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

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…

Aspects of forward scattering in FeSe thin films

Last year we showed that you get ridiculously high superconducting temperatures if the electron-phonon coupling is strongly peaked around zero momentum transfer, so-called forward scattering. While the paper from that time is just accepted in the New Journal of Physics, we came up with a new paper discussing many of the more subtle details – for example about the vertex corrections, quasiparticle interference and gap structure. This week on the arXiv!

(PS: I’ve updated the publication list, a lot of things from last year are now peer-reviewed published somewhere, such as our MBL-paper in Physical Review Letters, or the topological classification in Phys. Rev. B!)

Title: Aspects of electron-phonon interactions with strong forward scattering in FeSe Thin Films on SrTiO3 substrates

Y. Wang, K. Nakatsukasa, L. Rademaker, T. Berlijn, and S. Johnston

vertexdiagrams

Abstract: Mono- and multilayer FeSe thin films grown on SrTiO3 and BiTiO3 substrates exhibit a greatly enhanced superconductivity over that found in bulk FeSe. A number of proposals have been advanced for the mechanism of this enhancement. One possibility is the introduction of a cross-interface electron- phonon (e-ph) interaction between the FeSe electrons and oxygen phonons in the substrates that is peaked in the forward scattering (small q) direction due to the two-dimensional nature of the interface system. Motivated by this, we explore the consequences of such an interaction on the superconducting state and electronic structure of a two-dimensional system using Migdal-Eliashberg theory. This interaction produces not only deviations from the expectations of conventional phonon-mediated pairing but also replica structures in the spectral function and density of states, as probed by angle-resolved photoemission spectroscopy, scanning tunneling microscopy/spectroscopy, and quasi-particle interference imaging. We also discuss the applicability of Migdal-Eliashberg theory for a situation where the e-ph interaction is peaked at small momentum transfer and in the FeSe/STO system.

arXiv:1602.00656

arXiv preprint: Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology

Title: Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology

ti

Abstract: We show that the local in-gap Greens function of a band insulator G0(ϵ,k,r=0), with r the position perpendicular to a codimension-1 or -2 impurity, reveals the topological nature of the phase. For a topological insulator, the eigenvalues of this Greens function attain zeros in the gap, whereas for a trivial insulator the eigenvalues remain nonzero. This topological classification is related to the existence of in-gap bound states along codimension-1 and -2 impurities. Whereas codimension-1 impurities can be viewed as ‘soft edges’, the result for codimension-2 impurities is nontrivial and allows for a direct experimental measurement of the topological nature of 2d insulators.

Reference: Robert-Jan Slager, Louk Rademaker, Jan Zaanen, Leon Balents, arXiv:1504.04881 (2015)

arXiv preprint: Glassy dynamics in geometrically frustrated Coulomb liquids without disorder

Title: Glassy dynamics in geometrically frustrated Coulomb liquids without disorder

glass

Abstract: We show that introducing long-range Coulomb interactions immediately lifts the massive ground state degeneracy induced by geometric frustration for electrons on quarter-filled triangular lattices in the classical limit. Important consequences include the stabilization of a stripe-ordered crystalline (global) ground state, but also the emergence of very many low-lying metastable states with amorphous “stripe-glass” spatial structures. Melting of the stripe order thus leads to a frustrated Coulomb liquid at intermediate temperatures, showing remarkably slow (viscous) dynamics, with very long relaxation times growing in Arrhenius fashion upon cooling, as typical of strong glass formers. On shorter time scales, the system falls out of equilibrium and displays the aging phenomena characteristic of supercooled liquids above the glass transition. Our results show remarkable similarity with the recent observations of charge-glass behavior in ultra-clean triangular organic materials of the θ-(BEDT-TTF)2 family.

Reference: Samiyeh Mahmoudian, Louk Rademaker, Arnaud Ralko, Simone Fratini, Vladimir Dobrosavljevic; arXiv:1412.4441 (2014).

arXiv preprint: The Instability of a Quantum Superposition of Time Dilations

Title: The Instability of a Quantum Superposition of Time Dilations

Abstract: Using the relativistic concept of time dilation we show that a superposition of gravitational potentials can lead to nonunitary time evolution. For sufficiently weak gravitational potentials one can still define, for all intents and purposes, a global coordinate system. A probe particle in a superposition of weak gravitational fields will, however, experience dephasing due to the different time dilations. The corresponding instability timescale is accessible to experiments, and can be used as a degree of macroscopicity. Finally, we suggest an experiment with smoothly tunable amplification in a microwave interferometer that allows a quantitative study of the quantum to classical boundary.

