5 research outputs found
Quantum Metric Induced Phases in Moir\'e Materials
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 Moir\'e
materials leading to symmetry breaking and interaction driven Fermi liquids.
This phenomenology stems from a remarkable interplay between the quantum
geometry and interactions 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 turn, when dominant, an extremely strongly coupled problem into an
effectively weakly coupled one, and may also serve as a guiding principle for
designing material setups.Comment: 6+9 page
Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers
Remarkable recent experiments have observed fractional quantum anomalous Hall
(FQAH) effects at zero field and unusually high temperatures in twisted
semiconductor bilayer MoTe. Intriguing observations in these experiments
such as the absence of integer Hall effects at twist angles where a fractional
Hall effect is observed, do however remain unexplained. The experimental phase
diagram as a function of twist angle remains to be established. By
comprehensive numerical study, we show that band mixing has large qualitative
and quantitative effects on the energetics of competing states and their energy
gaps throughout the twist angle range . This lays the
ground for the detailed realistic study of a rich variety of strongly
correlated twisted semiconductor multilayers and an understanding of the phase
diagram of these fascinating systems.Comment: 5 + 2 pages, 7 Figure
Geometry, Topology and Emergence in Moiré Systems
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
Topological lattice models with constant Berry curvature
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 bosonic 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.Comment: 7 + 3 pages, 7 figure