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Higher-order Topological Knots and the classification of non-Hermitian lattices under symmetry
Yifan Wang, Wladimir A. Benalcazar
In two dimensions, Hermitian lattices with non-zero Chern numbers and non-Hermitian lattices with a higher-order skin effect (HOSE) bypass the constraints of the Nielsen-Ninomiya n…
A mono-atomic orbital-based 1D topological crystalline insulator
Gengming Liu, Violet Workman, Jiho Noh +4
Topological crystalline insulators (TCIs) are classified by topological invariants defined with respect to the crystalline symmetries of their gapped bulk. The bulk-boundary corres…
Nonlinear breathers with crystalline symmetries
Frank Schindler, Vir B. Bulchandani, Wladimir A. Benalcazar
Nonlinear lattice models can support "discrete breather" excitations that stay localized in space for all time. By contrast, the localized Wannier states of linear lattice models a…
Prevalence of two-dimensional photonic topology
Ali Ghorashi, Sachin Vaidya, Mikael Rechtsman +3
The topological characteristics of photonic crystals have been the subject of intense research in recent years. Despite this, the basic question of whether photonic band topology i…
Realization of a Z classified chiral-symmetric higher-order topological insulator in a coupling-inversion acoustic crystal
Dongyi Wang, Yuanchen Deng, Mourad Oudich +3
Higher-order topological band theory has transformed the landscape of topological phases in quantum and classical systems. Here, we experimentally demonstrate a two-dimensional (2D…
Response to polarization and weak topology in Chern insulators
Sachin Vaidya, Mikael C. Rechtsman, Wladimir A. Benalcazar
Chern insulators present a topological obstruction to a smooth gauge in their Bloch wave functions that prevents the construction of exponentially-localized Wannier functions - thi…
Topological Phases of Photonic Crystals under Crystalline Symmetries
Sachin Vaidya, Ali Ghorashi, Thomas Christensen +2
Photonic crystals (PhCs) have emerged as a popular platform for realizing various topological phases due to their flexibility and potential for device applications. In this article…
Observation of degenerate zero-energy topological states at disclinations in an acoustic lattice
Yuanchen Deng, Wladimir A. Benalcazar, Ze-Guo Chen +3
Building upon the bulk-boundary correspondence in topological phases of matter, disclinations have recently been harnessed to trap fractionally quantized density of states (DoS) in…
Topological phases of the dimerized Hofstadter butterfly
Zheng-Wei Zuo, Wladimir A. Benalcazar, Yunzhe Liu +1
In this work, we study the topological phases of the dimerized square lattice in the presence of an external magnetic field. The dimerization pattern in the lattice's hopping ampli…
Higher-order topological pumping and its observation in photonic lattices
Wladimir A. Benalcazar, Jiho Noh, Mohan Wang +3
The discovery of the quantization of particle transport in adiabatic pumping cycles of periodic structures by Thouless [Phys. Rev. B 27, 6083 (1983)] linked the Chern number, a top…
A fractional corner anomaly reveals higher-order topology
Christopher W. Peterson, Tianhe Li, Wladimir A. Benalcazar +2
Spectral measurements of boundary localized in-gap modes are commonly used to identify topological insulators via the bulk-boundary correspondence. This can be extended to high-ord…
Trapped state at a dislocation in a weak magnetomechanical topological insulator
Inbar Hotzen Grinberg, Mao Lin, Wladimir A. Benalcazar +2
Topological insulators (TIs) are characterized by an insulating bulk and symmetry protected bound state on their boundaries. A "strong" topological insulator is characterized by ro…
Boundary-obstructed topological phases
Eslam Khalaf, Wladimir A. Benalcazar, Taylor L. Hughes +1
Symmetry protected topological (SPT) phases are gapped phases of matter that cannot be deformed to a trivial phase without breaking the symmetry or closing the bulk gap. Here, we i…
Robust temporal pumping in a magneto-mechanical topological insulator
Inbar Hotzen Grinberg, Mao Lin, Cameron Harris +4
The transport of energy through 1-dimensional (1D) waveguiding channels can be affected by sub-wavelength disorder, resulting in undesirable localization and backscattering phenome…
Fractional disclination charge in two-dimensional symmetric topological crystalline insulators
Tianhe Li, Penghao Zhu, Wladimir A. Benalcazar +1
Robust fractional charge localized at disclination defects has been recently found as a topological response in symmetric 2D topological crystalline insulators (TCIs). In t…
Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice
S. N. Kempkes, M. R. Slot, J. J. van den Broeke +6
Quantum simulators are an essential tool for understanding complex quantum materials. Platforms based on ultracold atoms in optical lattices and photonic devices led the field so f…
Strong nonreciprocity in modulated resonator chains through synthetic electric and magnetic fields
Christopher W. Peterson, Wladimir A. Benalcazar, Mao Lin +2
We study nonreciprocity in spatiotemporally modulated 1D resonator chains from the perspective of equivalent 2D resonator arrays with a synthetic dimension and transverse synthetic…
Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
Christopher W. Peterson, Wladimir A. Benalcazar, Taylor L. Hughes +1
The modern theory of electric polarization in crystals associates the dipole moment of an insulator with a Berry phase of its electronic ground state [1, 2]. This concept constitut…
Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
Wladimir A. Benalcazar, B. Andrei Bernevig, Taylor L. Hughes
We extend the theory of dipole moments in crystalline insulators to higher multipole moments. In this paper, we expand in great detail the theory presented in Ref. 1, and extend it…
Topological protection of photonic mid-gap cavity modes
Jiho Noh, Wladimir A. Benalcazar, Sheng Huang +4
Defect modes in two-dimensional periodic photonic structures have found use in a highly diverse set of optical devices. For example, photonic crystal cavities confine optical modes…