We extend the notion of fragile topology to periodically-driven systems. We demonstrate driving-induced fragile topology in two different models, namely, the Floquet honeycomb model and the Floquet $π$-flux square-lattice model. In both cases, we discover a rich phase diagram that includes Floquet fragile topological phases protected by crystalline rotation or mirror symmetries, Floquet Chern insulators, and trivial atomic phases, with distinct boundary features. Remarkably, the transitions between different phases can be feasibly achieved by simply tuning the driving amplitudes, which is a unique feature of driving-enabled topological phenomena. Moreover, corner-localized fractional charges are identified as a ``smoking-gun'' signal of fragile topology in our systems. Our work paves the way for studying and realizing fragile topology in Floquet systems.
Although fragile topology has been intensely studied in static crystals in terms of Wannier obstruction, it is not clear how to generalize the concept to dynamical systems. In this work, we generalize the concept of fragile topology, and provide a definition of fragile topology for noninteracting Floquet crystals, which we refer to as dynamical fragile topology. In contrast to the static fragile topology defined by Wannier obstruction, dynamical fragile topology is defined for the nontrivial quantum dynamics characterized by the obstruction to static limits (OTSL). Specifically, the OTSL of a …
Weyl semimetals and nodal line semimetals are characterized by linear electronic bands touching at zero-dimensional points and one-dimensional lines, respectively. Recently, it has been predicted that nodal line semimetals can be driven into tunable Floquet-Weyl semimetals by circularly polarized light. Here, we study the occurrence of interface states between two regions of a nodal line semimetal shined by two beams of light with opposite circular polarizations. Within a minimal model, we find remarkable modifications of the energy structure by tuning the polarized light, such as the possible…
We analyze the phase diagram of multilayer-graphene sandwiched between identical transition metal dichalcogenides. Recently realized in all van-der-Wall heterostructures, these sandwiches induce sizable (1-15 meV) spin orbit coupling in the graphene, offering a way to engineer topological band-structures in a pristine and gate-tunable platform. We find a rich phase diagram that depends on the number of layers $N$ and the gate-tunable perpendicular electric field. For $N > 1$ and odd, the system is a strong 2D topological insulator with a gap equal to the strength of proximity-induced Ising spi…
We propose a system of coupled quantum dots in proximity to a superconductor and driven by separate ac potentials to realize and detect Floquet Majorana fermions. We show that the appearance of Floquet Majorana fermions can be finely controlled in the expanded parameter space of the drive frequency, amplitude, and phase difference across the two dots. While these Majorana fermions are not topologically protected, the highly tunable setup provides a realistic system for observing the exotic physics associated with Majorana fermions as well as their dynamical generation and manipulation.
Confinement-Tunable Synthetic Gauge Fields and Floquet Topological Phenomena in a Driven Quantum Wire Qubit
University of Abomey-Calavi（阿博梅-卡利维大学）；University of Dschang（德尚大学）；Quantum Materials and Computing Group - QMaCG（量子材料与计算群 - QMaCG）；Instituteur principal de l’enseignement général, Délégation Régionale de l’Ouest, Délégation Départementale de la Menoua, Arrondissement de Nkong-Ni, École Publique de Batsing’la Chefferie, Bafou, Cameroun（喀麦隆巴富，班辛拉酋长国公立学校，孔克尼区，梅努瓦省教育厅，西部大区教育厅，普通教育首席教师）；University of Yaoundé I（雅温得第一大学）
In the presence of a circularly polarized mid-infrared radiation graphene develops dynamical band gaps in its quasi-energy band structure and becomes a Floquet insulator. Here we analyze how topologically protected edge states arise inside these gaps in the presence of an edge. Our results show that the gap appearing at $\hbarΩ/2$, where $\hbar Ω$ is the photon energy, is bridged by two chiral edge states whose propagation direction is set by the direction of the polarization of the radiation field. Therefore, both the propagation direction and the energy window where the states appear can be …
In this paper, we discuss the effect of a periodically driving circularly polarized laser beam in the high frequency limit, on the band structure and thermal transport properties of type-I and type-II Weyl semimetals (WSMs). We develop the notion of an effective Fermi surface stemming from the time-averaged Floquet Hamiltonian and discuss its effects on the steady-state occupation numbers of electrons and holes in the linearized model. In order to compute the transport coefficients averaged over a period of the incident laser source, we employ the Kubo formalism for Floquet states and show tha…
We propose a tunable optical setup to engineer topologically nontrivial flat bands in twisted bilayer graphene under circularly polarized light. Using both analytical and numerical calculations, we demonstrate that nearly flat bands can be engineered at small twist angles near the magic angles of the static system. The flatness and the gaps between these bands can be tuned optically by varying laser frequency and amplitude. We study the effects of interlayer hopping variations on Floquet flat bands and find that lattice relaxation favors their formation. Furthermore, we find that, once formed,…
