On Friday 7 October 2022 I had the pleasure of giving a presentation at the LPS Orsay, just south of Paris, France. Since the group there has a lot of interest in strong correlations and topology, it was a good time to present an overview of my TMD-related work from last year.
Abstract: The recent revolution in moiré materials started with the discovery of correlated insulators and superconductivity in twisted bilayer graphene. I will show that much stronger electron correlations appear in moiré bilayers of transition-metal dichalcogenides (TMDs). After introducing the origin of flat bands in TMD moirés (including ARPES results), I will discuss theoretical predictions for a range of exotic phenomena: the amorphous Wigner-Mott electron slush; the 3/4 chiral spin liquid; and metal-insulator criticality.
While the difference between insulators and metals is strictly speaking only defined at zero temperature, it has become commonplace to identify systems with a negative temperature-derivative of the resistivity (dR/dT < 0) as insulators. This is, however, misleading. In particular, sufficiently close to a metal-insulator transition a system can have dR/dT < 0 yet reach a finite zero-temperature resistivity, meaning it is actually a metal. Such ‘fake insulators’ can obscure the interpretation of Mott- and band metal-insulator transitions.
In a recent presentation at the workshop “New Spin on Molecular Quantum Materials” held by SPICE in Mainz (Germany), I discussed this phenomenon of ‘fake insulators’ in depth, and comparing it to recent experimental results in graphene and TMD bilayers. The presentation can be watched online:
At the Lemanic Quantum Science School (LQSS) I gave a short introduction into the magic of strongly correlated quantum matter and why twisted Moiré heterostructures are interesting. You can download the slides of the presentation here:
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!
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.
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.
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