Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder

Zhou, Longwen; Du, Qianqian

doi:10.1103/physreva.101.033607

Cited by 25 publications

(33 citation statements)

References 123 publications

(151 reference statements)

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“…Recently, spin-

extensions of the CL model have also been explored in several studies [ 81 , 82 , 83 ], leading to the discoveries of richer topological features. Furthermore, when time-periodic drivings are applied to the spin-

CL, a series of Hermitian Floquet topological phases in the CII symmetry class were found [ 84 ]. Each of these phases is characterized by a pair of even-integer topological winding numbers, quantized dynamics of bulk states, together with degenerate quartets of zero and

Floquet edge modes under the OBC [ 84 ].…”

Section: Model and Symmetrymentioning

confidence: 99%

“…Furthermore, when time-periodic drivings are applied to the spin-

Floquet edge modes under the OBC [ 84 ]. In this work, the construction of our system can be viewed as a non-Hermitian extension of the model studied in Ref.…”

Section: Model and Symmetrymentioning

confidence: 99%

“…In this work, the construction of our system can be viewed as a non-Hermitian extension of the model studied in Ref. [ 84 ], and will be referred to as the non-Hermitian periodically quenched two-leg ladder (PQTLL).…”

Section: Model and Symmetrymentioning

confidence: 99%

“…Following the symmetry analysis in the last section and the topological characterizations of Hermitian Floquet phases [ 84 , 93 ], the Floquet operator

in the

’s time frame possesses a topological winding number

, which can be defined as:

where

, k is the quasimomentum,

is the sublattice symmetry operator, and the trace is taken over all the internal degrees of freedom including spins and sublattices.

is usually called the

-matrix [ 94 ], which takes the form of a biorthogonal projector:

Here

are the indices of the two Floquet quasienergy bands, whose real parts are positive.…”

Section: Topological Invariants and Phase Diagramsmentioning

confidence: 99%

“…With the help of

in Equation ( 17 ) and the topological characterization of chiral symmetric Floquet systems [ 86 ], we can construct another pair of topological winding numbers

as:

According to Ref. [ 84 ], these invariants would only take even-integer values, and they provide a complete characterization for all 1D Hermitian Floquet topological phases in the CII symmetry class. Furthermore, the requirement of two invariants reveals the difference between Floquet and non-driven systems.…”

Section: Topological Invariants and Phase Diagramsmentioning

confidence: 99%

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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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“…Recently, spin-

Floquet edge modes under the OBC [ 84 ].…”

Section: Model and Symmetrymentioning

confidence: 99%

“…Furthermore, when time-periodic drivings are applied to the spin-

Floquet edge modes under the OBC [ 84 ]. In this work, the construction of our system can be viewed as a non-Hermitian extension of the model studied in Ref.…”

Section: Model and Symmetrymentioning

confidence: 99%

Section: Model and Symmetrymentioning

confidence: 99%

“…Following the symmetry analysis in the last section and the topological characterizations of Hermitian Floquet phases [ 84 , 93 ], the Floquet operator

in the

’s time frame possesses a topological winding number

, which can be defined as:

where

, k is the quasimomentum,

is the sublattice symmetry operator, and the trace is taken over all the internal degrees of freedom including spins and sublattices.

is usually called the

-matrix [ 94 ], which takes the form of a biorthogonal projector:

Here

are the indices of the two Floquet quasienergy bands, whose real parts are positive.…”

Section: Topological Invariants and Phase Diagramsmentioning

confidence: 99%

“…With the help of

in Equation ( 17 ) and the topological characterization of chiral symmetric Floquet systems [ 86 ], we can construct another pair of topological winding numbers

as:

Section: Topological Invariants and Phase Diagramsmentioning

confidence: 99%

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

Zhou

2020

Entropy

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Floquet engineering of topological metal states and hybridization of edge states with bulk states in dimerized two-leg ladders

