36 research outputs found
Dislocation Non-Hermitian Skin Effect
We demonstrate that crystal defects can act as a probe of intrinsic
non-Hermitian topology. In particular, in point-gapped systems with periodic
boundary conditions, a pair of dislocations may induce a non-Hermitian skin
effect, where an extensive number of Hamiltonian eigenstates localize at only
one of the two dislocations. An example of such a phase are two-dimensional
systems exhibiting weak non-Hermitian topology, which are adiabatically related
to a decoupled stack of Hatano-Nelson chains. Moreover, we show that strong
two-dimensional point-gap topology may also result in a dislocation response,
even when there is no skin effect present with open boundary conditions. For
both cases, we directly relate their bulk topology to a stable dislocation
non-Hermitian skin effect. Finally, and in stark contrast to the Hermitian
case, we find that gapless non-Hermitian systems hosting bulk exceptional
points also give rise to a well-localized dislocation response.Comment: 6 pages, 4 figures, supplement included, accepted manuscrip
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Aspects of Topology in Quantum Phases of Matter: a Journey Through Lands Both Flat and Not
Topological quantum phases of matter are often characterized by the presence of fractionalized quasiparticles, which exhibit non-trivial braiding statistics or carry fractional quantum numbers, or of protected gapless surface states. In this thesis, we study topological phases in two and three spatial dimensions, from the perspective of searching for new exotic quantum phases and of characterizing their experimental signatures. We first study topological defects in fermionic paired superfluids and discover that in the presence of a multiply quantized vortex, such a state hosts unpaired fermions in the BCS regime. We predict that these unpaired fermions will result in an experimentally measurable deviation of the system's angular momentum from its value in the BEC regime. Focusing on two-dimensions, we then study superconductors coupled to dynamically fluctuating electromagnetism, and establish a universal framework for studying the low-energy physics of such systems. We derive topological field theories describing all spin-singlet superconductors which naturally capture the interplay of symmetry and topology in these gapped states.The remainder of this thesis is focused on a novel class of long-range entangled states of matter, known as “fracton” phases, in both two- and three-dimensions. These phases exhibit an intriguing phenomenology, most surprising of which is the presence of excitations which are immobile in isolation. Studying the non-equilibrium dynamics of gapped fracton phases, we discover that they naturally exhibit glassy quantum dynamics in the absence of quenched disorder, and hence may have potential technological applications as robust quantum memories. Finally, we conclude with a description of fracton phases as higher-rank tensor gauge theories and discuss the emergent phases of matter in which a finite density of fractons or their bound states may exist
Symmetric tensor gauge theories on curved spaces
Fractons and other subdimensional particles are an exotic class of emergent quasi-particle excitations with severely restricted mobility. A wide class of models featuring these quasi-particles have a natural description in the language of symmetric tensor gauge theories, which feature conservation laws restricting the motion of particles to lower-dimensional sub-spaces, such as lines or points. In this work, we investigate the fate of symmetric tensor gauge theories in the presence of spatial curvature. We find that weak curvature can induce small (exponentially suppressed) violations on the mobility restrictions of charges, leaving a sense of asymptotic fractonic/sub-dimensional behavior on generic manifolds. Nevertheless, we show that certain symmetric tensor gauge theories maintain sharp mobility restrictions and gauge invariance on certain special curved spaces, such as Einstein manifolds or spaces of constant curvature
Rotational Symmetry Protected Edge and Corner States in Abelian topological phases
Spatial symmetries can enrich the topological classification of interacting
quantum matter and endow systems with non-trivial strong topological invariants
(protected by internal symmetries) with additional "weak" topological indices.
In this paper, we study the edge physics of systems with a non-trivial shift
invariant, which is protected by either a continuous or
discrete rotation symmetry, along with internal
charge conservation. Specifically, we construct an interface between two
systems which have the same Chern number but are distinguished by their Wen-Zee
shift and, through analytic arguments supported by numerics, show that the
interface hosts counter-propagating gapless edge modes which cannot be gapped
by arbitrary local symmetry-preserving perturbations. Using the Chern-Simons
field theory description of two-dimensional Abelian topological orders, we then
prove sufficient conditions for continuous rotation symmetry protected gapless
edge states using two complementary approaches. One relies on the algebraic
Lagrangian sub-algebra framework for gapped boundaries while the other uses a
more physical flux insertion argument. For the case of discrete rotation
symmetries, we extend the field theory approach to show the presence of
fractional corner charges for Abelian topological orders with gappable edges,
and compute them in the case where the Abelian topological order is placed on
the two-dimensional surface of a Platonic solid. Our work paves the way for
studying the edge physics associated with spatial symmetries in symmetry
enriched topological phases.Comment: 9 + 2 pages, 2 figures. Added references and improved discussion in
Sec I