Fake Insulators: What are they, and how to spot them?

The traditional view of a metal-insulator transition is wrong, instead, at a MIT the critical curve diverges and there is a metallic regime with negative dR/dT: “fake insulators”.

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:

You can also download the slides of this presentation (in pptx, 51 MB).

How to recognize the universal aspects of Mott criticality?

Similar quantum critical scaling behavior close to a interaction-driven Metal-Insulator Transition (MIT) has been observed in dilute 2DEGs, organic materials and recently TMD moiré bilayers.

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)

Spin-Orbit Coupling in Transition Metal Dichalcogenide Heterobilayer Flat Bands

To my surprise I found out that the flat bands of TMD heterobilayers automatically have a spin-orbit coupling that makes them realizations of the Kane-Mele model. This is different from the original Wu-MacDonald model where they say its a triangular lattice Hubbard model. Now on the arXiv!

Spin-Orbit Coupling in Transition Metal Dichalcogenide Heterobilayer Flat Bands
Louk Rademaker, arXiv:2111.06208
Abstract: The valence flat bands in transition metal dichalcogenide (TMD) heterobilayers are shown to exhibit strong intralayer spin-orbit coupling. This is reflected in a simple tight-binding model with spin-dependent complex hoppings based on the continuum model. A perpendicular electric field causes interlayer hybridization, such that the effective model is equivalent to the Kane-Mele model of topological insulators. The proposed model can be used as a starting point to understand interactions and the experimentally observed topological phases.

Spin-valley symmetry breaking and Chern insulators in twisted graphene structures

Watch my 15-minute presentation on spin-valley symmetry breaking and Chern insulators, given on 13 August on the online Moiré-Twistronics workshop.

At the online Moiré-Twistronics workshop last week I gave a short presentation on our work on Chern insulators in twisted bilayer graphene and twisted mono-bilayer graphene. It was a great online conference, so check their website for recordings of most other talks there.

Download the slides for this presentation (pdf, 24 MB).

Scaling Theory of Few-Body Delocalization

I’m quite proud of my latest single-author paper, in which I explore a new direction in the field of disordered interacting systems. I dub it: “Few-Body Delocalization“, and I investigate the question: given that single-particle states are all localized in d ≤ 2 dimen- sions, how can many-particle states become delocalized?

In the end, using scaling theory and some numerics I show that there exists a delocalization transition for n-particle bound states in d dimensions when n + d ≥ 4. Read more on arXiv:2107.06364.

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

My recent density functional theory-based work on bilayer jacutingaite (Pt2HgSe3) 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.

Slow Nonthermalizing Dynamics in a Quantum Spin Glass

Most spins remain localized and only a small fraction of ‘resonant’ spins become ergodic, in a one-dimensional long-range 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)