**Topic 1: General introduction to 2D materials and vdW heterostructures – Lecturer: Dr. Reyes CALVO**

The discovery of graphene has given rise to a promising research field based on the unique properties of bi-dimensional van der Waals materials. For some of these materials, new properties arise in the single layer which are distinct to those of the bulk. For example, the single layer of the 1T’ phase of WTe2 is an inverted bulk semiconductor while its bulk is a semimetal; a direct gap and a pseudospin degree of freedom appear in the single layer of WSe2 or MoS2, which in bulk are indirect gap semiconductors preserving inversion symmetry. Some other 2D-materials maintain certain bulk properties such as superconductivity (NbSe2) or magnetic order (CrI3) down to the single layer limit, although modified by the 2D confinement. The properties of single (few) layers of these materials can be easily modified by proximity to other 2D materials or substrates. Single or few layer samples of different materials can be easily stacked in hybrid van der Waals heterostructures or transferred on to different substrates by direct growth and or by exfoliation and stamping techniques. Novel material properties can be engineered through an educated choice of the above components and the control of the induced interaction and proximity effects between them. As in a “Lego” game, materials with the desired properties can be combined with almost endless possibilities.

**Topic 2: Methods and techniques in studying of 2D materials – Lecturers: Dr. Reyes CALVO and Dr. Nurit AVRAHAM**

The discovery of topological systems at the crossover between the seventies and the eighties of the past century has permitted to have a better insight into the properties of solid-state systems. A gap in the band structure of a solid could hide more information than just a region of empty states. One of the experimental methods that play a major role in the experimental discovery of topological materials and their properties is scanning tunneling microscopy and spectroscopy (STM). Being a surface probe, this technique has the power to probe the unique properties of the exotic topological surface states. This tutorial will introduce the concept of topological materials and will explain the phenomenology of various topological phases. The students will understand the principle of operation of STM, and how to probe these materials using scanning tunneling microscopy and spectroscopy, and what type of information one can extract with this technique. This topic will demonstrate it by reviewing experimental studies on several novel quantum materials, starting from Graphene and moving to topological insulators (2D, 3D, layered), as well as, Weyl semimetal and 1D topological superconductors.

**Topic 3: Topological insulators and Topological Phases – Lecturers: Dr. Nurit AVRAHAM and Dr. Dario BERCIOUX**

Topological classification of electronic phases of matter has become a major concept in condensed matter physics in the last decade. Originally discussed in the context of the quantum Hall effect topological classification was later generalized to realistic materials such as topological insulators (TI) and later to Weyl and Dirac semimetals. Common to these topological phases *robust* surface states, with unique properties, that owe their existence to the presence of a topological bulk. In topological insulators, for example, the bulk is insulating but the surface is conduction. Not only that, the direction of the electron motion on the surface depends on the direction of their spins. In a Weyl semimetal, there exist unique surface states, called Fermi arcs. In the presence of magnetic field the electrons assume a circular motion where, in part of it, they flow on the surface, and in part of it, they dive into the bulk. Intriguingly, these odd effects are not disrupted by small defects in a crystal; if there’s some flaw in the surface, the current simply flows around it. It is impossible to get rid of these surface state. These robustness and other unique properties make these topological materials desirable for spintronic devices and for quantum computation. In this set of lecture, lecturers will introduce several toy models for investigating the typical properties of topological systems. The lecture will start from the simplest of the topological model, the SSH (Su-Schrieffer-Heeger) model for the modeling of solitons on polyacetylene. The lecture will continue with an introduction to the physics of graphene and the Kane-Mele spin-orbit coupling, and the quantum Hall and the quantum spin-Hall effects. Finally, lecturers will introduce a simple tight-binding model for investigating three-dimensional topological insulators. All the lectures will be complemented by numerical proofs obtained within the Wolfram Language (Mathematica).

**Topic 4: Novel devices based on 2D materials and vdW heterostructures – Lecturer: Philippe DOLLFUS**

This series of lectures is devoted to the electronic and thermal properties of graphene, graphene nanostructures and other 2D materials like transition metal dichalcogenides (TMDs), with emphasis on device applications. After introducing the main features and peculiarities of electron and phonon transport in this type of materials, we will describe how they can be efficiently computed with a view to device investigation. In particular, this topic will focus on

**Topic 5: Machine-learning in Materials Science and condensed matter physics, Lecturer: Dr. PHAM Tien Lam, JAIST – Japan**

Human beings have always paid significant attention to learning nature’s “game” by observation and imagination of natural phenomena, and we have observed the vast diversity of nature and unified different natural phenomena in a small set of fundamental variables or laws. This consideration of science is strongly related to the field of data-mining, which is developed to discover hidden knowledge from a data set. Recently, the increasing volume of available experimental and quantum-computational material data, together with the development of machine-learning techniques, has provided new opportunities for developing techniques that help researchers accelerate the discovery and comprehension of new materials and phenomena. However, machine-learning is not familiar to many materials scientist, researchers, or students. In this tutorial, this lecture is designed to intuitively introduce the fundamentals of machine-learning and how it can be utilized to solve some materials science issues. The tutorial contains three parts: basic programming with python, a brief introduction of machine-learning, and materials informatics. In the first part, the lecturer will focus on the basics of python,

**Topic 6: Hands-on on Computation in Physics and Materials. Lecturers: Dr. NGUYEN Tuan Hung and Dr. LE Van Lich**

A broad range of physics and materials problems involve multi-scale phenomena. The computational study of these problems thus demands the development of novel materials and computational tools. This Hands-on provides the opportunity to students and researchers from different fields faced with multi-scaling problems from nanoscale to microscale by using two methods, so-called density functional theory (DFT) and phase field (PF). The DFT is the