Type-II corner modes in topolectrical circuits (original) (raw)
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System size dependent topological zero modes in coupled topolectrical chains
Physical review, 2022
In this paper, we demonstrate the emergence and disappearance of topological zero modes (TZMs) in a coupled topolectrical (TE) circuit lattice. Specifically, we consider non-Hermitian TE chains in which TZMs do not occur in the individual uncoupled chains, but emerge when these chains are coupled by inter-chain capacitors. The coupled system hosts TZMs which show size-dependent behaviours and vanish beyond a certain critical size. In addition, the emergence or disappearance of the TZMs in the open boundary condition (OBC) spectra for a given size of the coupled system can be controlled by modulating the signs of its inverse decay length. Analytically, trivial and non-trivial phases of the coupled system can be distinguished by the differing ranks of their corresponding Laplacian matrix. The TE circuit framework enables the physical detection of the TZMs via electrical impedance measurements. Our work establishes the conditions for inducing TZMs and modulating their behavior in coupled TE chains.
Valley Hall Effect and Kink States in Topolectrical Circuits
arXiv (Cornell University), 2022
We investigate the emergence of topological valley Hall and kink states in a two-dimensional topolectrical (TE) model as a result of broken chiral and reflection symmetries. The TE system consists of two segments hosting distinct topological states with opposite signs of the valley Hall index, and separated by a heterojunction. In the practical circuit, the valley Hall index can be flipped between the two segments by modulating the onsite potential on the sublattice nodes of the respective segments. The presence of resistive coupling, which introduces non-Hermiticity in the system, subsequently leads to the emergence of gapped and gapless valley and kink states in the admittance spectra. These topological modes can be detected electrically by the impedance readouts of the system which can be correlated to its admittance spectra. Finally, we confirm the robustness of the valley Hall and kink states via realistic LTspice simulation taking into account the tolerance windows and parasitic effects inherent in circuit components. Our study demonstrates the applicability of TE circuit networks as a platform to realize and tune valley-dependent and kink topological phenomena.
Chiral surface and hinge states in higher-order Weyl semimetallic circuits
arXiv (Cornell University), 2023
We propose a 3D topolectrical (TE) network that can be tuned to realize various higher-order topological gapless and chiral phases. We first study a higher-order Dirac semimetal phase that exhibits a hinge-like Fermi arc linking the Dirac points. This circuit can be extended to host highly tunable first-and second-order Weyl semimetal phases by introducing a non-reciprocal resistive coupling in the x − y plane that breaks time reversal symmetry. The first-and second-order Weyl points are connected by zero-admittance surface and hinge states, respectively. We also study the emergence of first-and second-order chiral modes induced by resistive couplings between similar nodes in the z-direction. These modes respectively occur in the midgap of the surface and hinge admittance bands in our circuit model without the need for any external magnetic field.
Chiral topological insulators, superconductors, and other competing orders in three dimensions
Physical Review B, 2010
We discuss the proximate phases of a three-dimensional system with Dirac-like dispersion. Using the cubic lattice with plaquette -flux as a model, we find, among other phases, a chiral topological insulator and singlet topological superconductor. While the former requires a special "chiral" symmetry, the latter is stable as long as time reversal and SU͑2͒ spin rotation symmetry are present. These phases are characterized by stable surface Dirac fermion modes, and by an integer topological invariant in the bulk. The key features of these phases are readily understood in a two dimensional limit with an appropriate pairing of Dirac nodes between layers. This Dirac node-pairing picture is also shown to apply to Z 2 topological insulators protected by time-reversal symmetry. The nature of pointlike topological defects in these phases is also investigated, revealing an interesting duality relation between these topological phases and the Neel phase.
