A 25 h series of courses devoted to the basics of 2D materials and research on these materials in Grenoble will be held from the 4th to the 8th of June, 2018, with the support of the local Nanosciences Foundation.

Grenoble is a lively breeding ground for 2D materials – graphene, boron nitride, transition metal dichalcogenides, ultrathin oxides, etc. This is one of the very few places worldwide involving such a high number of scientists. Overall about 10 large research laboratories are concerned, all supported by Grenoble Alpes University, CEA, CNRS, Grenoble INP, and INRIA.

The courses will be given by local actors. They are primarily intended for undergraduate students and young researchers, and are also open to other local staff with interest in this actively developing field. Four main topics will be covered: basic properties, materials science, analytical techniques and physical properties.

Registration is free but compulsory, and must be completed before the 25th of May, 2018, using the following link. Meals will be at the participants' expense, except for a lunch buffet offered the last day. The courses will be held on the CNRS campus (exact location to be announced).

The courses are eligible as part of the training program to be completed by Ph.D. students registered at Grenoble's Physics Doctoral School in relation with their research topic. A certificate will be delivered for subsequent validation of the 25 h of courses by the Doctoral School.

Program of the school:
(F = fundamental properties, M = materials science, A = analytical methods, P = physical properties):

Day 1, Monday 4th, room D420, Institut Néel
Welcome address 9:15-9:30 A. Fontaine
(F) Structure and membrane properties of 2D materials 9:30-10:30 J. Coraux
(F) Group theory applied to 2D materials 10:45-11:45 B. Canals
(M) Preparation (MBE, CVD) of 2D materials 13:30-15:00 J. Coraux, M. Jamet
(M) Van der Waals Heterostructures : from stacks to devices 15:15-16:45 V. Bouchiat
Day 2, Tuesday 5th, room D420, Institut Néel
(F) Electronic band structure of 2D materials 9:00-10:30 A. Cresti
(F) Vibrational properties in 2D materials 10:45-12:15 D. Basko
(A) Scanning tunneling microscopy and spectroscopy on 2D materials 14:00-16:00 V. Renard, J.-Y. Veuillen
Day 3, Wednesday 6th, room K223, Institut Néel
(P) Electro/optomechanics with 2D materials 9:00-10:00 O. Arcizet
(P) Quantum phase transition in/with 2D materials 10:15-12:15 P. Rodière, M.-A. Méasson
(M) Graphene-based materials for electrochemical storage 14:00-16:00 L. Dubois, F. Duclairoir
Day 4, Thursday 7th, room D420, Institut Néel
(P) Electronic magnetotransport in 2D materials 9:00-11:00 Th. Champel
(A) 2D materials and X-ray diffraction 11:15-12:15 G. Renaud
(P) Introduction to the Berry phase and application to 2D materials 14:00-16:00 P. Bruno
Day 5, Friday 8th, room K223, Institut Néel
(P) Excitons in 2D materials 9:00-11:00 C. Faugeras, J. Kasprzak
(P) Optics and magneto-optics of topological materials 11:15-12:15 M. Orlita
Buffet lunch, "Salle des convivalités", Institut Néel 12:15-14:00
(A) Low-voltage aberration correction transmission electron microscopy for 2D materials 14:00-15:00 H. Okuno
(A) Photoemission techniques for 2D materials 15:00-16:00 O. Renault

Abstracts of the courses:

  • Structural and membrane properties of 2D materials (J. Coraux) - An idealised view of 2D materials considers them as perfectly flat atomic lattices with long-range cristalline order. From this description a classification can be derived on simple crystallographic arguments, and this is the basis for understanding many of the collective excitations of the materials, and to derive, for instance, the electronic and phononic band structure. Yet, the expression “2D materials” itself is, strictly speaking, incorrect. They indeed live in a 3D world and rather behave as deformable membranes. Related to their vibrational properties they exhibit strongly nonlinear mechanical behaviours, tend to form nanoripples, have unusual thermal expansion, and are prone to mechanical instabilities. I will address these different aspects, from the 2D idealised view to the more realistic membrane description for suspended or on-substrate materials such as graphene and transition metal dichalcogenides.

  • Group theory applied to 2D materials (B. Canals) - The goal of this lecture is to introduce the notion of group and its relation with symmetry, but not only. An abstract group is an algebraic structure, the study of which allows to reduce the complexity of problems in condensed matter, unveil fundamental properties, or provide a practical toolbox, for instance. Examples shall be given, which in fact are related to the representation of the group structure, i.e. not the abstract group, but the way it acts on the physical space(s).

  • Introduction to the Berry phase (P. Bruno) - soon announced

  • Electronic band structure of 2D materials (A. Cresti) - I will start by briefly revising the basics of the band structure theory and by illustrating the main physical quantities we can obtain from it. Then, I will introduce the first-neighbor tight-binding Hamiltonian model for graphene, calculate the electronic structure of 2D graphene and graphene ribbons, derive the Dirac-like low-energy approximation, and discuss the effect of spin-orbit coupling. Finally, I will provide an overview of the electronic structure of the main 2D materials beyond graphene, an in particular monolayer transition metal dichalcogenides.

