Hofstadter subband ferromagnetism in twisted bilayer graphene

The beautiful measurements of Yu Saito and Andrea Young display clear Chern insulator states. The sequence of C=-1, -2, -3, -4 states from the left can be understood as arising from spontaneous valley and spin polarization.

Together with the Yu Saito and Andrea Young (UC Santa Barbara) we wrote a paper about symmetry broken states in the presence of large magnetic fields in twisted bilayer graphene.

Read here more about it, on the arXiv.

Topological Flat Bands and Correlated States in Twisted Monolayer-Bilayer Graphene

We have been working on twisted monolayer bilayer graphene (tMBG) for a while when suddenly three groups put their experimental results last week on the arXiv (UCSB, Columbia, Manchester). So we had to rush writing up everything we had, and now you can read our postdictions about the quantum anomalous Hall effect in tMBG!

Title: Topological Flat Bands and Correlated States in Twisted Monolayer-Bilayer Graphene
Authors: Louk Rademaker, Ivan Protopopov, Dmitry Abanin
Abstract: Monolayer graphene placed with a twist on top of AB-stacked bilayer graphene hosts topological flat bands in a wide range of twist angles. The dispersion of these bands and gaps between them can be efficiently controlled by a perpendicular electric field, which induces topological transitions accompanied by changes of the Chern numbers. In the regime where the applied electric field induces gaps between the flat bands, we find a relatively uniform distribution of the Berry curvature. Consequently, interaction-induced valley- and/or spin-polarized states at integer filling factors are energetically favorable. In particular, we predict a quantum anomalous Hall state at filling factor ν=1 for a range of twist angles 1<θ<1.4. Furthermore, to characterize the response of the system to magnetic field, we computed the Hofstadter butterfly and the Wannier plot, which can be used to probe the dispersion and topology of the flat bands in this material.
Reference: arXiv:2004.14964

A Practical Introduction to Density Functional Theory

At the University of Geneva a group of enthusiastic graduate students have instigated a seminar series devoted to ‘relevant techniques in many-body physics’: the “ToolBoX“. I had the honor of providing the first set of lectures on density functional theory, for which I prepared some notes with exercises.. Download it here below!

For the lazy students, you can download all the pseudopotentials and input files here.

Direct evidence for flat bands in twisted bilayer graphene from nano-ARPES

Constant energy cuts of the ARPES intensity near the K-point shows four circles centered around the Gamma points of the mini-Brillouin zones. Top row shows the experimental data, bottom row are my theoretical predictions.

Today our paper appeared on the arXiv describing the evidence for flat bands in twisted bilayer graphene. A really great effort, with experiments in Leiden and Barcelona and with our local Genevan Simone Lisi leading the ARPES effort. I’m very happy to have provided some theoretical work on this.

Read more on the arXiv…

Twisted bilayer graphene, Kitaev quenches and spontaneous symmetry breaking

The month november was quite successful publication-wise, as four of my publications have been accepted.

Quenching the Kitaev honeycomb model
Starting from an antiferromagnet, let it evolve with Kitaev’s spin liquid honeycomb model. I developed the technique to study what happens next, a combination of Majorana Loschmidt echo’s and gauge field Monte Carlo. A prethermal regime appears, characterized by magnetization oscillations that can be described by the toric code. Accepted by SciPost.

An Introduction to Spontaneous Symmetry Breaking
Together with Aron Beekman and Jasper van Wezel, I wrote a lecture notes on the basics of spontaneous symmetry breaking. Aimed at graduate students, it is a modern overview containing both the classics (Mermin-Wagner theorem, Nambu-Goldstone modes) as well as modern notions (tower of states, type A/B symmetry breaking, topology). Accepted by SciPost Lecture Notes.

Exact ground state of the Lieb-Mattis Hamiltonian as a superposition of Néel states
The Lieb-Mattis Hamiltonian was originally used to show that the ground state of the Heisenberg antiferromagnet is a symmetric singlet state. How then, one might wonder, does the symmetry broken antiferromagnetic state arise? Well, read my published work in Physical Review Research. 

Charge smoothening and band flattening due to Hartree corrections in twisted bilayer graphene
Together with Paula Mellado I calculated the Hartree corrections in twisted bilayer graphene when doping away from charge neutrality. Surprisingly, the charge transfer we observe between AB/BA and AA regions of the Moiré unit cell makes the flat bands even flatter. Published in Physical Review B.