We propose a class of photonic Floquet topological insulators based on staggered helical lattices and an efficient numerical method for calculating their Floquet bandstructure. The lattices support anomalous Floquet topological insulator phases with vanishing Chern number and tunable topological transitions. At the critical point of the topological transition, the bandstructure hosts a single unpaired Dirac cone, which yields a variety of unusual transport effects: a discrete analogue of conical diffraction, weak antilocalization not limited by intervalley scattering, and suppression of Anders…
Interlayer Coupling and Floquet-Driven Topological Phases in Bilayer Haldane Lattices
Zhejiang Normal University（浙江师范大学）；Khazar University（哈扎尔大学）；Quaid-I Azam University Islamabad（巴基斯坦奎德-阿扎姆大学伊斯兰堡分校）；Institute for Research in Fundamental Sciences (IPM)（伊朗基础科学研究院）
Periodically driven systems can host so called anomalous topological phases, in which protected boundary states coexist with topologically trivial Floquet bulk bands. We introduce an anomalous version of reflection symmetry protected topological crystalline insulators, obtained as a stack of weakly-coupled two-dimensional layers. The system has tunable and robust surface Dirac cones even though the mirror Chern numbers of the Floquet bulk bands vanish. The number of surface Dirac cones is given by a new topological invariant determined from the scattering matrix of the system. Further, we find…
The non-Hermiticity caused breakdown of the bulk-boundary correspondence (BBC) in topological phase transition was cured by the skin effect for the systems with chiral symmetry and translation invariance. However, periodic driving, as an active tool in engineering exotic topological phases, breaks the chiral symmetry, and the inevitable disorder destroys the translation invariance. Here, we propose a scheme to retrieve the BBC and establish a complete description of the topological phases of the periodically driven non-Hermitian system both with and without the translation invariance. The demo…
Floquet engineering is a convenient strategy to induce nonequilibrium phenomena in molecular and solid-state systems, or to dramatically alter the physicochemical properties of matter, bypassing costly and time-consuming synthetic modifications. In this article, we investigate theoretically some interesting consequences of the fact that an originally achiral molecular system can exhibit nonzero circular dichroism (CD) when it is driven with elliptically polarized light. More specifically, we consider an isotropic ensemble of small cyclic molecular aggregates in solution whose local low-frequen…
Two-dimensional periodically driven systems can host an unconventional topological phase unattainable for equilibrium systems, termed the Anomalous Floquet-Anderson insulator (AFAI). The AFAI features a quasi-energy spectrum with chiral edge modes and a fully localized bulk, leading to non-adiabatic but quantized charge pumping. Here, we show how such a Floquet phase can be realized in a driven, disordered Quantum Anomalous Hall insulator, which is assumed to have two critical energies where the localization length diverges, carrying states with opposite Chern numbers. Driving the system at a …
Second-order topological insulators (SOTI) exhibit protected gapless boundary states at their hinges or corners. In this paper, we propose a generic means to construct SOTIs in static and Floquet systems by coupling one-dimensional topological insulator wires along a second dimension through dimerized hopping amplitudes. The Hamiltonian of such SOTIs admits a Kronecker sum structure, making it possible for obtaining its features by analyzing two constituent one-dimensional lattice Hamiltonians defined separately in two orthogonal dimensions. The resulting topological corner states do not rely …
Multi-Weyl semimetals(m-WSMS) are characterized by anisotropic non-linear energy dispersion along 2-D plane and a linear dispersion in orthogonal direction. They have topological charge J and are realized when two or multiple Weyl nodes with nonzero net monopole charge bring together onto a high-symmetry point. The model Hamiltonians of such systems show various phases such as trivial normal insulators (NIs), WSMs and quantum anomalous Hall(QAH) states depending on the model parameters. We study a periodic driving of such Hamiltonians in trivial NI phase by circularly polarized light and shows…
The protection of qubit coherence is an essential task in order to build a practical quantum computer able to manipulate, store and read quantum information with a high degree of fidelity. Recently, it has been proposed to increase the operation time of a qubit by means of strong pulses to achieve a dynamical decoupling of the qubit from its environment. We propose and demonstrate a simple and highly efficient alternative pulse protocol based on Floquet modes, which increases the decoherence time in a number of materials with different spin Hamiltonians and environments. We demonstrate the reg…
