Bulk detection of time-dependent topological transitions in quenched chiral models

D’Errico, Alessio; Colandrea, Francesco Di; Barboza, Raouf; Dauphin, Alexandre; Lewenstein, Maciej; Massignan, Pietro; Marrucci, Lorenzo; Cardano, Filippo

doi:10.1103/physrevresearch.2.023119

Cited by 20 publications

(9 citation statements)

References 60 publications

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“…The deviations of

from quantization are due to finite-time effects, which will gradually go to zero with the increase of the number of driving periods t . Numerically, we checked that the time-averaged mean chiral displacements

remain close to quantization for

driving periods, which should be within reach in current or near-term experiments in photonic [ 126 , 127 ] and cold atom [ 128 , 129 ] systems.…”

Section: Mean Chiral Displacementsmentioning

confidence: 81%

Floquet Second-Order Topological Phases in Momentum Space

Zhou

2021

Nanomaterials

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Higher-order topological phases (HOTPs) are characterized by symmetry-protected bound states at the corners or hinges of the system. In this work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven systems, which are demonstrated in a two-dimensional extension of the quantum double-kicked rotor. The found Floquet HOTPs are protected by chiral symmetry and characterized by a pair of topological invariants, which could take arbitrarily large integer values with the increase of kicking strengths. These topological numbers are shown to be measurable from the chiral dynamics of wave packets. Under open boundary conditions, multiple quartets Floquet corner modes with zero and π quasienergies emerge in the system and coexist with delocalized bulk states at the same quasienergies, forming second-order Floquet topological bound states in the continuum. The number of these corner modes is further counted by the bulk topological invariants according to the relation of bulk-corner correspondence. Our findings thus extend the study of HOTPs to momentum-space lattices and further uncover the richness of HOTPs and corner-localized bound states in continuum in Floquet systems.

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“…The deviations of

remain close to quantization for

driving periods, which should be within reach in current or near-term experiments in photonic [ 126 , 127 ] and cold atom [ 128 , 129 ] systems.…”

Section: Mean Chiral Displacementsmentioning

confidence: 81%

Floquet Second-Order Topological Phases in Momentum Space

Zhou

2021

Nanomaterials

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“…9b then reveals the topological nature of the quench. As a last comment we stress that our protocol differs from the chiral displacement method introduced and used in [55][56][57][58]. The mean chiral displacement depends on the unit-cell convention.…”

Section: Measuring the Chiral Polarizationmentioning

confidence: 99%

Geometry and topology tango in ordered and amorphous chiral matter

2022

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Systems as diverse as mechanical structures and photonic metamaterials enjoy a common geometrical feature: a sublattice or chiral symmetry first introduced to characterize electronic insulators. We show how a real-space observable, the chiral polarization, distinguishes chiral insulators from one another and resolve long-standing ambiguities in the very concept of their bulk-boundary correspondence. We use it to lay out generic geometrical rules to engineer topologically distinct phases, and design zero-energy topological boundary modes in both crystalline and amorphous metamaterials.

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“…The MCD was first introduced as a dynamical probe to the winding numbers of 1D topological insulators in the symmetry classes AIII and BDI [ 98 ], and later extended to Floquet systems [ 93 , 99 , 100 ], two-dimensional systems [ 101 ], many-body systems [ 102 ], systems in other symmetry classes [ 84 ], and recently also to non-Hermitian systems [ 50 , 51 , 53 ]. In the meantime, the MCD has also been measured experimentally in photonic [ 98 , 103 ] and cold atom [ 104 , 105 ] setups. In this section, we further generalize the MCD to non-Hermitian Floquet systems in the CII symmetry class, and employ it to dynamically characterize the topological phases found in the non-Hermitian PQTLL model.…”

Section: Dynamical Probe To the Topological Phasesmentioning

confidence: 99%

“…Furthermore, a quantized jump of the MCD is observed every time when the system passes through a topological phase transition point. Experimentally, the MCDs have been measured in both the cold atom [ 104 , 105 ] and photonic systems [ 98 , 103 ], in which non-Hermiticity and driving fields can also be implemented [ 1 ]. Furthermore, the MCDs may also be detected directly in momentum space with the help of a recently proposed setup certaining the nitrogen-vacancy-center in diamond [ 36 ].…”

Section: Dynamical Probe To the Topological Phasesmentioning

confidence: 99%

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

Zhou

2020

Entropy

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Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical, and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them characterized by a pair of even-integer topological invariants ( w 0 , w π ) ∈ 2 Z × 2 Z . Under the open boundary condition, these invariants further predict the number of zero- and π -quasienergy modes localized around the edges of the system. We finally construct a generalized version of the mean chiral displacement, which could be employed as a dynamical probe to the topological invariants of non-Hermitian Floquet phases in the CII symmetry class. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.

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Bulk detection of time-dependent topological transitions in quenched chiral models

Cited by 20 publications

References 60 publications

Floquet Second-Order Topological Phases in Momentum Space

Floquet Second-Order Topological Phases in Momentum Space

Geometry and topology tango in ordered and amorphous chiral matter

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

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