Measurement of Corner-Mode Coupling in Acoustic Higher-Order Topological Insulators
Frontiers in Physics, 2021
Recent developments of band topology have revealed a variety of higher-order topological insulators (HOTIs). These HOTIs are characterized by a variety of different topological invariants, making them different at a fundamental level. However, despite such differences, the fact that they all sustain higher-order topological boundary modes poses a challenge to phenomenologically tell them apart. This work presents experimental measurements of the coupling effects of topological corner modes (TCMs) existing in two different types of two-dimensional acoustic HOTIs. Although both HOTIs have a similar four-site square lattice, the difference in magnetic flux per unit cell dictates that they belong to different types of topologically nontrivial phases—one lattice possesses quantized dipole moments, but the other is characterized by quantized quadrupole moment. A link between the topological invariants and the response line shape of the coupled TCMs is theoretically established and experim...
Selective enhancement of topologically induced interface states in a dielectric resonator chain
Nature communications, 2015
The recent realization of topological phases in insulators and superconductors has advanced the search for robust quantum technologies. The prospect to implement the underlying topological features controllably has given incentive to explore optical platforms for analogous realizations. Here we realize a topologically induced defect state in a chain of dielectric microwave resonators and show that the functionality of the system can be enhanced by supplementing topological protection with non-hermitian symmetries that do not have an electronic counterpart. We draw on a characteristic topological feature of the defect state, namely, that it breaks a sublattice symmetry. This isolates the state from losses that respect parity-time symmetry, which enhances its visibility relative to all other states both in the frequency and in the time domain. This mode selection mechanism naturally carries over to a wide range of topological and parity-time symmetric optical platforms, including coup...
Tunable Dirac interface states in topological superlattices
Physical Review B
Relativistic Dirac fermions are ubiquitous in condensed-matter physics. Their mass is proportional to the material energy gap and the ability to control and tune the mass has become an essential tool to engineer quantum phenomena that mimic high energy particles and provide novel device functionalities. In topological insulator thin films, new states of matter can be generated by hybridizing the massless Dirac states that occur at material surfaces. In this paper, we experimentally and theoretically introduce a platform where this hybridization can be continuously tuned: the Pb1-xSnxSe topological superlattice. In this system, topological Dirac states occur at the interfaces between a topological crystalline insulator Pb1-xSnxSe and a trivial insulator, realized in the form of topological quantum wells (TQW) epitaxially stacked on top of each other. Using magnetooptical transmission spectroscopy on high quality molecular beam epitaxy grown Pb1-xSnxSe superlattices, we show that the penetration depth of the TQW interface states and therefore their Dirac mass is continuously tunable with temperature. This presents a pathway to engineer the Dirac mass of topological systems and paves the way towards the realization of emergent quantum states of matter using Pb1-xSnxSe topological superlattices.
Arxiv preprint arXiv: …, 2010
Angle resolved photoemission spectroscopy (ARPES) studies were performed on two compounds (TlBiTe2 and TlBiSe2) from a recently proposed three dimensional topological insulator family in Thallium-based III-V-VI2 ternary chalcogenides. For both materials, we show that the electronic band structures are in broad agreement with the ab initio calculations; by surveying over the entire surface Brillouin zone (BZ), we demonstrate that there is a single Dirac cone reside at the center of BZ, indicating its topological non-triviality. For TlBiSe2, the observed Dirac point resides at the top of the bulk valance band, making it a large gap (≥200meV ) topological insulator; while for TlBiTe2, we found there exist a negative indirect gap between the bulk conduction band at M point and the bulk valance band near Γ, making it a semi-metal at proper doping. Interestingly, the unique band structures of TlBiTe2 we observed further suggest TlBiTe2 may be a candidate for topological superconductors.
Geometrically induced electric polarization in conical topological insulators
Journal of Applied Physics, 2012
We study the topological magnetoelectric effect on a conical topological insulator when a point charge q is near the cone apex. The Hall current induced on the cone surface and the image charge configuration are determined. We also study a kind of gravitational Aharonov-Bohm effect in this geometry and realize a phase diference betwen the components of the wavefunctions (spinors) upon closed parallel transport around the (singular) cone tip. Concretely, a net current flowing towards cone apex (or botton) shows up, yielding electric polarization of the conical topological insulator. Such an effect may be detected, for instance, by means of the net accumulated Hall charge near the apex. Once it depends only on the geometry of the material (essetially, the cone apperture angle) this may be faced as a microscopic scale realization of (2+1)-dimensional Einstein gravity.