SciPost Submission Page
Geometry and Topology Tango in Ordered and Amorphous Chiral Matter
by Marcelo Guzmán, Denis Bartolo, David Carpentier
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | David Carpentier · Marcelo Guzmán |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202106_00037v3 (pdf) |
| Code repository: | https://doi.org/10.5281/zenodo.5721386 |
| Date accepted: | 2021-12-16 |
| Date submitted: | 2021-12-02 15:32 |
| Submitted by: | Guzmán, Marcelo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Systems as diverse as mechanical structures and photonic metamaterials enjoy a common geometrical feature: a sublattice or chiral symmetry first introduced to characterize electronic insulators. We show how a real-space observable, the chiral polarization, distinguishes chiral insulators from one another and resolve long-standing ambiguities in the very concept of their bulk-boundary correspondence. We use it to lay out generic geometrical rules to engineer topologically distinct phases, and design zero-energy topological boundary modes in both crystalline and amorphous metamaterials.
Author comments upon resubmission
List of changes
Line 123:
We changed “Although seemingly identical to…” to “This definition differs from…”
Line 128:
We added “This difference is simply explained by considering the mean chiral displacement (MCD) defined on a 1D lattice given a definition of a unit cell. It is defined per wavepacket $\psi$ as ${\rm MCD}=\expval{\mathbb C x_{\text{UC}}}{\psi}$, with $x_{\text{UC}}$ being the position operator at the scale of the unit cell. By definition, $x_{\text{UC}}$ is defined as an integer multiple of the length $a$ of the unit cell. In contrast, equation~\eqref{eq:defPolarization} depends on the actual position of the sites: $x=x_{\text{UC}}+\delta x$, where $\delta x$ is a sublattice correction to the unit-cell position .”
Line 444:
we changed the last paragraph: “As a last comment we stress that although our protocol is close to the chiral displacement method….” to
“As a last comment we stress that our protocol differs from the chiral displacement method introduced and used in~\cite{cardano2017detection,maffei2018topological,st2020measuring,d2020bulk}. The mean chiral displacement depends on the unit-cell convention. As a consequence, to probe the topology of 1D systems, conventional MCD protocols require two independent measurement protocols. They effectively correspond to measuring the mean chiral displacement given two possible unit cell choices. A topological invariant is then defined by the difference between the two measurements. The Chiral polarization method, which we introduce provides a one-step characterization of the topology of a chiral phase. »
line 747:
We changed “Although seemingly similar in its formal definition…” to “The chiral polarization which we extensively use in this article is an intrinsic (meta)material property , unlike the mean chiral displacement and the skew polarization. It is defined in real space,…”
Line 319:
We have changed “…taking advantge of the so-called pencil-matrix method [51].”
To
“…taking advantage of the matrix pencil method detailed in Appendix D.”
Line 678:
We have changed “Here, we introduce an alternative method based on the matrix pencil of the projected positions.”
To
“Here, we introduce an alternative method based on the matrix pencil of the projected positions (for a general introduction to matrix pencils see [68] and pages 375 and 461 of [69] ).”
Requested language modifications of Anonymous referee:
Line 53-54:
“… spread frantically across…”
to
“spanned ”
Line 87:
“… intimate interplay…”
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“…interplay…”
Line 166
“… intimate relation…”
to
“…relation…”
Line 205:
“… to illuminate the very definition…”
to
”… to clarify the definition…”
Line 278:
“… illuminates the geometrical implication…”
to
“…reveals the geometrical implication…”
Line 450:
“… the frame topology and the frame geometry conspire…”
to
“… the frame topology and the frame geometry act together …”
Line 458:
“This subtle tango…”
to
“This interplay…”
Published as SciPost Phys. 12, 038 (2022)
Reports on this Submission
Report
First of all, I would like to thank the authors for correcting me and clarifying my confusion concerning the difference between the chiral polarization and the mean chiral displacement.
The authors have addressed all of the points I had raised during the previous round. I have no further comments and I believe the work should be published as is.