skip to main content


Title: DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene
Strong interactions between electrons occupying bands of opposite (orlike) topological quantum numbers (Chern =\pm1 = ± 1 ),and with flat dispersion, are studied by using lowest Landau level (LLL)wavefunctions. More precisely, we determine the ground states for twoscenarios at half-filling: (i) LLL’s with opposite sign of magneticfield, and therefore opposite Chern number; and (ii) LLL’s with the samemagnetic field. In the first scenario – which we argue to be a toy modelinspired by the chirally symmetric continuum model for twisted bilayergraphene – the opposite Chern LLL’s are Kramer pairs, and thus thereexists time-reversal symmetry ( \mathbb{Z}_2 ℤ 2 ).Turning on repulsive interactions drives the system to spontaneouslybreak time-reversal symmetry – a quantum anomalous Hall state describedby one particle per LLL orbital, either all positive Chern |{++\cdots+}\rangle | + + ⋯ + ⟩ or all negative |{--\cdots-}\rangle | − − ⋯ − ⟩ .If instead, interactions are taken between electrons of like-Chernnumber, the ground state is an SU(2) S U ( 2 ) ferromagnet, with total spin pointing along an arbitrary direction, aswith the \nu=1 ν = 1 spin- \frac{1}{2} 1 2 quantum Hall ferromagnet. The ground states and some of theirexcitations for both of these scenarios are argued analytically, andfurther complimented by density matrix renormalization group (DMRG) andexact diagonalization.  more » « less
Award ID(s):
1916958
NSF-PAR ID:
10207501
Author(s) / Creator(s):
;
Date Published:
Journal Name:
SciPost Physics Core
Volume:
3
Issue:
2
ISSN:
2666-9366
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract Motivated by recent experimental work on moiré systems in a strong magnetic field, we compute the compressibility as well as the spin correlations and Hofstadter spectrum of spinful electrons on a honeycomb lattice with Hubbard interactions using the determinantal quantum Monte Carlo method. While the interactions in general preserve quantum and anomalous Hall states, emergent features arise corresponding to an antiferromagnetic insulator at half-filling and other incompressible states following the Chern sequence ± (2 N  + 1). These odd integer Chern states exhibit strong ferromagnetic correlations and arise spontaneously without any external mechanism for breaking the spin-rotation symmetry. Analogs of these magnetic states should be observable in general interacting quantum Hall systems. In addition, the interacting Hofstadter spectrum is qualitatively similar to the experimental data at intermediate values of the on-site interaction. 
    more » « less
  2. null (Ed.)
    A major recent breakthrough in materials science is the emergence of intrinsic magnetism in two-dimensional (2D) crystals, which opens the door to more cutting-edge fields in the 2D family and could eventually lead to novel data-storage and information devices with further miniaturization. Herein we propose an experimentally feasible 2D material, Fe 2 I 2 , which is an intrinsic room-temperature ferromagnet exhibiting perpendicular magnetic anisotropy (PMA). Using first-principles calculations, we demonstrate that single-layer (SL) Fe 2 I 2 is a spin-gapless semiconductor with a spin-polarized Dirac cone and linear energy dispersion in one spin channel, exhibiting promising dissipation-less transport properties with a Fermi velocity up to 6.39 × 10 5 m s −1 . Our results reveal that both strain and ferroelectric polarization switching could induce an out-of- to in-plane spin reorientation in the 2D Fe 2 I 2 layer, revealing its advantage in assembling spintronic devices. In addition, spin–orbit coupling (SOC) triggers a topologically nontrivial band gap of 301 meV with a nonzero Chern number (| C | = 2), giving rise to a robust quantum anomalous Hall (QAH) state. The 2D crystal also exhibits high carrier mobilites of 0.452 × 10 3 and 0.201 × 10 3 cm 2 V −1 s −1 for the electrons and holes, respectively. The combination of these unique properties renders the 2D Fe 2 I 2 ferromagnet a promising platform for high efficiency multi-functional spintronic applications. 
    more » « less
  3. Abstract

    Flat band moiré superlattices have recently emerged as unique platforms for investigating the interplay between strong electronic correlations, nontrivial band topology, and multiple isospin ‘flavor’ symmetries. Twisted monolayer-bilayer graphene (tMBG) is an especially rich system owing to its low crystal symmetry and the tunability of its bandwidth and topology with an external electric field. Here, we find that orbital magnetism is abundant within the correlated phase diagram of tMBG, giving rise to the anomalous Hall effect in correlated metallic states nearby most odd integer fillings of the flat conduction band, as well as correlated Chern insulator states stabilized in an external magnetic field. The behavior of the states at zero field appears to be inconsistent with simple spin and valley polarization for the specific range of twist angles we investigate, and instead may plausibly result from an intervalley coherent (IVC) state with an order parameter that breaks time reversal symmetry. The application of a magnetic field further tunes the competition between correlated states, in some cases driving first-order topological phase transitions. Our results underscore the rich interplay between closely competing correlated ground states in tMBG, with possible implications for probing exotic IVC ordering.

     
    more » « less
  4. Electrons in moiré flat band systems can spontaneously break time-reversal symmetry, giving rise to a quantized anomalous Hall effect. In this study, we use a superconducting quantum interference device to image stray magnetic fields in twisted bilayer graphene aligned to hexagonal boron nitride. We find a magnetization of several Bohr magnetons per charge carrier, demonstrating that the magnetism is primarily orbital in nature. Our measurements reveal a large change in the magnetization as the chemical potential is swept across the quantum anomalous Hall gap, consistent with the expected contribution of chiral edge states to the magnetization of an orbital Chern insulator. Mapping the spatial evolution of field-driven magnetic reversal, we find a series of reproducible micrometer-scale domains pinned to structural disorder.

     
    more » « less
  5. Abstract

    The physical realization of Chern insulators is of fundamental and practical interest, as they are predicted to host the quantum anomalous Hall (QAH) effect and topologically protected chiral edge states which can carry dissipationless current. Current realizations of the QAH state often require complex heterostructures and sub-Kelvin temperatures, making the discovery of intrinsic, high temperature QAH systems of significant interest. In this work we show that time-reversal symmetry breaking Weyl semimetals, being essentially stacks of Chern insulators with inter-layer coupling, may provide a new platform for the higher temperature realization of robust chiral edge states. We present combined scanning tunneling spectroscopy and theoretical investigations of the magnetic Weyl semimetal, Co3Sn2S2. Using modeling and numerical simulations we find that depending on the strength of the interlayer coupling, chiral edge states can be localized on partially exposed kagome planes on the surfaces of a Weyl semimetal. Correspondingly, our dI/dVmaps on the kagome Co3Sn terraces show topological states confined to the edges which display linear dispersion. This work provides a new paradigm for realizing chiral edge modes and provides a pathway for the realization of higher temperature QAH effect in magnetic Weyl systems in the two-dimensional limit.

     
    more » « less