Harnessing the unique features of topological materials for the development of a new generation of topological based devices is a challenge of paramount importance. Using Floquet scattering theory combined with atomistic models we study the interplay between laser illumination, spin and topology in a two-dimensional material with spin-orbit coupling. Starting from a topological phase, we show how laser illumination can selectively disrupt the topological edge states depending on their spin. This is manifested by the generation of pure spin currents and spin-polarized charge photocurrents under…
Despite intense interest in realizing topological phases across a variety of electronic, photonic and mechanical platforms, the detailed microscopic origin of topological behavior often remains elusive. To bridge this conceptual gap, we show how hallmarks of topological modes - boundary localization and chirality - emerge from Newton's laws in mechanical topological systems. We first construct a gyroscopic lattice with analytically solvable edge modes, and show how the Lorentz and spring restoring forces conspire to support very robust "dangling bond" boundary modes. The chirality and locality…
Recent electron spin resonance experiments on CaWO$_4$:Gd$^{3+}$ and on other magnetic impurities have demonstrated that sustained Rabi oscillations can be created by driving a magnetic moment with a microwave field frequency slightly larger than the Larmor frequency and tuned to the Floquet resonance together with another microwave field (image drive). These observations are confirmed by the new experimental results reported in this paper. We investigate several mechanisms of decoherence and dissipation by using a combination of numerical and analytical techniques. The first microscopic model…
The discovery of the fractional quantum Hall effect in GaAs-based semiconductor devices has lead to new advances in condensed matter physics, in particular the possibility for exotic, topological phases of matter that possess fractional, and even non-Abelian, statistics of quasiparticles. One of the main limitations of the experimental systems based on GaAs has been the lack of tunability of the effective interactions between two-dimensional electrons, which made it difficult to stabilize some of the more fragile states, or induce phase transitions in a controlled manner. Here we review the re…
Topological phases with large Chern numbers have important implications. They were previously predicted to exist by considering fabricated long-range interactions or multi-layered materials. Stimulated by recent wide interests in Floquet topological phases, here we propose a scheme to engineer large-Chern-number phases with ease by periodic quenching. Using a two-band system as an example, we theoretically show how a variety of topological phases with widely tunable Chern numbers can be generated by periodic quenching between two simple Hamiltonians that otherwise give low Chern numbers. The o…
Anyons have recently received great attention due to their promising application in topological quantum computation. The best validated system that enjoys the anyonic excitations are the Laughlin states. The quasi-particles in Laughlin states are neither fermions nor bosons but possess the discrete statistical angle ? = ?=m, with m being an integer. Here we report a possible realization of the universal Abelian anyons, whose statistical angle can be tuned continuously by external parameters and can take any arbitrary values interpolating ? = 0 and ? = ?. The proposed setup is the surface state…
Creating and manipulating topological states is a key goal of condensed matter physics. Periodic driving offers a powerful method to manipulate electronic states, and even to create topological states in solids. Here, we investigate the tunable Floquet states in a periodically driven higher-order nodal line semimetal with both spatial inversion and time-reversal symmetries. We found that the Floquet Weyl semimetal states, which support both one-dimensional hinge Fermi arc and two-dimensional surface Fermi arc states, can be induced in the higher-order nodal-line semimetal by shining circularly…
We show that Floquet engineering using bicircular light (BCL) is a versatile way to control magnetic symmetries and topology in materials. The electric field of BCL, which is a superposition of two circularly polarized light waves with frequencies that are integer multiples of each other, traces out a rose pattern in the polarization plane that can be chosen to break selective symmetries, including spatial inversion. Using a realistic low-energy model, we theoretically demonstrate that the three-dimensional Dirac semimetal Cd$_3$As$_2$ is a promising platform for BCL Floquet engineering. Witho…
Topological acoustics is an emerging field that lies at the intersection of condensed matter physics, mechanical structural design and acoustics engineering. It explores the design and construction of novel artificial structures, such as acoustic metamaterials and phononic crystals, to manipulate sound waves robustly, taking advantage of topological protection. Early work on topological acoustics was limited to duplicating topological phases that have been understood in condensed matter systems, but recent advances have shifted the paradigm to exploring novel topological concepts that are diff…
