Observation of unidirectional backscattering-immune topological electromagnetic states
TL;DR: It is demonstrated that, like their electronic counterparts, electromagnetic CESs can travel in only one direction and are very robust against scattering from disorder; it is found that even large metallic scatterers placed in the path of the propagating edge modes do not induce reflections.
Abstract: One of the most striking phenomena in condensed-matter physics is the quantum Hall effect, which arises in two-dimensional electron systems subject to a large magnetic field applied perpendicular to the plane in which the electrons reside. In such circumstances, current is carried by electrons along the edges of the system, in so-called chiral edge states (CESs). These are states that, as a consequence of nontrivial topological properties of the bulk electronic band structure, have a unique directionality and are robust against scattering from disorder. Recently, it was theoretically predicted that electromagnetic analogues of such electronic edge states could be observed in photonic crystals, which are materials having refractive-index variations with a periodicity comparable to the wavelength of the light passing through them. Here we report the experimental realization and observation of such electromagnetic CESs in a magneto-optical photonic crystal fabricated in the microwave regime. We demonstrate that, like their electronic counterparts, electromagnetic CESs can travel in only one direction and are very robust against scattering from disorder; we find that even large metallic scatterers placed in the path of the propagating edge modes do not induce reflections. These modes may enable the production of new classes of electromagnetic device and experiments that would be impossible using conventional reciprocal photonic states alone. Furthermore, our experimental demonstration and study of photonic CESs provides strong support for the generalization and application of topological band theories to classical and bosonic systems, and may lead to the realization and observation of topological phenomena in a generally much more controlled and customizable fashion than is typically possible with electronic systems.
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TL;DR: The robustness of edge states against external influence is a phenomenon that has been successfully applied to electron transport as mentioned in this paper, and it is predicted that the same concept can also lead to improved optical devices.
Abstract: The robustness of edge states against external influence is a phenomenon that has been successfully applied to electron transport. A study now predicts that the same concept can also lead to improved optical devices. Topological protection might, for example, reduce the deleterious influence of disorder on coupled-resonator optical waveguides.
838 citations
TL;DR: In this paper, a topolectrical circuit design for realizing the corner modes is presented, where the modes appear as topological boundary resonances in the corner impedance profile of the circuit.
Abstract: Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological corner mid-gap states protected by the bulk spectral gap, reflection symmetries and a spectral symmetry. Here we introduce a topolectrical circuit design for realizing such corner modes experimentally and report measurements in which the modes appear as topological boundary resonances in the corner impedance profile of the circuit. Whereas the quantized bulk quadrupole moment of an electronic crystal does not have a direct analogue in the classical topolectrical-circuit framework, the corner modes inherit the identical form from the quantum case. Due to the flexibility and tunability of electrical circuits, they are an ideal platform for studying the reflection symmetry-protected character of corner modes in detail. Our work therefore establishes an instance where topolectrical circuitry is employed to bridge the gap between quantum theoretical modelling and the experimental realization of topological band structures.
809 citations
TL;DR: In this paper, the authors summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices.
Abstract: Originating from the studies of two-dimensional condensed-matter states, the concept of topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, are now entering the realm of photonics. In this Review, we summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures. Topological photonic structures offer unique features such as reflection-free and non-reciprocal devices. This Review highlights the experimental progress in the relatively new field of photonic topology.
760 citations
TL;DR: It is demonstrated that topological insulator lasers are theoretically possible and experimentally feasible and shown that the underlying topological properties lead to highly efficient lasers, robust to defects and disorder, with single-mode lasing even at conditions high above the laser threshold.
