Emergent quantum matter in artificial two-dimensional materials

Original Lecturer Ass. Prof. Jose Lado, Aalto University

Coordinators Prof. Tero Heikkilä and Ass. Prof. Shawulienu Kezilebieke, University of Jyväskylä

2023 course instructor Dr Pauli Virtanen, University of Jyväskylä

Original version: 8.-12.8. 2022 in the University of Jyväskylä campus and online in Zoom

For a 2023 summer school version, see below.

Link to the telegram group: this is where you can discuss the problems with other students and with the course organizers.

Course contents

Van der Waals materials have risen as one the most powerful platforms to explore exotic quantum states in materials. The disruptive impact of 2D materials in physics stems from three key properties of these compounds. First, the variety of electronic orders in these compounds, ranging from conventional states to unconventional ones, rivaling the most exotic bulk compounds. Second, the existence of different electronic orders provides an outstanding starting point to engineer new quantum states by combining different materials. And third, the van der Waals nature of these materials allows engineering emergent electronic states by creating artificial lattices stemming from moire patterns. In this summer course, we will introduce and review some of the most recent developments in quantum van der Waals materials, focusing on the emergence of artificial exotic quantum matter in these systems. The topics covered include:

Introduction to van der Waals quantum materials
Introduction to interacting phases of matter: mean-field theory, symmetry breaking, emergent quasiparticles
Conventional and unconventional superconductivity in van der Waals heterostructures
Ferromagnetism, antiferromagnetism and magnons in monolayer ferromagnets
Quantum magnetism, quantum spin-liquids and spinons in van der Waals materials
Artificial moire electronic states in twisted van der Waals heterostructures
Topological van der Waals matter: quantum spin Hall insulators, integer and fractional Chern insulators
Van der Waals multiferroic materials

The lecture notes in the above menu will be made public prior to each day's lecture. Stay tuned!

Learning goals

After the course, students will know about the different possibilities in engineering artificial topological matter with van der Waals materials. The students will learn the basics of conventional and unconventional superconductivity, fractionalization in van der Waals quantum magnets, and topological states emerging in two-dimensional materials. The students will gain an overview of different exotic quantum states in van der Waals materials, and in particular, the emergence of unconventional quasiparticles in collective quantum matter. The course will provide a strong background for future studies in quantum materials, quantum electronics, and quantum technologies.

Prerequisites:

Introductory solid state physics or materials physics
Introductory quantum mechanics

Links to the slides

Problem solving sessions

The problem solving sessions will utilize the open source code Pyqula. All students should have access to a computer where this code has been installed. The preferred option is bringing your own laptop as that way you can run the code also after the course. Those for whom this is not feasible will be provided computer access by some means.

Jyväskylä summer school 2023

This course is offered as an online version in the Jyväskylä summer school in August 2023. This means that the students can take the course whenever they wish. Passing the course will require working on all sets of exercises and compiling a video (can be long) where they explain some exercises and their solutions from each five sets of problems. During the course there will be voluntary on-site guiding sessions in the lecture room FYS2 at 13-14 on each day of the summer school. The aim of these sessions is to help the students complete the exercises, but they will not be actual teaching sessions.

In other words, to complete the course:

Install Anaconda python and the pyqula package on your computer
Watch the video lectures of each topic (see Lecture material links on top of the page)
Work on the exercises of each topic
If needed, consult the lecture notes of the topic to aid making exercises
After each exercise, film a roughly 10-minute video where you explain some of the problems and their solutions (e.g., with Zoom screen sharing)
At the end, share your complete video with Tero Heikkilä, Tero.T.Heikkila@jyu.fi, to get the credits.

Please note that the video explanation does not have to be fault-free or practiced! We welcome partial solutions and your explanations of what was difficult to understand. What we need to see is a genuine effort to work on the problems.

Getting credits from the online course

Our aim is to make the course such that students can learn the topic on their own from the material. A possible way to do this is to start with the first video in each lecture topic, then proceed to exercises, and when in trouble continue with the further videos. Completing all exercises is not mandatory, but you can consider them as a buffet: choose the most tasty and interesting problem to work with, but remember every time also to try something new and take yourself outside your confort zone.

For students in Finland, we plan to create a scheme where the students can get credits by recording a video of themselves working on the exercises and explaining what they are doing. The course will amount to two credit points, in analogy with the Jyväskylä summer school course.

For students outside Finland we cannot give credits within the Finnish university system, but they must get them from their own universities.