اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدElectric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
544
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 to cover associated topological pumping phenomena, and a novel class of 3D insulator with chiral hinge states. In quantum-mechanical crystalline insulators, higher multipole bulk moments manifest themselves by the presence of boundary-localized moments of lower dimension, in exact correspondence with the electromagnetic theory of classical continuous dielectrics. In the presence of certain symmetries, these moments are quantized, and their boundary signatures are fractionalized. These multipole moments then correspond to new SPT phases. The topological structure of these phases is described by nested Wilson loops, which reflect the bulk-boundary correspondence in a way that makes evident a hierarchical classification of the multipole moments. Just as a varying dipole generates charge pumping, a varying quadrupole generates dipole pumping, and a varying octupole generates quadrupole pumping. For non-trivial adiabatic cycles, the transport of these moments is quantized. An analysis of these interconnected phenomena leads to the conclusion that a new kind of Chern-type insulator exists, which has chiral, hinge-localized modes in 3D. We provide the minimal models for the quantized multipole moments, the non-trivial pumping processes and the hinge Chern insulator, and describe the topological invariants that protect them.
قيم البحث
اقرأ أيضاً
In this article we extend the celebrated Berry-phase formulation of electric polarization in crystals to higher electric multipole moments. We determine the necessary conditions under which, and minimal models in which, the quadrupole and octupole mo
ments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they manifest topologically protected corner states carrying fractional charge, i.e., fractionalization at the boundary of the boundary. To characterize these new insulating phases of matter, we introduce a new paradigm whereby `nested Wilson loops give rise to a large number of new topological invariants that have been previously overlooked. We propose three realistic experimental implementations of this new topological behavior that can be immediately tested.
The bulk-boundary correspondence, which links a bulk topological property of a material to the existence of robust boundary states, is a hallmark of topological insulators. However, in crystalline topological materials the presence of boundary states
in the insulating gap is not always necessary since they can be hidden in the bulk energy bands, obscured by boundary artifacts of non-topological origin, or, in the case of higher-order topology, they can be gapped altogether. Crucially, in such systems the interplay between symmetry-protected topology and the corresponding symmetry defects can provide a variety of bulk probes to reveal their topological nature. For example, bulk crystallographic defects, such as disclinations and dislocations, have been shown to bind fractional charges and/or robust localized bound states in insulators protected by crystalline symmetries. Recently, exotic defects of translation symmetry called partial dislocations have been proposed as a probe of higher-order topology. However, it is a herculean task to have experimental control over the generation and probing of isolated defects in solid-state systems; hence their use as a bulk probe of topology faces many challenges. Instead, here we show that partial dislocation probes of higher-order topology are ideally suited to the context of engineered materials. Indeed, we present the first observations of partial-dislocation-induced topological modes in 2D and 3D higher-order topological insulators built from circuit-based resonator arrays. While rotational defects (disclinations) have previously been shown to indicate higher-order topology, our work provides the first experimental evidence that exotic translation defects (partial dislocations) are bulk topological probes.
The modern theory of electric polarization has recently been extended to higher multipole moments, such as quadrupole and octupole moments. The higher electric multipole insulators are essentially topological crystalline phases protected by underlyin
g crystalline symmetries. Henceforth, it is natural to ask what are the consequences of symmetry breaking in these higher multipole insulators. In this work, we investigate topological phases and the consequences of symmetry breaking in generalized electric quadrupole insulators. Explicitly, we generalize the Benalcazar-Bernevig-Hughes model by adding specific terms in order to break the crystalline and non-spatial symmetries. Our results show that chiral symmetry breaking induces an indirect gap phase which hides corner modes in bulk bands, ruining the topological quadrupole phase. We also demonstrate that quadrupole moments can remain quantized even when mirror symmetries are absent in a generalized model. Furthermore, it is shown that topological quadrupole phase is robust against a unique type of disorder presented in the system.
We study the properties of a family of anti-pervoskite materials, which are topological crystalline insulators with an insulating bulk but a conducting surface. Using ab-initio DFT calculations, we investigate the bulk and surface topology and show t
hat these materials exhibit type-I as well as type-II Dirac surface states protected by reflection symmetry. While type-I Dirac states give rise to closed circular Fermi surfaces, type-II Dirac surface states are characterized by open electron and hole pockets that touch each other. We find that the type-II Dirac states exhibit characteristic van-Hove singularities in their dispersion, which can serve as an experimental fingerprint. In addition, we study the response of the surface states to magnetic fields.
Topological photonics provides a fundamental framework for robust manipulation of light, including directional transport and localization with built-in immunity to disorder. Combined with an optical gain, active topological cavities hold special prom
ise for a design of light-emitting devices. Most studies to date have focused on lasing at topological edges of finite systems or domain walls. Recently discovered higher-order topological phases enable strong high-quality confinement of light at the corners. Here we demonstrate lasing action of corner states in a nanophotonic topological cavity. We identify four multipole corner modes with distinct emission profiles via hyperspectral imaging and discern signatures of non-Hermitian radiative coupling of leaky topological states. In addition, depending on the pump position in a large-size cavity, we selectively generate lasing from either edge or corner states within the topological bandgap. Our findings introduce pathways to engineer collective resonances and tailor generation of light in active topological circuits.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
