Topological origin of quantized transport in non-Hermitian Floquet chains

Höckendorf, Bastian; Alvermann, Andreas; Fehske, Holger

doi:10.1103/physrevresearch.2.023235

Cited by 40 publications

(27 citation statements)

References 45 publications

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“…In a many-body description, this would call for a combination of the Floquet and the Lindblad techniques, which is a combination is a fundamental, unresolved problem 37 . Note added in proof: After submission of the final manuscript, a study on a very similar subject appeared 38 .…”

Section: Discussionmentioning

confidence: 99%

Observation of topological transport quantization by dissipation in fast Thouless pumps

et al. 2020

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Quantized dynamics is essential for natural processes and technological applications alike. The work of Thouless on quantized particle transport in slowly varying potentials (Thouless pumping) has played a key role in understanding that such quantization may be caused not only by discrete eigenvalues of a quantum system, but also by invariants associated with the nontrivial topology of the Hamiltonian parameter space. Since its discovery, quantized Thouless pumping has been believed to be restricted to the limit of slow driving, a fundamental obstacle for experimental applications. Here, we introduce non-Hermitian Floquet engineering as a new concept to overcome this problem. We predict that a topological band structure and associated quantized transport can be restored at driving frequencies as large as the system’s band gap. The underlying mechanism is suppression of non-adiabatic transitions by tailored, time-periodic dissipation. We confirm the theoretical predictions by experiments on topological transport quantization in plasmonic waveguide arrays.

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Section: Discussionmentioning

confidence: 99%

Observation of topological transport quantization by dissipation in fast Thouless pumps

et al. 2020

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“…Similarly, we can consider angle-gapped spectra of the Floquet operator in other dimensions. Compared to the angle-gapped case where the topological invariants dictate the appearance of edge modes inside the angle gaps, the above non-contractible loops in the Floquet spectra give rise to unidirectional topological charge pumping [140].…”

Section: B Angle-gapless Topologymentioning

confidence: 97%

“…While for the angle-gapless system, the Floquet Hamiltonian is generally not continuous in k for any chosen branch cut. There is no additional spectrum constraints on the quasienergies, which arises many intriguing properties, such as the unidirectional charge pumping [140] and the enhancement of boundary transport relative to bulk motion in waveguide lattices [139]. These differences also yield distinct classification procedures for the anglegapped and angle-gapless cases, as demonstrated in the next section.…”

Section: B Gap Condition Of the Floquet Operatormentioning

confidence: 99%

“…A complete topological classification of FNH systems based on their underlying symmetries is not only of fundamental significance but also experimentally relevant. A periodically driven non-Hermitian system features non-unitary quantum dynamics and describes a variety of physical settings, e.g., photonic systems with ubiquitous gain and loss or nonreciprocal effects under Floquet driving [134][135][136][137][138][139][140][141][142][143], ultracold atoms with dissipation interacting with an external electromagnetic field [144][145][146][147][148][149], and non-unitary quantum walks [150][151][152][153][154].…”

Section: Introductionmentioning

confidence: 99%

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Symmetry and topological classification of Floquet non-Hermitian systems

Liu,

Hu,

Chen

2021

Preprint

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“…Similarly, in response to a temperature gradient, without any external magnetic field, it generate a transverse Hall voltage, known as the anomalous Nernst effect [9,[12][13][14]. Coupled with the Boltzmann transport theory, the modified semiclassical equations have been employed to study transport in topological insulators [15], Chern Insulators [16], Weyl Semi-Metals [13,14,[17][18][19][20][21][22], Kondo Insulators [23], Rashba systems [24,25], optical lattices and quasicrystals [26,27], superconductors [28], non-Hermitian systems [29,30], as well as in various other systems [31][32][33][34][35][36][37]. Non-linear effects in transport have also been studied within this formalism [38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Energy magnetization and transport in systems with a non-zero Berry curvature in a magnetic field

Archisman¹,

Mukerjee²

2021

Preprint

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We demonstrate that the well-known expression for the charge magnetization of a sample with a non-zero Berry curvature can be obtained by demanding that the Einstein relation holds for the electric transport current. We extend this formalism to the transport energy current and show that the energy magnetization must satisfy a particular condition. We provide a physical interpretation of this condition and relate the energy magnetization to circulating energy currents due to chiral edge states. We further obtain an expression for the energy magnetization analogous to the one previously obtained for the charge magnetization. We also solve the Boltzmann Transport Equation for the non-equilibrium distribution function in 2D for systems with a non-zero Berry curvature in a magnetic field. This distribution function can be used to obtain the regular Hall response in time-reversal invariant samples with a non-zero Berry curvature, for which there is no anomalous Hall response.

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Topological origin of quantized transport in non-Hermitian Floquet chains

Cited by 40 publications

References 45 publications

Observation of topological transport quantization by dissipation in fast Thouless pumps

Observation of topological transport quantization by dissipation in fast Thouless pumps

Symmetry and topological classification of Floquet non-Hermitian systems

Energy magnetization and transport in systems with a non-zero Berry curvature in a magnetic field

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