Adolfo G. Grushin, Álvaro Gómez-León, Titus Neupert
We respond to the comments expressed by L. D'Alessio in arXiv:1412.3481 on our work "Floquet Fractional Chern Insulators" [Phys. Rev. Lett. 112, 156801 (2014)]. We confirm the central result that the ground state of the effective Hamiltonian is an interacting fractional Chern insulator.
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Intervalley Band Crossing and Transition of Fractional Chern Insulators in Floquet Twisted Bilayer MoTe$_2$
研究光子驱动下MoTe₂双层的能隙区间带交叉及Floquet分数切赫绝缘体的相变，通过Floquet理论推导有效哈密顿量并分析谷极化行为变化。
Fractional Chern insulators are theoretically predicted states of electronic matter with emergent topological order. They exhibit the same universal properties as the fractional quantum Hall effect, but dispose of the need to apply a strong magnetic field. However, despite intense theoretical work, an experimental realization for these exotic states of matter is still lacking. Here we show that doped graphene turns into a fractional Chern insulator, when irradiated with high-intensity circularly polarized light. We derive the effective steady state band structure of light-driven graphene using…
In a recent paper [Phys. Rev. Lett. 112 156801 (2014)], Grushin et al. studied a Fermi-Hubbard-model for spinful electrons on a honeycomb lattice coupled to an external polarized electric field. By computing the Floquet Hamiltonian perturbatively to order $ω^{-1}$ (where $ω$ is the frequency of the drive) they predicted that, for specific values of the driving and filling, the system can transition into a Fractional Chern Insulator. In this comment we point out that: i) the calculation of the Floquet Hamiltonian misses some terms of order $ω^{-1}$ and ii) the assumption that the Floquet bands …
Multiple Floquet Chern insulator phases in the spin-charge coupled triangular-lattice ferrimagnet: Crucial role of higher-order terms in the high-frequency expansion
本文在三角Kondo晶格模型中通过圆偏振光辐照发现两种Floquet Chern绝缘体相，揭示其源于高频展开的高阶Brillouin-Wigner项，拓展了Floquet工程在简单非多子格晶格中的适用范围。
Floquet Fractional Chern Insulators and Competing Phases in Twisted Bilayer Graphene
本研究利用Floquet理论和精确对角化，在圆偏振光驱动的转角双层石墨烯中发现了广泛参数区域内的Floquet分数陈绝缘体态，并揭示了其与电荷密度波、费米液体的竞争关系。
Fractional Chern insulators are the proposed phases of matter mimicking the physics of fractional quantum Hall states on a lattice without an overall magnetic field. The notion of Floquet fractional Chern insulators refers to the potential possibilities to generate the underlying topological bandstructure by means of Floquet engineering. In these schemes, a highly controllable and strongly interacting system is periodically driven by an external force at a frequency such that double tunneling events during one forcing period become important and contribute to shaping the required effective ene…
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 …
Visualizing Berry curvature in a Floquet-Chern insulator
本文利用圆二色性Tr-ARPES直接映射Bi2Se3表面光诱导的Berry曲率，验证了Floquet-Chern绝缘体拓扑性质，为光诱导拓扑相变提供直接探测手段。
Floquet Chern Insulators and Radiation-Induced Zero Resistance in Irradiated Graphene
本研究通过圆极化光照射石墨，预测了Floquet Chern绝缘体和由辐射诱导的零电阻状态，揭示了非平衡条件下石墨的新型物态及电导特性。
Network models for equilibrium integer quantum Hall (IQH) transitions are described by unitary scattering matrices, that can also be viewed as representing non-equilibrium Floquet systems. The resulting Floquet bands have zero Chern number, and are instead characterized by a chiral Floquet (CF) winding number. This begs the question: How can a model without Chern number describe IQH systems? We resolve this apparent paradox by showing that non-zero Chern number is recovered from the network model via the energy dependence of network model scattering parameters. This relationship shows that, de…
We propose a simple scheme for the realization of a topological quasienergy band structure with ultracold atoms in a periodically driven optical square lattice. It is based on a circular lattice shaking in the presence of a superlattice that lowers the energy on every other site. The topological band gap, which separates the two bands with Chern numbers $\pm 1$, is opened in a way characteristic to Floquet topological insulators, namely, by terms of the effective Hamiltonian that appear in subleading order of a high-frequency expansion. These terms correspond to processes where a particle tunn…
We propose a defect-to-edge topological quantum quench protocol that can efficiently inject electric charge from defect-core states into a chiral edge current of an induced Chern insulator. The initial state of the system is assumed to be a Mott insulator, with electrons bound to topological defects that are pinned by disorder. We show that a "critical quench" to a Chern insulator mass of order the Mott gap shunts charge from defects to the edge, while a second stronger quench can trap it there and boost the edge velocity, creating a controllable current. We apply this idea to a skyrmion charg…