  • Vibrational properties of 2D materials (D. Basko) - I will start by discussing common properties of 2D crystals, their stability, and macroscopic theory of elastic waves in a 2D membrane. Then I will pass to the microscopic description of lattice vibrations, dynamical matrix, acoustic and optical phonons, symmetry properties. This part is material-specific; most of it will be presented for the simpler case of graphene, and I will briefly mention the classification of phonon modes in TMDCs. Next, i will introduce electron-phonon coupling in graphene and TMDCs. Finally, I will discuss how crystal vibrations can be probed by infrared and Raman spectroscopy.

  • Graphene growth on surfaces (J. Coraux) - It has been known for decades that surfaces of metals and metal carbides (e.g. SiC) can be covered by graphite, and in proper conditions, by even a single layer graphene. Long ago this was seen as a detrimental effect, a pollution that would alter the catalytic activity of metals or make insulating substrates become conductive on their surface. Starting from the mid-2000’s, researchers have realised that they may be able to control nucleation and growth on surfaces to prepare very high quality graphene, over large surfaces and in reproducible ways. In several respects growth of graphene on surfaces is a non conventional problem. In this lecture I will try to highlight these specificities, to stress key concepts of nucleation and growth, and to apply them to understand how graphene nucleates or growth, with or without defects. I will also give practical considerations on the preparation of graphene, that is controlled by a few groups in Grenoble.

  • CVD and MBE of 2D TMDCs (M. Jamet) - In this lecture, I will present the different methods to grow TMDCs. After a short introduction on these materials and their remarkable physical properties, I will describe the chemical and physical routes to produce such TMDC materials on large areas. I will mainly focus on chemical vapor deposition and the molecular beam epitaxy. The basic principles of both techniques will be discussed as well as the key parameters to adjust in order to obtain high-quality TMDC monolayers. In a second part, I will compare the advantages of both techniques regarding the electronic and optical properties of TMDC layers, the growth of alloys, doped layers (electrical and magnetic) and heterostructures.

  • Van der Waals Heterostructures: from stacks to devices (V. Bouchiat) - The isolation of graphene, in 2004 unlocked the physics of 2D crystals. This area was enriched 8 years ago by the isolation of a myriad of other 2D crystals such as hexagonal boron nitride, black phosphorus, transition metal dichalcogenides etc. The possibility of stacking these 2D materials with precise control down to the single atomic layer using van der Waals interactions has soon expanded even further the possibilities of this field of research. Indeed stacking layers on top of each other allows to fabricate new materials that help to tailor the interactions between the 2D crystals sandwiched together. A trove of novel electronic and optical properties associated to these couplings making van der Waals heterostructures a large field of its own. I will provide a comprehensive overview of the techniques to produce, stabilize and characterize these artificial materials, the new properties they offer and provide keys to better understand the already rich literature and future research directions both at the fundamental and applied levels.

  • Graphene-based materials for electrochemical storage and conversion (L. Dubois, F. Duclairoir) - Graphene and, very recently, other 2D materials are among the various materials that are investigated for electrochemical storage and conversion. Graphene with its high electrical conductivity, mechanical flexibility, its remarkable theoretical surface area, its ability to be found under different structuration degree (single layer, stacked layered materials, macroscopic assemblies…) and its propensity to be functionalized is an ideal candidate as active material or conductive scaffold for Li-ion batteries, supercapacitors and fuel-cells. This lecture will consist in an introductory parts on two electrochemical storage devices that are Li-ion batteries and supercapacitors. Issues linked to electrode formulation and electrolyte choices will be addressed. The chemical preparation and functionalization of graphene – dedicated to these applications - will be described. The interest of graphene and to some extent 2D materials will be summarized and literature case examples will be presented and explained. The last part of the course will deal about energy conversion with the introduction to fuel-cell operating. Here also the interest of 2D materials will be explained and case examples described.

  • 2D Materials probed by diffraction techniques (G. Renaud) - Almost all properties of 2D materials are very intimately linked to their atomic structure at the angstrom level, together with the organization in domains separated by defect. I will show on a few examples including epitaxial graphene and TMDCs that the technique of Grazing Incidence X-Ray Diffraction is very well suited to investigate the structural properties averaged over large areas. Using Synchrotron radiation, the detailed positions of atoms in the 2D sheet in epitaxy on a substrate and in the possible Moiré surface supercell can be determined with high accuracy. The average structure, symmetry, unit cell lattice parameters, domain size, rotation distributions and inhomogeneous strain are easily inferred from reciprocal space measurements. Most importantly, these measurements can be performed in situ, e.g. in Ultra-High Vacuum during growth, using standard growth techniques such as Molecular Beam Epitaxy or Chemical Vapor Deposition, possibly used in combination or during annealing or intercalation or even operando during e.g. catalysis.

