arXiv subjects

Hengbin Cheng

Publications and source records attributed to Hengbin Cheng.

5 recordsLinked to original sources

arXiv2026

Weyl Points and Fermi Arc Surface States in a Self-assemblable Zinc-Blende Photonic Crystal

Colloidal self-assembly has long been proposed as a method for growing large-scale three-dimensional photonic crystals with important optical properties in visible and near-infrared wavelength regimes, where top down lithographic fabrication fails. While much of the focus in these systems has been on producing a photonic band gap, such lattices can also give rise to topological features of photonic bands. To date, there has been no proposal for realizing topological photonic features in photonic crystals that may be self-assembled. In 3D, Weyl points are topological band degeneracies that are of particular interest due to their robustness to perturbations and their corresponding Fermi arc surface states. In order to realize Weyl points, either time-reversal or inversion symmetry must be broken, and no previous self-assembled colloidal photonic crystal has exhibited either property. Here, we propose a new zinc-blende structure, built off of recent progress in self-assembling diamond photonic crystals, which lacks inversion symmetry and supports photonic Weyl points. Furthermore, we show that the geometry can be optimized to make the Weyl point and its Fermi arc surface states experimentally observable in the photonic crystal's projected band structure. Finally, we perform molecular dynamics simulations to demonstrate that the geometry we propose for observing Weyl points is capable of being self-assembled with realistic interparticle interactions. Together, these results provide a platform for the assembly of large-scale photonic crystals supporting topological degeneracies and robust Fermi arc surface states in the visible and near-infrared.

physics.optics↗

arXiv2022

Monopole topological resonators

Among the many far-reaching consequences of the potential existence of a magnetic monopole, it induces topological zero modes in the Dirac equation, which were derived by Jackiw and Rebbi 46 years ago and have been elusive ever since. Here, we show that the monopole and multi-monopole solutions can be constructed in the band theory by coupling the three-dimensional Dirac points in hedgehog spatial configurations through Dirac-mass engineering. We then experimentally demonstrate such a monopole bound state in a structurally-modulated acoustic crystal as a cavity device. These monopole resonators not only support an arbitrary number of degenerate mid-gap modes, but also offer the optimal single-mode behavior possible -- whose modal spacing is inversely proportional to the cubic root of the modal volume. Our work completes the kink-vortex-monopole trilogy of zero modes and provides the largest free spectral range for sizable resonators.

cond-mat.mes-hall↗

arXiv2021

Theoretical analysis of glide-Z_2 magnetic topological photonic crystals

Gapped systems with glide symmetry can be characterized by a Z_2 topological invariant. We study the magnetic photonic crystal with a gap between the second and third lowest bands, which is characterized by the nontrivial glide-Z_2 topological invariant that can be determined by symmetry-based indicators. We show that under the space group No. 230 (Ia-3d), the topological invariant is equal to half of the number of photonic bands below the gap, and therefore, the band gap between the second and third lowest bands is always topologically nontrivial, and to realize the topological phase, we need to open a gap for the Dirac point at the P point by breaking time-reversal symmetry. With staggered magnetization, the photonic bands are gapped, and the photonic crystal becomes topological, whereas with uniform magnetization, a gap does not open, which can be attributed to the minimal band connectivity exceeding two in this case. By introducing the notion of Wyckoff positions, we show how the topological characteristics are determined from the structure of the photonic crystals.

physics.optics↗

arXiv2020

Discovering topological surface states of Dirac points

Dirac materials, unlike the Weyl materials, have not been found in experiments to support intrinsic topological surface states, as the surface arcs in existing systems are unstable against symmetry-preserving perturbations. Utilizing the proposed glide and time-reversal symmetries, we theoretically design and experimentally verify an acoustic crystal of two frequency-isolated three-dimensional Dirac points with $Z_2$ monopole charges and four gapless helicoid surface states.

cond-mat.mtrl-sci↗

arXiv2019

Crystallographic splitting theorem for band representations and fragile topological photonic crystals

The fundamental building blocks in band theory are band representations (BRs): bands whose infinitely-numbered Wannier functions are generated (by action of a space group) from a finite number of symmetric Wannier functions centered on a point in space. This work aims to simplify questions on a multi-rank BR by splitting it into unit-rank bands, via the following crystallographic splitting theorem: being a rank-$N$ BR is equivalent to being splittable into a finite sum of bands indexed by $\{1,2,\ldots,N\}$, such that each band is spanned by a single, analytic Bloch function of $k$, and any symmetry in the space group acts by permuting $\{1,2,\ldots,N\}$. Applying this theorem, we develop computationally efficient methods to determine whether a given energy band (of a tight-binding or Schr\"odinger Hamiltonian) is a BR, and, if so, how to numerically construct the corresponding symmetric Wannier functions. Thus we prove that rotation-symmetric topological insulators in class AI are fragile, meaning that the obstruction to symmetric Wannier functions is removable by addition of BRs. An implication of fragility is that its boundary states, while robustly covering the bulk energy gap in finite-rank tight-binding models, are unstable if the Hilbert space is expanded to include all symmetry-allowed representations. These fragile insulators have photonic analogs that we identify; in particular, we prove that an existing photonic crystal built by Yang et al. [Nature 565, 622 (2019)] is fragile topological with removable surface states, which disproves a widespread perception of 'topologically-protected' surface states in time-reversal-invariant, gapped photonic/phononic crystals. Our theorem is finally applied to derive various symmetry obstructions on the Wannier functions of topological insulators, and to prove their equivalence with the nontrivial holonomy of Bloch functions.

cond-mat.str-el↗