultrashort optical pulses are used to create a non-equilibrium high carrier density. However, this EHP state can also be reached via continuous wave (CW) excitation. In most semiconductors, the high carrier density needed for the EHP phase transition cannot be reached using CW light since nonlinear recombination processes limit the equilibrium carrier density. However, the mechanical properties of monolayer TMDs can be used to manipulate the electronic structure to change the carrier dynamics, allowing for high carrier densities to be reached through CW excitation. Specifically, by applying strain, the energy offset between direct K-K and indirect Γ-K transitions can be used to shift the carrier population between valleys. By interchanging different transition metals or chalcogens, we can change the indirect-direct energy offset creating an EHP predominately in the indirect transition or direct transition. This has a profound impact on the optical properties of the EHP, providing an avenue to engineer novel opto-electronic devices.   

Excitonic and lattice contributions to the charge density wave in 1T-TiSe2 revealed by a relaxation bottleneck

Using time- and angle-resolved photoemission spectroscopy (TR-ARPES), we have studied the femtosecond dynamics of the charge density wave (CDW) in 1T-TiSe₂. This material exhibits a commensurate CDW with a (2 x 2 x 2) lattice distortion below 200 K for which the mechanism is still debated today. One of the recurring problems is disentangling the contributions from the electronic and lattice-driven order. Here, we have observed the photo-induced suppression of the CDW in real-time by tracking the valence band maximum at the Γ-point following an intense laser pulse. The timescales of gap closing and band-replica unfolding (< 200 fs), and the relatively low fluence required for these processes are suggestive of an excitonic mechanism. During recovery, coherent oscillations of the CDW gap are observed relating to the A_1g (3.4 THz) mode. A detailed pump fluence dependence reveals several regimes, including impeded recovery at high fluence. This bottleneck coincides with a change in the dominant frequency seen in the oscillations. Using complementary time-resolved reflectivity, we have established the threshold fluence of this phenomenon to be F > 60 μJ cm^-2. Our work is supported by a rate equation model which highlights the crucial role of excitons and phonons in this complex system.   

Elecromagnetic Fileld dependendent Coulomb renormalisation in Dirac Materials

Condensed matter physics is witnessing a rapid expansion of materials with Dirac fermion quasiparticle excitations. In recent works it has been shown that a full understanding of the optical properties of such materials requires one to go beyond the standard approach of the semiconductor Bloch equations (SBEs). In his influential paper Ishikawa derived an extended version of the SBEs for graphene using the formalism of instantaneous eigenstates. More recently his approach was generalised further for the case of a gapped material. These generalised Dirac-Bloch (DBEs) equations reproduce novel and previously unexplained nonlinear optical properties of graphene and gapped graphene, however they do not include Coulomb interactions that are in general very strong in two dimensional semiconductors. starting from the quantisation of the instantaneous Dirac field we include Coulomb interactions and provide a fully renormalised version of the DBEs. By solving these equations we account for the linear optical properties of 2D Dirac semiconductor. We discuss how the absorption spectrum evolves as the energy gap is reduced to zero. We then study the strong Coulomb coupling regime in which the excitons form a relativistic Bose-Einsten condensate.
  

Excited excitonic states in second harmonic spectra of 2D materials with ab-initio many-body methods

First principles calculations of the second harmonic generation (SHG) of various semiconducting 2D materials including transition metal dichalcogenides (TMDs) are performed using a time-dependent Bethe-Salpeter Equation (TDBSE) nonequilibrium Green’s function approach. It is shown that by increasing simulation time, spectral resolution can be improved, resolving features in the SHG spectrum that can be attributed to excited states of excitons. By comparing the differences in excited exciton energies to the differences observed experimentally, a calibration metric for the degree of over- or under-binding of the excitons can be formulated. Moreover, the degree to which substrate screening in these materials modifies not only the binding energy and the fundamental gap, but also the relative energies of excited states, is explored. The relative intensities of the excited exciton peaks in the SHG are also examined for the additional layer of information they can provide beyond corresponding peaks in the first-order spectra. This focus on a more precise understanding of excitonic resonances in the second harmonic spectrum lays the groundwork for a more systematic use of this TDBSE method for studying nonlinear optical properties in 2D materials.