  • Scanning tunneling microscopy and spectroscopy on 2D materials (V. Renard, J.-Y. Veuillen) - Scanning tunneling microscopy (STM) is one of the most powerful probe to investigate 2D materials because it combines atomically-resolved real space imaging of surfaces, with reciprocal space analysis and spectroscopic capabilities. In this lecture, after a brief overview of the experimental technique and of its theoretical background, several examples of STM inputs in the understanding of 2D materials physics will be addressed. In particular, we will study the structural characterization of moirés in van der Waals stacks and their effect on electronic properties. We will also show how the band dispersion E(k) and information on the nature of the electronic states can be recovered from quasi-particle interferences images.

  • Low voltage aberration corrected transmission electron microscopy for 2D materials (H. Okuno) / Photoemission techniques for 2D materials (O. Renault) - First part of the lecture concerns an atomic structure analysis of 2D materials. Low voltage aberration corrected transmission electron microscopy will be presented as a tool to visualize atomic structure of atomically thin 2D layers. Study of atomic defects with their dynamics and local chemical analysis will be demonstrated. A second aspect of the course will be dedicated to photoemission-based techniques: photoelectron spectroscopy (XPS, PES) for the determination of chemical states and work function; micron-scale angle-resolved photoemission (micro-ARPES) in the photoelectron emission microscope (PEEM) for investigating local band structure.

  • Electronic magnetotransport in 2D materials (Th. Champel) - The purpose of this lecture is to provide an introduction to the physics of the quantum Hall effects. After a general description of the transport properties of 2D electron gases in different magnetic field regimes, the focus will be mainly on the basic theoretical description of the integral quantum Hall effect (Landau levels, edge and bulk states). Finally, recent research directions (such as the observation of new phenomena, new materials, open theoretical questions) will also be addressed.

  • Electro/opto mechanics with 2D materials (O. Arcizet) - soon announced

  • Excitons in 2D materials (J. Kazsprack, C. Faugeras) - Some transition metal dichalcogenides of 2H-stacking (MX2 where M=Mo or W and X=S or Se or Te) are lamellar semiconductors with indirect band gaps ranging from the near infrared to the UV range of energy. Isolated in the form of monolayers, they become direct band gap semiconductors. Their optical response is dominated and determined by excitonic effects, owing to their two-dimensional character and reduced dielectric screening from the surrounding. Consequently, the binding energy and the absorption coefficient of these excitons is drastically enhanced with respect to their cousins existing in conventional semiconductor quantum wells. Furthermore, the interplay between inversion symmetry breaking and the strong spin-orbit interaction leads to unusual spin-valley properties, which can be addressed optically. In the first part of this lecture, we will describe the excitonic properties of monolayers from their reflectance and photoluminescence properties, their polarization properties related to the valley degree of freedom and the different dark or bright excitonic ground states that can be found in these different materials. We will then highlight the internal structure of these excitons based on the observation of exciton excited states and how they can be monitored by controlling the dielectric environment. We will then discuss multi-layers hosting so-called inter-layer excitons, i.e. composed of an electron and a hole located in neighbouring materials. In the second part, we will focus on the nonlinear optical properties of excitons in monolayers of transition metal dichalcogenides. We will sketch the link between the enhanced absorption, oscillator strength and the short radiative lifetime, occurring in a subpicosecond range. Such a short lifetime implies the homogeneous linewidth in a range of a few milli-electronVolts. Yet, the exciton line-shape is inhomogeneously broadened via the structural disorder. We will show how nonlinear spectroscopy disentangles homogeneous and inhomogeneous contributions to the spectral responses of these materials by inferring temporal dynamics of resonantly induced optical polarization. Using non-linear spectroscopy we will infer environmental effects, i.e. temperature, disorder and charge state exciton complexes, on the optical response. We will demonstrate drastic improvement and enhancement of the non-linear response in the monolayers shielded through the hetero-structuring.

  • Quantum phase transitions in/with 2D materials (M.-A. Méasson, P. Rodière) - In this lecture we will present an experimental view on the quantum phase transitions observed in the systems which have been reduced to few atomic layers or intrinsically 2D. We will focus on the electronic, lattice and spin degrees of freedom. A presentation of magnetic transitions and the question of the role of the strong thermal fluctuations in this context will be given. We will then present the charge-density-wave state observed in few systems and which persists in atomic layers systems. We will present the mechanism at the origin of this distortion, and explain why it can survive in 2D systems. Finally, after a general review on the superconducting state, its mechanism and its main characteristics, we will discuss the specific superconducting properties in 2D materials.

  • Optics and magneto-optics of topological materials (M. Orlita) - Zoology of topological materials (system dimensions, degeneracy, symmetry & protection); conical bands, density of states & Landau levels; intraband and interband excitations in conical bands; cyclotron resonance, Faraday rotation & Landau level spectroscopy.
Centre National de la Recherche Scientifique Commissariat à l'énergie atomique et aux énergies alternatives
Laboratoire d'alliances nanosciences-énergies du futur
Fondation Nanosciences
Université Grenoble Alpes
Institut polytechnique de Grenoble
Cross-disciplinary project NEED