77 research outputs found

### A Two-dimensional Algebraic Quantum Liquid Produced by an Atomic Simulator of the Quantum Lifshitz Model

Bosons have a natural instinct to condense at zero temperature. It is a
long-standing challenge to create a high-dimensional quantum liquid that does
not exhibit long-range order at the ground state, as either extreme
experimental parameters or sophisticated designs of microscopic Hamiltonian are
required for suppressing the condensation. Here, we show that ultra cold atoms
with synthetic spin-orbit coupling provide physicists a simple and practical
scheme to produce a two-dimensional algebraic quantum liquid at the ground
state. This quantum liquid arises at a critical Lifshitz point, where the
single-particle ground state shrinks to a point from a circle in the momentum
space, and many fundamental properties of two-dimensional bosons are changed in
its proximity. Such an ideal simulator of the quantum Lifshitz model allows
experimentalists to directly visualize and explore the deconfinement transition
of topological excitations, an intriguing phenomenon that is difficult to
access in other systems.Comment: 3 figure

### Structure and Topology of Band Structures in the 1651 Magnetic Space Groups

The properties of electrons in magnetically ordered crystals are of interest
both from the viewpoint of realizing novel topological phases, such as magnetic
Weyl semimetals, and from the applications perspective of creating
energy-efficient memories. A systematic study of symmetry and topology in
magnetic materials has been challenging given that there are 1651 magnetic
space groups (MSGs). Here, by using an efficient representation of allowed band
structures, we obtain a systematic description of several basic properties of
free electrons in all MSGs in three dimensions as well as in the 528 magnetic
layer groups relevant to two dimensional magnetic materials. We compute
constraints on electron fillings and band connectivity compatible with
insulating behavior. Also, by contrasting with atomic insulators, we identify
band topology entailed by the symmetry transformation of bands, as determined
by the MSG alone. We give an application of our results to identifying
topological semimetals arising in periodic arrangements of hedgehog-like
magnetic textures.Comment: (9 + 34) pages; 3 figures; (2+19) tables; v2: close to published
versio

### Symmetry-based Indicators of Band Topology in the 230 Space Groups

The interplay between symmetry and topology leads to a rich variety of
electronic topological phases, protecting states such as the topological
insulators and Dirac semimetals. Previous results, like the Fu-Kane parity
criterion for inversion-symmetric topological insulators, demonstrate that
symmetry labels can sometimes unambiguously indicate underlying band topology.
Here we develop a systematic approach to expose all such symmetry-based
indicators of band topology in all the 230 space groups. This is achieved by
first developing an efficient way to represent band structures in terms of
elementary basis states, and then isolating the topological ones by removing
the subset of atomic insulators, defined by the existence of localized
symmetric Wannier functions. Aside from encompassing all earlier results on
such indicators, including in particular the notion of filling-enforced quantum
band insulators, our theory identifies symmetry settings with previously hidden
forms of band topology, and can be applied to the search for topological
materials.Comment: 9+21 pages; (2+1) figures, (4+20) tables; v2: references added; title
changed; results for quasi-2D and 1D systems adde

### Fragile topological phases in interacting systems

Topological phases of matter are defined by their nontrivial patterns of
ground-state quantum entanglement, which is irremovable so long as the
excitation gap and the protecting symmetries, if any, are maintained. Recent
studies on noninteracting electrons in crystals have unveiled a peculiar
variety of topological phases, which harbors nontrivial entanglement that can
be dissolved simply by the the addition of entanglement-free, but charged,
degrees of freedom. Such topological phases have a weaker sense of robustness
than their conventional counterparts, and are therefore dubbed "fragile
topological phases." In this work, we show that fragile topology is a general
concept prevailing beyond systems of noninteracting electrons. Fragile
topological phases can generally occur when a system has a $\mathrm{U}(1)$
charge conservation symmetry, such that only particles with one sign of the
charge are physically allowed (e.g. electrons but not positrons). We
demonstrate that fragile topological phases exist in interacting systems of
both fermions and of bosons.Comment: 14 pages. Comments welcome; v2: several discussions are improve

### Landau Level Degeneracy in Twisted Bilayer Graphene: Role of Symmetry Breaking

The degeneracy of Landau levels flanking charge neutrality in twisted bilayer
graphene is known to change from eight-fold to four-fold when the twist angle
is reduced to values near the magic angle of $\approx 1.05^\circ$. This
degeneracy lifting has been reproduced in experiments by multiple groups, and
is known to occur even in devices which do not harbor the correlated insulators
and superconductors. We propose $C_3$ symmetry breaking as an explanation of
such robust degeneracy lifting, and support our proposal by numerical results
on the Landau level spectrum in near-magic-angle twisted bilayer graphene.
Motivated by recent experiments, we further consider the effect of $C_2$
symmetry breaking on the Landau levels.Comment: 12 pages, 10 figure

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