At n=3/4 filling of the moiré flat band, transition metal dichalcogenide moiré bilayers will develop kagome charge order. We derived an effective spin model for the resulting localized spins and study its phase diagram using density matrix renormalization group simulations. Using realistic model parameters relevant for WSe2/WS2, we showed that this material can realize the exotic chiral spin liquid phase and the highly debated kagome spin liquid. Our work thus shows that the frustration and strong interactions present in TMD heterobilayers provide an exciting platform to study spin liquid physics.

Johannes Motruk, Dario Rossi, Dmitry A. Abanin, Louk Rademaker**arXiv:2211.15696**

## Doping a Wigner-Mott insulator: Electron slush in transition-metal dichalcogenide moiré heterobilayers

**Authors:** *Yuting Tan, Pak Ki Henry Tsang, Vladimir Dobrosavljević, Louk Rademaker***Abstract**: The moiré pattern induced by lattice mismatch in transition-metal dichalcogenide heterobilayers causes the formation of flat bands, where interactions dominate the kinetic energy. At fractional fillings of the flat valence band, the long-range electron interactions then induce Wigner-Mott crystals. In this Letter we investigate the nontrivial electronic phases appearing away from commensurate fillings. Here, competing phases arise that are either characterized as doped Wigner-Mott charge transfer insulators or alternatively, a novel state with frozen charge order yet is conducting: the ‘electron slush’. We propose that an extremely spatially inhomogeneous local density of states can serve as a key signature of the electron slush.**Reference**: arXiv:2210.07926 (2022)

## How to recognize the universal aspects of Mott criticality?

In our latest paper we compare several examples of two-dimensional electronic systems displaying **interaction-driven metal-insulator transitions** of the Mott type, including dilute two-dimension electron gases (2DEG) in semiconductors, Mott organic materials, as well as the recently discovered transition-metal dichalcogenide (TMD) moiré bilayers.

The amazing thing is: remarkably similar behavior is found in all these systems, which is starting to paint a robust picture of Mott criticality. Most notable, on the metallic side a resistivity maximum is observed whose temperature scale vanishes at the transition.

In this paper we compare the available experimental data on these systems to three existing theoretical scenarios: **spinon theory**, **Dynamical Mean Field Theory** (DMFT) and **percolation theory**. We show that the DMFT and percolation pictures for Mott criticality can be distinguished by studying the origins of the resistivity maxima using an analysis of the dielectric response.

Published in a special edition of Crystals.

Yuting Tan, Vladimir Dobrosavljevic, Louk Rademaker, *How to recognize the universal aspects of Mott criticality?*, Crystals 12, 932 (2022)

## Gate-tunable imbalanced Kane-Mele model in encapsulated bilayer jacutingaite

My recent density functional theory-based work on bilayer jacutingaite (Pt_{2}HgSe_{3}) is published in the journal Physical Review Materials!

**Title:** Gate-tunable imbalanced Kane-Mele model in encapsulated bilayer jacutingaite**Reference**: Louk Rademaker and Marco Gibertini, Phys. Rev. Materials 5, 044201 (2021)**Abstract**: *We study free, capped, and encapsulated bilayer jacutingaite (Pt2HgSe3) from first principles. While the freestanding bilayer is a large-gap trivial insulator, we find that the encapsulated structure has a small trivial gap due to the competition between sublattice symmetry breaking and sublattice-dependent next-nearest-neighbor hopping. Upon the application of a small perpendicular electric field, the encapsulated bilayer undergoes a topological transition towards a quantum spin Hall insulator. We find that this topological transition can be qualitatively understood by modeling the two layers as uncoupled and can be described by an imbalanced Kane-Mele model that takes into account the sublattice imbalance and the corresponding inversion-symmetry breaking in each layer. Within this picture, bilayer jacutingaite undergoes a transition from a 0+0 state, where each layer is trivial, to a 0+1 state, where an unusual topological state relying on Rashba-like spin orbit coupling emerges in only one of the layers.*

## Wavefunction collapse cover art for pss(b)

Our work on wavefunction collapse (*An experimental proposal to study spontaneous collapse of the wave function using two travelling wave parametric amplifiers*, see here on arXiv) has made it to the cover of the latest issue of Physica Status Solidi (b), with some nice cover art made by the first author Tom van der Reep.

See the full pss(b) issue here.

## Slow Nonthermalizing Dynamics in a Quantum Spin Glass

Just published in **Physical Review Letters**, our latest work on a quantum spin glass with unusual dynamics. Spin glasses and many-body localization (MBL) are prime examples of ergodicity breaking, yet their physical origin is quite different: the former phase arises due to rugged classical energy landscape, while the latter is a quantum-interference effect. Here, we study quantum dynamics of an isolated 1D spin glass under application of a transverse field. At high energy densities, the system is ergodic, relaxing via a resonance avalanche mechanism, that is also responsible for the destruction of MBL in nonglassy systems with power-law interactions. At low energy densities, the interaction-induced fields obtain a power-law soft gap, making the resonance avalanche mechanism inefficient. This leads to the persistence of the spin-glass order, as demonstrated by resonance analysis and by numerical studies. A small fraction of resonant spins forms a thermalizing system with long-range entanglement, making this regime distinct from the conventional MBL. The model considered can be realized in systems of trapped ions, opening the door to investigating slow quantum dynamics induced by glassiness.

Rademaker and Abanin, Phys. Rev. Lett. **125**, 260405 (2020)

## Study the Collapse of the Wave Function in Traveling‐Wave Parametric Amplifiers

The readout of a microwave qubit state occurs using an amplification chain that enlarges the quantum state to a signal detectable with a classical measurement apparatus. However, at what point in this process is the quantum state really “measured”? To investigate whether the “measurement” takes place in the amplification chain, in which a parametric amplifier is often chosen as the first amplifier, we proposed to construct a microwave interferometer that has such an amplifier added to each of its arms. Feeding the interferometer with single photons, the interference visibility depends on the gain of the amplifiers and whether a measurement collapse has taken place during the amplification process.

## Observation of flat bands in twisted bilayer graphene

My first paper with experimental groups is now published in ** Nature Physics**. Our work is a detailed characterization of twisted bilayer graphene, with as highlight the direct observation of flat bands using nano-ARPES. I calculated the expected ARPES spectra, which can be seen in Fig 3 and 4 of the paper.

The full paper is here: Observation of flat bands in twisted bilayer graphene

Also, you can read more about it on the website of the DQMP in Geneva.

## 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.