Abstract: INTRODUCTION Topological insulators emerged in condensed matter physics and constitute a new phase of matter, with insulating bulk and robust edge conductance that is immune to imperfections and disorder To date, topological protection is known to be a ubiquitous phenomenon, occurring in many physical settings, ranging from photonics and cold atoms to acoustic, mechanical, and elastic systems So far, however, most of these studies were carried out in entirely passive, linear, and conservative settings RATIONALE We propose topological insulator lasers: lasers whose lasing mode exhibits topologically protected transport without magnetic fields Extending topological physics to lasers is far from natural In fact, lasers are built on foundations that are seemingly inconsistent with the essence of topological insulators: They require gain (and thus are non-Hermitian), they are nonlinear entities because the gain must be saturable, and they are open systems because they emit light These properties, common to all lasers, cast major doubts on the possibility of harnessing topological features to make a topological insulator laser Despite this common mindset, we show that the use of topological properties leads to highly efficient lasers, robust to defects and disorder, with single-mode lasing even at conditions high above the laser threshold RESULTS We demonstrate that topological insulator lasers are theoretically possible and experimentally feasible We consider two configurations involving planar arrays of coupled active resonators The first is based on the Haldane model, archetypical for topological systems The second model, geared toward experiment, constitutes an aperiodic array architecture creating an artificial magnetic field We show that by introducing saturable gain and loss, it is possible to make these systems lase in a topological edge state In this way, the lasing mode exhibits topologically protected transport; the light propagates unidirectionally along the edges of the cavity, immune to scattering and disorder, unaffected by the shape of the edges Moreover, we show that the underlying topological properties not only make the system robust to fabrication and operational disorder and defects, they also lead to a highly efficient single-mode lasing that remains single-mode even at gain values high above the laser threshold The figure describes the geometry and features of a topological insulator laser based on the Haldane model while adding saturable gain, loss, and an output port The cavity is a planar honeycomb lattice of coupled microring resonators, pumped at the perimeter with a lossy interior We show that under these conditions, lasing occurs at the topological edge mode, which has unidirectional flux and is extended around the perimeter with almost-uniform intensity The topological cavities exhibit higher efficiency than the trivial cavity, even under strong disorder For the topological laser with a small gap, the topological protection holds as long as the disorder level is smaller than the gap size DISCUSSION The concept of the topological insulator laser alters current understanding of the interplay between disorder and lasing, and opens exciting possibilities at the interface of topological physics and laser science, such as topologically protected transport in systems with gain We show here that the laser system based on the archetypal Haldane model exhibits topologically protected transport, with features similar to those of its passive counterpart This behavior means that this system is likely to have topological invariants, despite the nonhermiticity Technologically, the topological insulator laser offers an avenue to make many semiconductor lasers operate as one single-mode high-power laser The topological insulator laser constructed from an aperiodic array of resonators was realized experimentally in an all-dielectric platform, as described in the accompanying experimental paper by Bandres et al
753 citations
TL;DR: This work shows theoretically and experimentally the existence of states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices, and finds analytical closed form solutions of topological PT-Symmetric interface states.
Abstract: Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.
743 citations
References
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TL;DR: This study reports an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation and reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions.
Abstract: Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrodinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.
18,958 citations
TL;DR: If a three-dimensionally periodic dielectric structure has an electromagnetic band gap which overlaps the electronic band edge, then spontaneous emission can be rigorously forbidden.
Abstract: It has been recognized for some time that the spontaneous emission by atoms is not necessarily a fixed and immutable property of the coupling between matter and space, but that it can be controlled by modification of the properties of the radiation field. This is equally true in the solid state, where spontaneous emission plays a fundamental role in limiting the performance of semiconductor lasers, heterojunction bipolar transistors, and solar cells. If a three-dimensionally periodic dielectric structure has an electromagnetic band gap which overlaps the electronic band edge, then spontaneous emission can be rigorously forbidden.
12,787 citations
TL;DR: In this paper, an experimental investigation of magneto-transport in a high-mobility single layer of Graphene is presented, where an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene is observed.
Abstract: When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron–hole degeneracy and vanishing carrier mass near the point of charge neutrality1,2. Indeed, a distinctive half-integer quantum Hall effect has been predicted3,4,5 theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction—a consequence of the exceptional topology of the graphene band structure6,7. Recent advances in micromechanical extraction and fabrication techniques for graphite structures8,9,10,11,12 now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.
11,122 citations
Journal Article•
TL;DR: An experimental investigation of magneto-transport in a high-mobility single layer of graphene observes an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene.
Abstract: When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron–hole degeneracy and vanishing carrier mass near the point of charge neutrality. Indeed, a distinctive half-integer quantum Hall effect has been predicted theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction—a consequence of the exceptional topology of the graphene band structure. Recent advances in micromechanical extraction and fabrication techniques for graphite structures now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.
10,112 citations