| 1. |
- Abouelkomsan, Ahmed, 1995-
(författare)
-
Geometry, Topology and Emergence in Moiré Systems
- 2022
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The experimental discovery of correlated insulators and superconductivity in highly tunable Van der Waals heterostructures, such as twisted bilayer graphene, has highlighted the role of moiré patterns, resulting from tiny relative twists or lattice constant mismatches, in realizing strongly correlated physics. A key ingredient is the existence of very narrow flat bands where interaction effects are dominant.In this thesis and the accompanying papers, we theoretically study a number of experimentally relevant moiré systems. We generally show that strong interactions combined with the geometry and the topology of the underlying flat bands can result in a plethora of distinct quantum many-body phases ranging from topological order to multiferroicity. Of particular importance are lattice analogues of the fractional quantum Hall effect known as fractional Chern insulators. They harbour peculiar phenomena such as fractional charge and statistics and provide a route towards realizing topologically ordered states at high temperature. A ubiquitous feature of the many-body physics is the emergence of unique particle-hole dualities driven by the geometry of band-projected interactions.
|
|
| 2. |
- Abouelkomsan, Ahmed, 1995-, et al.
(författare)
-
Multiferroicity and Topology in Twisted Transition Metal Dichalcogenides
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Van der Waals heterostructures have recently emerged as an exciting platform for investigating the effects of strong electronic correlations, including various forms of magnetic or electrical orders. Here, we perform an unbiased exact diagonalization study of the effects of interactions on topological flat bands of twisted transition metal dichalcogenides (TMDs) at odd integer fillings. We find that Chern insulator phases, expected from interaction-induced spin and valley polarization of the bare band structure, are quite fragile, and give way to spontaneous multiferroic order -- coexisting ferroelectricity and ferromagnetism, in presence of long-range Coulomb repulsion. We provide a simple real-space picture to understand the phase diagram as a function of interaction range and strength. Our findings establish twisted TMDs as a novel and highly tunable platform for multiferroicity, with potential applications to electrical control of magnetism.
|
|
| 3. |
- Abouelkomsan, Ahmed, 1995-, et al.
(författare)
-
Quantum metric induced phases in Moiré materials
- 2023
-
Ingår i: Physical Review Research. - 2643-1564. ; 5:1
-
Tidskriftsartikel (refereegranskat)abstract
- We show that, quite generally, quantum geometry plays a major role in determining the low-energy physics in strongly correlated lattice models at fractional band fillings. We identify limits in which the Fubini-Study metric dictates the ground states and show that this is highly relevant for Moiré materials leading to symmetry breaking and interaction driven Fermi liquids. This phenomenology stems from a remarkable interplay between the quantum geometry and interaction which is absent in continuum Landau levels but generically present in lattice models where these terms tend to destabilize, e.g., fractional Chern insulators. We explain this as a consequence of the fundamental asymmetry between electrons and holes for band projected normal ordered interactions, as well as from the perspective of a self-consistent Hartree-Fock calculation. These basic insights about the role of the quantum metric, when dominant, turn an extremely strongly coupled problem into an effectively weakly coupled one, and may also serve as a guiding principle for designing material setups. We argue that this is a key ingredient for understanding symmetry-breaking phenomena recently observed in Moiré materials.
