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Biased bilayer graphene (BBG) is an important system for studies of excitonic effects in graphene--based systems, with its easily tunable bandgap. This bandgap is governed by an external gate voltage, allowing one to tune the optical response of the system. In this paper, we study the excitonic linear and nonlinear optical response of Bernal stacked BBG as a function of the gate voltage, both for in--plane (IP) and out--of--plane (OOP) directions. Based on a semi-analytical model of the electronic structure of BBG describing the influence of gate voltage on excitonic binding energies, we focus our discussion on both the IP and OOP excitonic response. Both linear and second harmonic generation (SHG) nonlinear responses are shown to be very sensitive to the gate voltage, as both the interband momentum matrix elements and the bandgap of the system will vary greatly with bias potential., Comment: 18 pages, 8 figures

The optical properties of two-dimensional materials are exceptional in several respects. They are highly anisotropic and frequently dominated by excitonic effects. Dipole-allowed second order non-linear optical properties require broken inversion symmetry. Hence, several two-dimensional materials show strong in-plane (IP) non-linearity but negligible out-of-plane (OOP) response due to vertical symmetry. By considering buckled hexagonal monolayers, we analyze the critical role of broken vertical symmetry on their excitonic optical response. Both linear as well as second order shift current and second harmonic response are studied. We demonstrate that substantial OOP non-linear response can be obtained, in particular, through off-diagonal tensor elements coupling IP excitation to OOP response. Our findings are explained by excitonic selection rules for OOP response and the impact of dielectric screening on excitons is elucidated., Comment: 20 pages, 8 figures

With the ever-growing interest in quantum computing, understanding the behaviour of excitons in monolayer quantum dots has become a topic of great relevance. In this paper, we consider a Wannier exciton confined in a triangular quantum dot of hexagonal Boron Nitride. We begin by outlining the adequate basis functions to describe a particle in a triangular enclosure, analyzing their degeneracy and symmetries. Afterwards, we discuss the excitonic hamiltonian inside the quantum dot and study the influence of the quantum dot dimensions on the excitonic states., Comment: 5 figures

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 scattering, the relevance of each transition between excitonic states is also considered. Finally, we discuss the contribution of free carrier scattering to the excitonic linewidth, analyzing both its temperature and carrier density dependence., Comment: 16 pages, 5 figures

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 insulator phase. We also investigate the excitonic contribution to their optical conductivity and discuss the associated optical selection rules., Comment: 9 pages, 5 figures

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., Comment: 31 pages, 111 references; we welcome comments and requests to add additional references; several changes relatively to version V1

Trilayer graphene is receiving an increasing level of attention due to its stacking--dependent magnetoelectric and optoelectric properties, and its more robust ferromagnetism relative to monolayer and bilayer variants. Additionally, rhombohedral stacked trilayer graphene presents the possibility of easily opening a gap via either an external electric field perpendicular to the layers, or via the application of external strain. In this paper, we consider an external electric field to open a bandgap in rhombohedral trilayer graphene and study the excitonic optical response of the system. This is done via the combination of a tight binding model with the Bethe--Salpeter equation, solved semi--analytically and requiring only a simple numerical quadrature. We then discuss the valley--dependent optical selection rules, followed by the computation of the excitonic linear optical conductivity for the case of a rhombohedral graphene trilayer encapsulated in hexagonal boron nitride. The tunability of the excitonic resonances via an external field is also discussed, together with the increasing localization of the excitonic states as the field increases., Comment: 17 pages, 6 figures

In this paper, we employ a fully microscopic approach to the study of interlayer excitons in hetero-bilayers. We use Fowler's and Karplus' method to access the dynamical polarizability of non--interacting interlayer excitons in a $\mathrm{WSe}_{2}/\mathrm{WS}_{2}$--based van der Waals heterostructure. Following from the calculation of the linear polarizability, we consider Svendsen's variational method to the calculation of the dynamic third--order polarizability. With this variational method, we study both two--photon absorption and third--harmonic generation processes for interlayer excitons in a $\mathrm{WSe}_{2}/\mathrm{WS}_{2}$ hetero--bilayer, discussing the various selection rules of intra--excitonic energy level transitions., Comment: 13 pages, 7 figures

In this paper we develop a fully microscopic theory of the polarizability of excitons in transition metal dichalcogenides. We apply our method to the description of the excitation $2$p dark states. These states are not observable in absorption experiments but can be excited in a pump-probe experiment. As an example we consider $2$p dark states in WSe\textsubscript{2}. We find a good agreement between recent experimental measurements and our theoretical calculations., Comment: 10 pages, 4 figures; we welcome comments and requests for adding relevant references to the topic