Reference: Louk Rademaker, Tom van der Reep, Nick Van den Broeck, Bob van Waarde, Marc de Voogd, Tjerk Oosterkamp; arXiv:1410.2303.

arXiv preprint: How bilayer excitons can greatly enhance thermoelectric efficiency

Title: How bilayer excitons can greatly enhance thermoelectric efficiency

thermo

Abstract: Currently, one of the major nanotechnological challenges is to design thermoelectric devices that have a high figure of merit. To that end, we propose to use bilayer excitons. Bilayer exciton systems are shown to have an improved thermopower and an enhanced electric counterflow and thermal conductivity, with respect to regular semiconductor-based thermoelectrics. Here we present a roadmap towards experimental realization of a bilayer exciton thermocouple. A bilayer exciton heterostructures of p- and n-doped Bi2Te3 can have a figure of merit zT∼60. Another material suggestion is to make a bilayer out of electron-doped SrTiO3 and hole-doped Ca3Co4O9.

Reference: Kai Wu, Louk Rademaker, Jan Zaanen; arXiv:1401.7770.

arXiv preprint: Exciton condensation in strongly correlated electron bilayers

Title: Exciton condensation in strongly correlated electron bilayers

Phase diagram of the exiton t-J model

Abstract:We studied the possibility of exciton condensation in Mott insulating bilayers. In these strongly correlated systems an exciton is the bound state of a double occupied and empty site. In the strong coupling limit the exciton acts as a hard-core boson. Its physics are captured by the exciton t-J model, containing an effective XXZ model describing the exciton dynamics only. Using numerical simulations and analytical mean field theory we constructed the ground state phase diagram. Three homogeneous phases can be distinguished: the antiferromagnet, the exciton checkerboard crystal and the exciton superfluid. For most model parameters, however, we predict macroscopic phase separation between these phases. The exciton superfluid exists only for large exciton hopping energy. Additionally we studied the collective modes and susceptibilities of the three phases. In the superfluid phase we find the striking feature that the bandwidth of the spin-triplet excitations, potentially detectable by resonant inelastic x-ray scattering (RIXS), is proportional to the superfluid density. The superfluid phase mode is visible in the charge susceptibility, measurable by RIXS or electron energy loss spectroscopy (EELS).

Reference: Louk Rademaker, Jeroen van den Brink, Jan Zaanen, Hans Hilgenkamp, arXiv:1310.0685

arXiv preprint: Determinant quantum Monte Carlo study of exciton condensation in the bilayer Hubbard model

Title: Determinant quantum Monte Carlo study of exciton condensation in the bilayer Hubbard model

The Bilayer Hubbard model.

Abstract: We studied the possibility of exciton condensation in a strongly correlated bilayer extended Hubbard model using Determinant Quantum Monte Carlo. To model both the onsite repulsion U and the interlayer interaction V we introduced a novel update scheme extending the standard Sherman-Morrison update. We observe that the sign problem increases dramatically with the inclusion of the interlayer interaction V, which prohibits at this stage a unequivocal conclusion regarding the presence of exciton condensation. However, enhancement of the interlayer tunneling results suggest that the strongest exciton condensation tendency lies around 10-20 % p/n-doping. Magnetic properties and conductivity turn out to be relatively independent of the interlayer interaction.

Reference: Louk Rademaker, Steve Johnston, Jan Zaanen, Jeroen van den Brink, arXiv:1310.0623

arXiv preprint: Influence of long-range interactions on charge ordering phenomena on a square lattice

Title: Influence of long-range interactions on charge ordering phenomena on a square lattice

Abstract: Usually complex charge ordering phenomena arise due to competing interactions. We have studied how such ordered patterns emerge from the frustration of a long-ranged interaction on a lattice. Using the lattice gas model on a square lattice with fixed particle density, we have identified several interesting phases; such as a generalization of Wigner crystals at low particle densities and stripe phases at densities in between rho = 1/3 and rho = 1/2. These stripes act as domain walls in the checkerboard phase present at half-filling. The phases are characterised at zero temperatures using numerical simulations, and mean field theory is used to construct a finite temperature phase diagram.

Reference: Louk Rademaker, Yohanes Pramudya, Jan Zaanen, Vladimir Dobrosavljevic, arXiv:1304.3643