|
|
| 4. |
- Abouelkomsan, Ahmed, 1995-
(författare)
-
Strongly Correlated Moiré Materials
- 2021
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Recent advances in materials science have established Moiré materials as a new highly tunable and versatile form of quantum matter. When two dimensional atomic layers are brought into proximity, a tiny relative twist or a slight lattice mismatch produces Moiré patterns manifested in a superlattice structure with a lattice constant that is much larger than the lattice constants of the constituent layers. The new length scale has dramatic consequences for the underlying properties. A particular distinctive feature of Moiré materials is the emergence of nearly flat bands upon tuning external parameters such as the twist angle or the applied gate voltage. In a flat band, the kinetic energy is quenched, and interactions are enhanced bringing us to the realm of strongly correlated systems. A prime example of Moiré materials is twisted bilayer graphene, formed by taking two graphene layers and twisting them relative to each other.On the other hand, a famous class of interaction-induced phases of matter are fractional quantum Hall states and their lattice analogues known as fractional Chern insulators. These topologically ordered phases represent a departure from the conventional Landau symmetry breaking classification of matter, seen in the absence of local order parameters and the presence of global topological properties insensitive to local perturbations. Identifying and manufacturing materials that could host fractional Chern insulator states has a great potential for technological use.In this thesis, we provide the necessary background required for understanding the results of the accompanying papers [Phys. Rev. Lett. 124, 106803 & Phys. Rev. Lett. 126, 026801]. The theory of fractional Chern insulators is discussed followed by an introduction to the Moiré models used. In the two accompanying papers, we theoretically study a number of flat band Moiré materials aiming at identifying the possible phases that occur at fractional band fillings using a combination of analytical and numerical techniques. By reformulating the problem in terms of holes instead of electrons, it's possible to identify a variety of emergent weakly interacting Fermi liquids from an initial strongly interacting problem. In addition, our findings also include several high temperature fractional Chern insulator states at different fillings without external magnetic field.
|
|
| 5. |
- Ghorashi, Sayed Ali Akbar, et al.
(författare)
-
Topological and Stacked Flat Bands in Bilayer Graphene with a Superlattice Potential
- 2023
-
Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 130:19
-
Tidskriftsartikel (refereegranskat)abstract
- We show that bilayer graphene in the presence of a 2D superlattice potential provides a highly tunable setup that can realize a variety of flat band phenomena. We focus on two regimes: (i) topological flat bands with nonzero Chern numbers, C, including bands with higher Chern numbers |C|>1 and (ii) an unprecedented phase consisting of a stack of nearly perfect flat bands with C=0. For realistic values of the potential and superlattice periodicity, this stack can span nearly 100 meV, encompassing nearly all of the low-energy spectrum. We further show that in the topological regime, the topological flat band has a favorable band geometry for realizing a fractional Chern insulator (FCI) and use exact diagonalization to show that the FCI is in fact the ground state at 1/3 filling. Our results provide a realistic guide for future experiments to realize a new platform for flat band phenomena.
|
|
| 6. |
- Liu, Zhao, et al.
(författare)
-
Gate-Tunable Fractional Chern Insulators in Twisted Double Bilayer Graphene
- 2021
-
Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 126:2
-
Tidskriftsartikel (refereegranskat)abstract
- We predict twisted double bilayer graphene to be a versatile platform for the realization of fractional Chern insulators readily targeted by tuning the gate potential and the twist angle. Remarkably, these topologically ordered states of matter, including spin singlet Halperin states and spin polarized states in Chern number C=1 and C=2 bands, occur at high temperatures and without the need for an external magnetic field.
|
|
| 7. |
- Varjas, Dániel, et al.
(författare)
-
Topological lattice models with constant Berry curvature
- 2022
-
Ingår i: SciPost Physics. - 2542-4653. ; 12:4
-
Tidskriftsartikel (refereegranskat)abstract
- Band geometry plays a substantial role in topological lattice models. The Berry curvature, which resembles the effect of magnetic field in reciprocal space, usually fluctuates throughout the Brillouin zone. Motivated by the analogy with Landau levels, constant Berry curvature has been suggested as an ideal condition for realizing fractional Chern insulators. Here we show that while the Berry curvature cannot be made constant in a topological two-band model, lattice models with three or more degrees of freedom per unit cell can support exactly constant Berry curvature. However, contrary to the intuitive expectation, we find that making the Berry curvature constant does not always improve the properties of fractional Chern insulator states. In fact, we show that an "ideal flatband" cannot have constant Berry curvature, equivalently, we show that the density algebra of Landau levels cannot be realised in any tight-binding lattice system.
|
|