In this colloquium, we review the research on excitons in van der Waals heterostructures from the point of view of variational calculations. We first make a presentation of the current and past literature, followed by a discussion on the connections between experimental and theoretical results. In particular, we focus our review of the literature on the absorption spectrum and polarizability, as well as the Stark shift and the dissociation rate. Afterwards, we begin the discussion of the use of variational methods in the study of excitons. We initially model the electron-hole interaction as a soft-Coulomb potential, which can be used to describe interlayer excitons. Using an \emph{ansatz}, based on the solution for the two-dimensional quantum harmonic oscillator, we study the Rytova-Keldysh potential, which is appropriate to describe intralayer excitons in two-dimensional (2D) materials. These variational energies are then recalculated with a different \emph{ansatz}, based on the exact wavefunction of the 2D hydrogen atom, and the obtained energy curves are compared. Afterwards, we discuss the Wannier-Mott exciton model, reviewing it briefly before focusing on an application of this model to obtain both the exciton absorption spectrum and the binding energies for certain values of the physical parameters of the materials. Finally, we briefly discuss an approximation of the electron-hole interaction in interlayer excitons as an harmonic potential and the comparison of the obtained results with the existing values from both first--principles calculations and experimental measurements., Comment: 20 pages, 3 appendixes, 115 references, we welcome comments and suggestions for additional references

The Schr\"odinger equation in a square or rectangle with hard walls is solved in every introductory quantum mechanics course. Solutions for other polygonal enclosures only exist in a very restricted class of polygons, and are all based on a result obtained by Lam\'e in 1852. Any enclosure can, of course, be addressed by finite element methods for partial differential equations. In this paper, we present a variational method to approximate the low-energy spectrum and wave-functions for arbitrary convex polygonal enclosures, developed initially for the study of vibrational modes of plates. In view of the recent interest in the spectrum of quantum dots of two dimensional materials, described by effective models with massless electrons, we extend the method to the Dirac-Weyl equation for a spin-1/2 fermion confined in a quantum billiard of polygonal shape, with different types of boundary conditions. We illustrate the method's convergence in cases where the spectrum in known exactly and apply it to cases where no exact solution exists., Comment: 17 pages, 10 figures

We report high-pressure x-ray diffraction and magnetization measurements combined with ab-initio calculations to demonstrate that the high-pressure optical and transport transitions recently reported in TiOCl, correspond in fact to an enhanced Ti3+-Ti3+ dimerization existing already at room temperature. Our results confirm the formation of a metal-metal bond between Ti3+ ions along the b-axis of TiOCl, accompanied by a strong reduction of the electronic gap. The evolution of the dimerization with pressure suggests a crossover from the spin-Peierls to a conventional Peierls situation at high pressures., Comment: 9pages, 4 figures

We report a systematic enhancement of the pressure dependence of TN in A2+[V2]O4 spinels as the V-V separation approaches the critical separation for a transition to itinerant-electron behavior. An intermediate phase between localized and itinerant electron behavior is identified in Zn[V2]O4 and Mg[V2]O4 exhibiting mobile holes as large polarons. In Zn[V2]O4, cooperative ordering of V-V pairs below a Ts=TN does not totally suppress the V3+-ion spins at ambient pressure, but makes TN to decrease with pressure. Our results demonstrate that Zn[V2]O4 and Mg[V2]O4 are less localized than previously thought.

Here we present experimental and computational evidences to support that rock-salt cubic VO is a strongly correlated metal with Non-Fermi-Liquid thermodynamics and an unusually strong spin-lattice coupling. An unexpected change of sign of metallic thermopower with composition is tentatively ascribed to the presence of a pseudogap in the density of states. These properties are discussed as signatures of the proximity to a magnetic quantum phase transition. The results are summarized in a new electronic phase diagram for the 3d monoxides, which resembles that of other strongly correlated systems. The structural and electronic simplicity of 3d monoxides make them ideal candidates to progress in the understanding of highly correlated electron systems., Comment: Submitted to Phys. Rev. B

New electronic phases have been identified and placed in the (T,H) phase diagram of metallic NaxCoO2. At low Na-content (x = 0.36), the magnetic susceptibility diverges with a power law T^(-n), n<1, and shows (T,H) scaling, indicating the proximity to a magnetic quantum phase transition. At high Na contents (x = 0.6) the mass of the quasiparticles does never diverge, but renormalizes and becomes strongly field dependent at low temperatures, forming a heavy Fermi-Liquid. Our results make superconducting NaxCoO2 a clear candidate for magnetically mediated pairing.

We report a complete analysis of the formal oxidation state of Co in NaxCoO2, in the interval 0.31

We report the divergence of the nonlinear component of the bulk susceptibility in NaxCoO2 (0.3

In this paper we address many of the fundamental open questions regarding the glassy behavior of the magnetic/electronic phase segregated state in rare earth perovskites. In particular, magnetic relaxation experiments support that the collective effects (memory, ageing, etc.) are due to interparticle interactions, rather than the double-exchange vs. superexchange competition. A careful study of the non-linear susceptibility in the critical region is performed, and the critical exponents contrasted with those of conventional spin-glasses and concentrated quenched ferrofluids. The phase segregated state constitutes a sort of self-generated assembly of magnetic particles in which magnetic interaction introduces collectivity among the clusters., Comment: 5 figures, 8 pages

Throughout a complete Electron Spin Resonance (ESR) and magnetization study of La0.5Ca0.5MnO3, we discuss about the nature of the complex phase-segregated state established in this compound below T~210 K. Between TN