Related papers: Wilson-Loop-Ideal Bands and General Idealization
We propose models of twisted multilayer graphene that exhibit exactly flat Bloch bands with arbitrary Chern numbers and ideal band geometries. The models are constructed by twisting two sheets of Bernal-stacked multiple graphene layers with…
Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high energy theories, quantum information, and condensed matter physics. In condensed matter systems, a wide range of…
Nonsymmorphic symmetries can enforce band connectivity that obstructs a single-band Wannier description. We show that a fractional translation $\mathcal{L}$ connecting distinct high-symmetry Wyckoff positions generically renders the Wannier…
Quantum geometry is a fundamental concept to characterize the local properties of quantum states. It is recently demonstrated that saturating certain quantum geometric bounds allows a topological Chern band to share many essential features…
We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model. The Wilson loops we consider preserve a…
The interplay between symmetry and topology in electronic band structures has been one of the central subjects in condensed-matter physics. Recently, it has been getting clear that a wide variety of useful information about the band…
In a quantum theory of gravity the gravitational Wilson loop, defined as a suitable quantum average of a parallel transport operator around a large near-planar loop, provides important information about the large-scale curvature properties…
At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and…
We propose a microscopic, weak-coupling mechanism by which generic Chern bands relax toward ideal bands. We consider coupling interacting electrons to a Caldeira-Leggett like Ohmic bosonic bath. Using the Born-Markov approximation, Slater…
Three-dimensional bond or site percolation theory on a lattice can be interpreted as a gauge theory in which the Wilson loops are viewed as counters of topological linking with random clusters. Beyond the percolation threshold large Wilson…
Weyl semimetals are examples of a new class of topological states of matter which are gapless in the bulk with protected surface states. Their low energy sector is characterized by massless chiral fermions which are robust against…
A set of recent results indicates that fractionally filled bands of Chern insulators in two dimensions support fractional quantum Hall states analogous to those found in fractionally filled Landau levels. We provide an understanding of…
We consider a family of twisted graphene multilayers consisting of $n$-untwisted chirally stacked layers, e.g., AB, ABC, etc, with a single twist on top of $m$-untwisted {chirally stacked} layers. Upon neglecting both trigonal warping terms…
Fractional Chern insulators (FCIs) in ideal flat bands with Chern number $C$ are commonly understood as color-entangled states constructed from $C$ copies of the lowest Landau level. In realistic moir\'e systems, however, the band geometry…
Many magnetic point-group symmetries induce a topological classification on crystalline insulators, dividing them into those that have a nonzero quantized Chern-Simons magnetoelectric coupling ("axion-odd" or "topological"), and those that…
The topology of electronic states in band insulators with mirror symmetry can be classified in two different ways. One is in terms of the mirror Chern number, an integer that counts the number of protected Dirac cones in the Brillouin zone…
Topological band theory has revolutionized our understanding of electronic structure of materials, in particular, a novel state - Weyl semimetal - has been predicted for systems with strong spin-orbit coupling (SOC). Here, a new class of…
Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting non-rotating isolated horizons as inner…
The general structure of the perturbative expansion of the vacuum expectation value of a product of Wilson-loop operators is analyzed in the context of Chern-Simons gauge theory. Wilson loops are opened into Wilson lines in order to unravel…
Exotic phases of matter emerge from the interplay between strong electron interactions and non-trivial topology. Owing to their lack of dispersion at the single-particle level, systems harboring flat bands are excellent testbeds for…