scholarly journals Simulating Floquet topological phases in static systems

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Selma Franca ◽  
Fabian Hassler ◽  
Ion Cosma Fulga
Keyword(s):  
Topological Insulators ◽  
Topological Phases ◽  
Topological System ◽  
Reflection Matrix ◽  
Back Scattering ◽  
Scattering Matrices ◽  
Floquet Operator ◽  
Static Systems ◽  
Time Periodic ◽  
External Driving

We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators. We consider D-dimensional HOTIs with gapless corner states which are weakly probed by external waves in a scattering setup. We find that the unitary reflection matrix describing back-scattering from the boundary of the HOTI is topologically equivalent to a (D-1)-dimensional nontrivial Floquet operator. To characterize the topology of the reflection matrix, we introduce the concept of `nested' scattering matrices. Our results provide a route to engineer topological Floquet systems in the lab without the need for external driving. As benefit, the topological system does not suffer from decoherence and heating.

scholarly journals Time-periodic corner states from Floquet higher-order topology

2022 ◽  
Vol 13 (1) ◽  
Author(s):  
Weiwei Zhu ◽  
Haoran Xue ◽  
Jiangbin Gong ◽  
Yidong Chong ◽  
Baile Zhang
Keyword(s):  
Three Dimensional ◽  
Higher Order ◽  
Topological Phases ◽  
Time Dynamics ◽  
Topological States ◽  
Acoustic Lattice ◽  
Static Systems ◽  
Time Invariant ◽  
Time Periodic ◽  
Spatial Axis

AbstractThe recent discoveries of higher-order topological insulators (HOTIs) have shifted the paradigm of topological materials, previously limited to topological states at boundaries of materials, to include topological states at boundaries of boundaries, such as corners. So far, all HOTI realisations have been based on static systems described by time-invariant Hamiltonians, without considering the time-variant situation. There is growing interest in Floquet systems, in which time-periodic driving can induce unconventional phenomena such as Floquet topological phases and time crystals. Recent theories have attempted to combine Floquet engineering and HOTIs, but there has been no experimental realisation so far. Here we report on the experimental demonstration of a two-dimensional (2D) Floquet HOTI in a three-dimensional (3D) acoustic lattice, with modulation along a spatial axis serving as an effective time-dependent drive. Acoustic measurements reveal Floquet corner states with double the period of the underlying drive; these oscillations are robust, like time crystal modes, except that the robustness arises from topological protection. This shows that space-time dynamics can induce anomalous higher-order topological phases unique to Floquet systems.

scholarly journals Unveiling Signatures of Topological Phases in Open Kitaev Chains and Ladders

Nanomaterials ◽  
2019 ◽  
Vol 9 (6) ◽  
pp. 894 ◽  
Author(s):  
Alfonso Maiellaro ◽  
Francesco Romeo ◽  
Carmine Antonio Perroni ◽  
Vittorio Cataudella ◽  
Roberta Citro
Keyword(s):  
Electrical Response ◽  
Differential Conductance ◽  
Model Parameters ◽  
Topological Phases ◽  
Topological Order ◽  
Topological Phase ◽  
Moderate Amount ◽  
Topological System ◽  
Isolated Systems

In this work, the general problem of the characterization of the topological phase of an open quantum system is addressed. In particular, we study the topological properties of Kitaev chains and ladders under the perturbing effect of a current flux injected into the system using an external normal lead and derived from it via a superconducting electrode. After discussing the topological phase diagram of the isolated systems, using a scattering technique within the Bogoliubov–de Gennes formulation, we analyze the differential conductance properties of these topological devices as a function of all relevant model parameters. The relevant problem of implementing local spectroscopic measurements to characterize topological systems is also addressed by studying the system electrical response as a function of the position and the distance of the normal electrode (tip). The results show how the signatures of topological order affect the electrical response of the analyzed systems, a subset of which being robust also against the effects of a moderate amount of disorder. The analysis of the internal modes of the nanodevices demonstrates that topological protection can be lost when quantum states of an initially isolated topological system are hybridized with those of the external reservoirs. The conclusions of this work could be useful in understanding the topological phases of nanowire-based mesoscopic devices.