Jangjan

Hosseini

2020

Sci Rep

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We consider asymmetric and symmetric dimerized two-leg ladders, comprising of four different lattice points per unit cell, illuminated by circularly polarized light. in the asymmetric dimerized ladder case, rungs are not perpendicular to the ladder's legs whereas the rungs are perpendicular to the legs for the symmetric one. Using the Floquet theory, we obtain an effective Hamiltonian to study topological properties of the systems. Depending on the dimerization strength and driving amplitude, it is shown that topologically protected edge states manifest themselves not only as a zero-energy band within the gap between conduction and valence band but also as finite-energy curved bands inside the gap of subbands. The latter one can penetrate into bulk states and hybridize with the bulk states revealing hybridized floquet topological metal phase with delocalized edge states in the asymmetric ladder case. However, in the symmetric ladder, the finite-energy edge states while remaining localized can coexist with the extended bulk states manifesting floquet topological metal phase. Topological states of matter with intriguing properties have attracted a lot of attention in various fields of physics, particularly, solid-state physics 1. Because of robustness of such states against ubiquitous perturbations 2 , materials hosting topological states will be excellent candidates for sensitive electronic applications. Topological insulators 3 along with topological superconductors 4 exhibiting topologically nontrivial phases have been interesting topics from theoretical and experimental view points. However, the known topological systems in the equilibrium situation which can indeed be used to realistic applications are limited to a few cases leading to exploring topological quantum states out-of-equilibrium 5. Beside materials including static topological phases, engineering of exotic nontrivial phases of quantum materials 6 has been developed by means of externally applied dynamical fields. Such approach provides a flexible and practical way to produce desired phases which are absent in the static counterparts. For instance, periodic driving establishes dynamical topological states, known as topological Floquet states 7-9. An interesting characteristic of the Floquet theory 10,11 is to add extra dimension in a quantum system through continuous evolution over all times within the driving period 9,12,13 providing higher-dimensional systems effectively. In the opposite limit, i.e., stroboscopic picture 6,8 , periodic driving manipulates the system parameters expanding phase diagram to values that are not easily accessible in undriven systems. Both of these two features pave the way to turn trivial phases of the system into exotic ones, such as Floquet topological semimetals 14,15 , Floquet topological superconductors 16,17 , and Floquet topological insulators 7,18. There are a variety of techniques for exerting time periodicity and establishing topologically protected edge states such as shining a matter with light 7,19-21 , sha...

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Out of equilibrium chiral higher order topological insulator on a π -flux square lattice

Bhat

Bera

2021

J. Phys.: Condens. Matter

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One of the hallmarks of bulk topology is the existence of robust boundary localized states. For instance, a conventional d dimensional topological system hosts d − 1 dimensional surface modes, which are protected by non-spatial symmetries. Recently, this idea has been extended to higher order topological phases with boundary modes that are localized in lower dimensions such as in the corners or in one dimensional hinges of the system. In this work, we demonstrate that a higher order topological phase can be engineered in a nonequilibrium state when the time-independent model does not possess any symmetry protected topological states. The higher order topology is protected by an emerging chiral symmetry, which is generated through the Floquet driving. Using both the exact numerical method and an effective high-frequency Hamiltonian obtained from the Brillouin-Wigner (BW) perturbation theory, we verify the emerging topological phase on a π-flux square lattice. We show that the localized corner modes in our model are robust against a chiral symmetry preserving perturbation and can be classified as ‘extrinsic’ higher order topological phase. Finally, we identify a two dimensional topological invariant from the winding number of the corresponding sublattice symmetric one dimensional model. The latter model belongs to class AIII of ten-fold symmetry classification of topological matter.

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Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder

Cited by 25 publications

References 123 publications

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

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

Floquet engineering of topological metal states and hybridization of edge states with bulk states in dimerized two-leg ladders

Out of equilibrium chiral higher order topological insulator on a π -flux square lattice

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