Quantum Anomalous Hall effect in Twisted Bilayer Graphene

At our weekly “Flat Club” in Geneva I presented on Friday 11 October the latest experiments from Andrea Young’s group, who observed the quantum anomalous Hall effect in twisted bilayer graphene. Download my slides here (PDF).

Title: Quantum Anomalous Hall effect in Twisted Bilayer Graphene

Abstract: A recent experiment brings together many topics discussed in earlier Flat Club meetings: namely the observation of a Quantum Anomalous Hall effect in magic angle twisted bilayer graphene aligned with hBN. In order to understand these results, we will discuss first the concept of a Chern insulator, its response in a magnetic field, and the role of ferromagnetism. Next, we will discuss how the alignment of hBN with twisted graphene opens up the possibility of creating a ferromagnetic Chern insulator. We will end with the experiments by the Young group who observed a QAH with a quantized rho_xy within 0.1% of h/e^2.

To read:
Serlin et al., Intrinsic quantized anomalous Hall effect in a moiré heterostructure, https://arxiv.org/abs/1907.00261

Unconventional Many-Body Localization in Long-Range Quantum Spin Glasses

At the Conference on “Complex Quantum Systems out of Equilibrium” in Murcia, Spain I presented my latest work with Dmitry Abanin on the relation between MBL and spin glasses. This work has been published on the arXiv now as well. The full presentation slides can be downloaded here (PDF).

Title: Unconventional Many-Body Localization in Long-Range Quantum Spin Glasses

Abstract: Spin glasses are a well-studied class of classical systems where random interactions lead to spin freezing at low temperatures. On the other hand, many-body localization is a quantum phe- nomenon where randomness and interactions lead to localization characterized by, amongst others, area law entanglement entropy and local integrals of motion. We show that a third, intermediate, state can emerge in a long-range one-dimensional spin glass under the applica- tion of a transverse field. At small applied fields and low temperatures the spin glass order remains, as characterized by the Edwards-Anderson order parameter. However, interacting low-energy spin resonances at large distances create unconventional long-range entanglement in eigenstates. The quench dynamics therefore display a wide variety in possible results: while some spins remain frozen, others ‘thaw’. The ”quantum spin glass” is therefore neither ergodic, nor many-body localized.

The nu=-2 state in Twisted Bilayer Graphene: A Bad Insulator?

At the “Mottness, Poor Conductors, and Strange Metals” Workshop at the Tsung-Dao Lee Institute, Shanghai, China I presented my work and some new speculations on twisted bilayer graphene. The full presentation can be downloaded here (PDF).

Title: The nu = -2 state in Twisted Bilayer Graphene: a bad Mott insulator?

Abstract: Twisted bilayer graphene near the ‘magic angle’ has shown a wealth of interesting states: superconductivity, ferromagnetism, correlated insulator states and a linear resistivity ‘strange metal’. I will focus on the state at carrier density nu = -2 relative to charge neutrality. At this filling the resistivity is minimal at around 4 K, above which there is reported linear resistivity and below which it is insulating. Using unbiased real-space Hartree-Fock calculations, we show that the nu = -2 state undergoes a charge transfer between “ring” and “center” orbitals leading to an even further flattening of the bands. Including a Hubbard interaction will then lead to a Mott insulator. However, unlike ‘strong’ Mott insulators like the cuprate parent compounds, this Mott state can easily be destroyed by temperature or magnetic field. I will discuss possible mechanisms for this ‘bad insulator’ behavior, including its relation to the multi-channel Kondo effect

Quenching the Kitaev honeycomb model

This work was presented first in a seminar at the University of Toronto on 18 October 2017. The slides of this presentation can be downloaded here (pptx, 13 MB).

Title: Quenching the Kitaev honeycomb model

Author: Louk Rademaker

kitaev

Abstract: I studied the non-equilibrium response of an initial Néel state under time evolution with the Kitaev honeycomb model. This time evolution can be computed using a random sampling over all relevant flux configurations. With isotropic interactions the system quickly equilibrates into a steady state valence bond solid. Anisotropy induces an exponentially long prethermal regime whose dynamics are governed by an effective toric code. Signatures of topology are absent, however, due to the high energy density nature of the initial state.

arXiv:1710.09761