In this paper, we theoretically investigate how laser fields change the nature of topological Kondo insulators(TKIs). By employing a prototypical model of TKIs, we treat the effect of the laser fields with Floquet theory, which gives effective description under high frequency laser fields. We derive the effective model of TKIs under the laser irradiation and discuss its topological properties. We demonstrate a possible realization of Floquet Chern insulators specified by various values of Chern number and reveal how the topological phase changes with increasing the laser light intensity. Furth…
The realization of synthetic gauge fields has attracted a lot of attention recently in relation with periodically driven systems and the Floquet theory. In ultra-cold atom systems in optical lattices and photonic networks, this allows to simulate exotic phases of matter such as quantum Hall phases, anomalous quantum Hall phases and analogs of topological insulators. In this paper, we apply the Floquet theory to engineer anisotropic Haldane models on the honeycomb lattice and two-leg ladder systems. We show that these anisotropic Haldane models still possess a topologically non-trivial band str…
Spacetime symmetry indicators for two-dimensional Floquet topological insulators
本文研究具有n重时间螺旋对称性的二维Floquet拓扑绝缘体，提出仅依赖高对称动量时间演化的对称性指标，并推导其与体态拓扑不变量的关系，简化了FTIs的材料实现与圆偏振光驱动系统研究。
Energy or quasienergy (QE) band spectra depending on two parameters may have a nontrivial topological characterization by Chern integers. Band spectra of 1D systems that are spanned by just one parameter, a Bloch phase, are topologically trivial. Recently, an ensemble of 1D Floquet systems, double kicked rotors (DKRs) depending on an external parameter, has been studied. It was shown that a QE band spanned by both the Bloch phase and the external parameter is characterized by a Chern integer, which determines the change in the mean angular momentum of a state in a band when the external parame…
We show that Floquet chiral topological superconductivity arises naturally in Josephson junctions made of magnetic topological insulator-superconductor sandwich structures. The Josephson phase modulation associated with an applied bias voltage across the junction drives the system into the anomalous Floquet chiral topological superconductor hosting chiral Majorana edge modes in the quasienergy spectrum, with the bulk Floquet bands carrying zero Chern numbers. The bias voltage acts as a tuning parameter enabling novel dynamical topological quantum phase transitions driving the system into a myr…
Floquet Topological Spin-Valley-Layertronics on a Layered Dice Lattice
本研究在层状骰子晶格体系中，利用圆偏振光、垂直位移场调控关联拓扑相，确立其为电控磁性与拓扑相的多功能平台，提供集成自旋-谷-层电子学的全电学方案。
Electronic bands featuring nontrivial bulk topological invariant manifest through robust gapless modes at the boundaries, e.g., edges and surfaces. As such this bulk-boundary correspondence is also operative in driven quantum materials. For example, a suitable periodic drive can convert a trivial insulator into a Floquet topological insulator (FTI) that accommodates nondissipative dynamic gapless modes at the interfaces with vacuum. Here we theoretically demonstrate that dislocations, ubiquitous lattice defects in crystals, can probe FTIs as well as unconventional $π$-trivial insulator in the …
Time-periodic perturbations due to classical electromagnetic fields are useful to engineer the topological properties of matter using the Floquet theory. Here we investigate the effect of quantized electromagnetic fields by focusing on the quantized light-matter interaction on the edge state of a quantum spin-Hall insulator. A Dicke-type superradiant phase transition occurs at arbitrary weak coupling, the electronic spectrum acquires a finite gap and the resulting ground state manifold is topological with Chern number $\pm 1$. When the total number of excitations is conserved, a photocurrent i…
Nontrivial topological properties from the cooperation of static perturbations and Floquet fields in type-II semi-Dirac semimetals
本研究理论探究II型半狄拉克半金属在静态微扰、双频正交偏振光驱动及二者协同作用下的拓扑与反常输运性质，揭示混合场景下的丰富拓扑现象及多种反常输运特征。
Floquet Exceptional Topological Insulator
本文提出通过 Floquet 工程在非厄米系统中实现 Floquet 异常拓扑绝缘体，揭示光诱导下体点能隙承载表面态、量子异常及动量切片中的非厄米趋肤效应。
Quantum state preparation of topological chiral spin liquids via Floquet engineering
本文提出在方形晶格自旋-1/2团簇上，通过Floquet工程对RVB初始态施加快速时间调制，实现拓扑手性自旋液体的量子态制备，并分析其拓扑性质及量子计算应用前景。
Tunable phase transitions from semimetals to Chern insulators in two-dimensional quadratic-band-crossing materials
本文系统研究了静态对称性破缺微扰和偏振光驱动的动态Floquet项如何调控二维二次能带交叉点材料的拓扑相变，揭示了Berry曲率的不同行为，并实现了从半金属到陈绝缘体的可调拓扑相变。
We demonstrate that the prototypical two-dimensional Chern insulator hosts exotic quantum multi-criticality in the presence of an appropriate periodic driving: a linear Dirac-like transition coexists with a nodal loop-like transition caused by emerging symmetries. The existence of multiple universality classes and scaling laws can be unambiguously captured by a single renormalization group approach based on the stroboscopic Floquet Hamiltonian, regardless of whether the topological transition is associated with the anomalous edge modes or not.
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