751 research outputs found
Symmetries as the guiding principle for flattening bands of Dirac fermions
Since the discovery of magic-angle twisted bilayer graphene (TBG), flat bands
in Dirac materials have become a prominent platform for realizing strong
correlation effects in electronic systems. Here we show that the symmetry group
protecting the Dirac cone in such materials determines whether a Dirac band may
be flattened by the tuning of a small number of parameters. We devise a
criterion that, given a symmetry group, allows for the calculation of the
number of parameters required to make the Dirac velocity vanish. This criterion
is employed to study band flattening in twisted bilayer graphene and in surface
states of 3D topological insulators. Following this discussion, we identify the
symmetries under which the vanishing of the Dirac velocity implies the
emergence of perfectly-flat bands. Our analysis allows us to construct
additional model Hamiltonians that display perfectly-flat bands at certain
points in the space of parameters: the first is a toy model of two coupled 3D
TI surfaces, and the second is a quasi-crystalline generalization of the chiral
model of TBG.Comment: 21 pages, 12 figures, Accepted to Physical Review
Geometric Stiffness in Interlayer Exciton Condensates
Recent experiments have confirmed the presence of interlayer excitons in the
ground state of transition metal dichalcogenide (TMD) bilayers. The interlayer
excitons are expected to show remarkable transport properties when they undergo
Bose condensation. In this work, we demonstrate that quantum geometry of Bloch
wavefunctions plays an important role in the phase stiffness of the Interlayer
Exciton Condensate (IEC). Notably, we identify a geometric contribution that
amplifies the stiffness, leading to the formation of a robust condensate with
an increased BKT temperature. Our results have direct implications for the
ongoing experimental efforts on interlayer excitons in materials that have
non-trivial geometry. We provide quantitative estimates for the geometric
contribution in TMD bilayers through a realistic continuum model with gated
Coulomb interaction, and find that the substantially increased stiffness allows
for an IEC to be realized at amenable experimental conditions
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