In this tutorial we introduce the reader to several theoretical methods of determining the exciton wave functions and the corresponding eigenenergies. The methods covered are either analytical, semi-analytical, or numeric. We make explicit all the details associated with the different methods, thus allowing newcomers to do research on their own, without experiencing a steep learning curve. The tutorial starts with a variational method and ends with a simple semi-analytical approach to solve the Bethe-Salpeter equation in two-dimensional (2D) gapped materials. For the first methods addressed in this tutorial, we focus on a single layer of hexagonal Boron Nitride (hBN) and of transition metal dichalcogenide (TMD), as these are exemplary materials in the field of 2D excitons. For explaining the Bethe- Salpeter method we choose the biased bilayer graphene, which presents a tunnable band gap. The system has the right amount of complexity (without being excessive). This allows the presentation of the solution of the Bethe-Salpeter equation in a context that can be easily generalized to more complex systems or to apply it to simpler models.
Scattering of excitons by free carriers is a phenomena which is especially important when considering moderately to heavily doped semiconductors in low temperature experiments, where the interaction of excitons with acoustic and optical phonons is reduced. In this paper, we consider the scattering of excitons by free carriers in monolayer hexagonal Boron Nitride encapsulated by a dielectric medium. We describe the excitonic states by variational wave functions, modeling the electrostatic interaction via the Rytova--Keldysh potential. Making the distinction between elastic and inelastic scatter…
Excitonic optical absorption in strained monolayer CrSBr
Universidad Autónoma de Madrid（马德里自治大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Universitat de València（瓦伦西亚大学）；Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC)（马德里材料科学研究所）
Many-body interactions between quasiparticles (electrons, excitons, and phonons) have led to the emergence of new complex correlated states and are at the core of condensed matter physics and material science. In low-dimensional materials, unique electronic properties for these correlated states could significantly affect their optical properties. Herein, combining photoluminescence, optical reflection measurements and theoretical calculations, we demonstrate an unconventional excitonic state and its bound phonon sideband in layered silicon diphosphide (SiP$_2$), in which the bound electron-ho…
When transition-metal dichalcogenide monolayers lack inversion symmetry, their low-energy single particle spectrum can described by tilted massive Dirac Hamiltonians. The so-called Janus materials fall into that category. Inversion symmetry can also be broken by the application of out-of-plane electric fields, or by the mere presence of a substrate. Here we explore the properties of excitons in TMDC monolayers lacking inversion symmetry. We find that exciton binding energies can be larger than the electronic band gap, making such materials promising candidates to host the elusive exciton insul…
Substrates have strong effects on optoelectronic properties of two-dimensional (2D) materials, which have emerged as promising platforms for exotic physical phenomena and outstanding applications. To reliably interpret experimental results and predict such effects at 2D interfaces, theoretical methods accurately describing electron correlation and electron-hole interaction such as first-principles many-body perturbation theory are necessary. In our previous work [Phys. Rev. B 102, 205113(2020)], we developed the reciprocal-space linear interpolation method that can take into account the effect…
We introduce and theoretically analyze the concept of manipulating optical chirality via strong coupling of the optical modes of chiral nanostructures with excitonic transitions in molecular layers or semiconductors. With chirality being omnipresent in chemistry and biomedicine, and highly desirable for technological applications related to efficient light manipulation, the design of nanophotonic architectures that sense the handedness of molecules or generate the desired light polarization in an externally controllable manner is of major interdisciplinary importance. Here we propose that such…
Two-dimensional (2D) materials van der Waals heterostructures (vdWHs) provides a revolutionary route towards high-performance solar energy conversion devices beyond the conventional silicon-based pn junction solar cells. Despite tremendous research progress accomplished in recent years, the searches of vdWHs with exceptional excitonic solar cell conversion efficiency and optical properties remain an open theoretical and experimental quest. Here we show that the vdWH family composed of MoSi$_2$N$_4$ and WSi$_2$N$_4$ monolayers provides a compelling material platform for developing high-performa…
We present an ab initio computational approach for the calculation of resonant Raman intensities, including both excitonic and non-adiabatic effects. Our diagrammatic approach, which we apply to two prototype, semiconducting layered materials, allows a detailed analysis of the impact of phonon-mediated exciton-exciton scattering on the intensities. In the case of bulk hexagonal boron nitride, this scattering leads to strong quantum interference between different excitonic resonances, strongly redistributing oscillator strength with respect to optical absorption spectra. In the case of MoS$_2$,…
Despite 2D materials holding great promise for a broad range of applications, the proliferation of devices and their fulfillment of real-life demands are still far from being realized. Experimentally obtainable samples commonly experience a wide range of perturbations (ripples and wrinkles, point and line defects, grain boundaries, strain field, doping, water intercalation, oxidation, edge reconstructions) significantly deviating the properties from idealistic models. These perturbations, in general, can be entangled or occur in groups with each group forming a complex perturbation making the …
Excitonic insulators host a condensate of electron-hole pairs at equilibrium, giving rise to collective many-body effects. Although several materials have emerged as excitonic insulator candidates, evidence of long-range coherence is lacking and the origin of the ordered phase in these systems remains controversial. Here, using ultrafast pump-probe microscopy, we investigate the possible excitonic insulator Ta$_2$NiSe$_5$. Below 328 K, we observe the anomalous micrometer-scale propagation of coherent modes at velocities of the order of $\sim10^5$ m/s, which we attribute to the hybridization be…
Quasiparticle effects and strong excitonic features in exfoliable 1D semiconducting materials
Università di Roma Tor Vergata（罗马托尔维加塔大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学）；Università Roma Tre（罗马第三大学）；Università degli studi di Milano Bicocca（米兰比可卡大学）；Paul Scherrer Institut (PSI)（保罗谢尔研究所）
Interaction induced topological states remain one of the fascinating phases in condensed matter physics. The exciton condensate has recently sparked renewed interest due to the discovery of new candidate materials and its driving force to realize exotic topological states. In this work, we explore the exciton orders induced high-order topology in the bilayer quantum spin Hall insulators and find that the topological excitonic corner states can be realized by tuning the gate and magnetic field. When an in-plane Zeeman field is applied to the system, two or four excitonic boundary-obstructed cor…
Innovations in imaging technology involves finding strategies and materials suitable for detection applications over the entire infrared range. Herein, we propose a new design concept based on the unique feature of an excitonic insulator, namely, negative exciton transition energy ($E_t$). We demonstrate this concept using first-principles $GW$-BSE calculations on one-dimensional organometallic wire (CrBz)$_\infty$. The pristine (CrBz)$_\infty$ exhibits an excitonic instability due to a negative $E_t$ for the lowest exciton. Substitutional doping can continuously tune the $E_t$ from $\sim$0 to…
Monolayer C$_3$N is an emerging two-dimensional indirect band gap semiconductor with interesting mechanical, thermal, and electronic properties. In this work we present a description of C$_3$N electronic and dielectric properties, focusing on the so-called momentum-resolved exciton band structure. Excitation energies and oscillator strengths are computed in order to characterize bright and dark states, and discussed also with respect to the crystal symmetry. Activation of excitonic states is observed for finite transferred momenta: Indeed, we find an active indirect exciton at $\sim$ 0.9 eV, s…
Exciton enhanced nonlinear optical responses in monolayer h-BN and MoS2: Insight from first-principles exciton-state coupling formalism and calculations
University of California at Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；National Center of Theoretical Physics（国家理论物理中心）；Institute of Atomic and Molecular Sciences, Academia Sinica（中央研究院原子与分子科学研究所）