scholarly journals Impact of magnetic dopants on magnetic and topological phases in magnetic topological insulators

2020 ◽  
Vol 102 (20) ◽  
Author(s):  
Thanh-Mai Thi Tran ◽  
Duc-Anh Le ◽  
Tuan-Minh Pham ◽  
Kim-Thanh Thi Nguyen ◽  
Minh-Tien Tran
Keyword(s):  
Topological Insulators ◽  
Topological Phases

scholarly journals The family of topological phases in condensed matter†

2013 ◽  
Vol 1 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Shun-Qing Shen
Keyword(s):  
Topological Insulators ◽  
Condensed Matter ◽  
Quantum States ◽  
Condensed Matter Physics ◽  
Topological Phases ◽  
Important Advance ◽  
Global Properties ◽  
The Family ◽  
Boundary States ◽  
Historic Development

Abstract The discovery of topological insulators and superconductors is an important advance in condensed matter physics. Topological phases reflect global properties of the quantum states in materials, and the boundary states are the characteristic of the materials. Such phases constitute a new branch in condensed matter physics. Here a historic development is briefly introduced, and the known family of phases in condensed matter are summarized.

scholarly journals Quantum Energy Expectation in Periodic Time-Dependent Hamiltonians via Green Functions

2009 ◽  
Vol 2009 ◽  
pp. 1-30
Author(s):  
César R. de Oliveira ◽  
Mariza S. Simsen
Keyword(s):  
Time Dependent ◽  
Green Functions ◽  
Quantum Energy ◽  
Expectation Value ◽  
Energy Expectation ◽  
Floquet Operator ◽  
Time Average ◽  
Time Periodic

LetUFbe the Floquet operator of a time periodic HamiltonianH(t). For each positive and discrete observableA(which we call aprobe energy), we derive a formula for the Laplace time average of its expectation value up to timeTin terms of its eigenvalues and Green functions at the circle of radiuse1/T. Some simple applications are provided which support its usefulness.

scholarly journals Topological phases: Isomorphism, homotopy and K-theory

2015 ◽  
Vol 12 (09) ◽  
pp. 1550098 ◽  
Author(s):  
Guo Chuan Thiang
Keyword(s):  
Topological Insulators ◽  
Vector Bundles ◽  
Equivalence Classes ◽  
Topological Phases ◽  
Winding Number ◽  
Symmetry Constraints ◽  
K Theory

Equivalence classes of gapped Hamiltonians compatible with given symmetry constraints, such as those underlying topological insulators, can be defined in many ways. For the non-chiral classes modeled by vector bundles over Brillouin tori, physically relevant equivalences include isomorphism, homotopy, and K-theory, which are inequivalent but closely related. We discuss an important subtlety which arises in the chiral Class AIII systems, where the winding number invariant is shown to be relative rather than absolute as is usually assumed. These issues are then analyzed and reconciled in the language of K-theory.

scholarly journals Realization of quasicrystalline quadrupole topological insulators in electrical circuits

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Bo Lv ◽  
Rui Chen ◽  
Rujiang Li ◽  
Chunying Guan ◽  
Bin Zhou ◽  
...  
Keyword(s):  
Circuit Design ◽  
Topological Insulators ◽  
Topological Phases ◽  
Quadrupole Moments ◽  
Impedance Spectra ◽  
Electrical Circuits ◽  
New Class ◽  
Artificial Materials ◽  
Higher Dimensional ◽  
Topological Boundary

AbstractQuadrupole topological insulators are a new class of topological insulators with quantized quadrupole moments, which support protected gapless corner states. The experimental demonstrations of quadrupole-topological insulators were reported in a series of artificial materials, such as photonic crystals, acoustic crystals, and electrical circuits. In all these cases, the underlying structures have discrete translational symmetry and thus are periodic. Here we experimentally realize two-dimensional aperiodic-quasicrystalline quadrupole-topological insulators by constructing them in electrical circuits, and observe the spectrally and spatially localized corner modes. In measurement, the modes appear as topological boundary resonances in the corner impedance spectra. Additionally, we demonstrate the robustness of corner modes on the circuit. Our circuit design may be extended to study topological phases in higher-dimensional aperiodic structures.

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