Random-walk topological transition revealed via electron counting

Engelhardt, Georg; Benito, Mónica; Platero, Gloria; Schaller, Gernot; Brandes, Tobias

doi:10.1103/physrevb.96.241404

Cited by 12 publications

(8 citation statements)

References 47 publications

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“…As we see later, the statistical distribution P (n,n ) (τ ) of the time difference τ between two consecutive jump events W n σ=1 and W n σ =−1 contains interesting information about the system dynamics [54]. This waiting-time experiment is sketched in Fig.…”

Section: B Transport Observablesmentioning

confidence: 97%

Tuning the Aharonov-Bohm effect with dephasing in nonequilibrium transport

Engelhardt

Cao

2019

Phys. Rev. B

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The Aharanov-Bohm (AB) effect, which predicts that a magnetic field strongly influences the wave function of an electrically charged particle, is investigated in a three site system in terms of the quantum control by an additional dephasing source. The AB effect leads to a non-monotonic dependence of the steady-state current on the gauge phase associated with the molecular ring. This dependence is sensitive to site energy, temperature, and dephasing, and can be explained using the concept of the dark state. Although the phase effect vanishes in the steady-state current for strong dephasing, the phase dependence remains visible in an associated waiting-time distribution, especially at short times. Interestingly, the phase rigidity (i.e., the symmetry of the AB phase) observed in the steady-state current is now broken in the waiting-time statistics, which can be explained by the interference between transfer pathways.

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Section: B Transport Observablesmentioning

confidence: 97%

Tuning the Aharonov-Bohm effect with dephasing in nonequilibrium transport

Engelhardt

Cao

2019

Phys. Rev. B

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“…In fact, this analogy opens up the possibility to simulate the topology of the fractional Josephson-effect by means of regular electron transport. This idea thus falls in line with a number of very recent proposals to im-plement topological behavior known from the quantum domain through (semi) classical dynamics, most notably the study of geometric and topological effects in the diffusion dynamics of polymers [43,44], or also the implementation of the Su-Schrieffer-Heeger (SSH) model through single electron transistors [45]. In addition, we emphasize that the here proposed simulator is potentially more stable than the fractional Josephson effect itself.…”

Section: B Analogy To Fractional Josephson Effectmentioning

confidence: 59%

“…In a similar spirit, the simulation of topo-logical features known from quantum coherent systems by means of a classical stochastic dynamics has been recently and prominently demonstrated in the diffusion of polymers [43,44], by exploiting the structural similarity between the Schrödinger equation and the diffusion equation. Likewise, the realization of a Su-Schrieffer-Heeger (SSH) model has been recently proposed using the fullcounting statistics of single electron transistors [45]. We note that we have reason to believe that in our particular case, the simulation might actually be more stable than the original.…”

Section: B Geometric Phases and Classical Analogy To Fractional Josep...mentioning

confidence: 89%

Fractional charges in conventional sequential electron tunneling

Riwar

2018

Preprint

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The notion of fractional charges was up until now reserved for quasiparticle excitations emerging in strongly correlated quantum systems, such as Laughlin states in the fractional quantum Hall effect, Luttinger quasiparticles, or parafermions. Here, we consider topological transitions in the full counting statistics of standard sequential electron tunneling, and find that they lead to the same type of charge fractionalization -strikingly without requiring exotic quantum correlations. This conclusion relies on the realization that fundamental integer charge quantization fixes the global properties of the transport statistics whereas fractional charges can only be well-defined locally. We then show that the reconciliation of these two contradicting notions results in a nontrivially quantized geometric phase defined in the detector space. In doing so, we show that detector degrees of freedom can be used to describe topological transitions in nonequilibrium open quantum systems. Moreover, the quantized geometric phase reveals a profound analogy between the fractional charge effect in sequential tunneling and fractional Josephson effect in topological superconducting junctions, where likewise the Majorana-or parafermions exhibit a charge which is at odds with the Cooper pair charge as the underlying unit of the supercurrent. In order to provide means for an experimental verification of our claims, we demonstrate the fractional nature of transport statistics at the example of highly feasible transport models, such as weakly tunnel-coupled quantum dots or charge islands. We then show that the geometric phase can be accessed through the detector's waiting time distribution. Finally, we find that topological transitions in the transport statistics could even lead to new applications, such as the unexpected possibility to directly measure features beyond the resolution limit of a detector.

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“…Furthermore, our numerical simulation of the temperature distribution elucidates a novel diffusion phenomenon for a honeycomb lattice system; the temperature field with wavenumber cannot diffuse into the bulk, which is attributed to the complete localization of the edge state with . Here, we stress that systems we discuss are classical systems in contrast to a previous work 41 analyzing topology of diffusion of electrons.…”

Section: Introductionmentioning

confidence: 99%

Bulk-edge correspondence of classical diffusion phenomena

Yoshida

Hatsugai

2021

Sci Rep

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We elucidate that diffusive systems, which are widely found in nature, can be a new platform of the bulk-edge correspondence, a representative topological phenomenon. Using a discretized diffusion equation, we demonstrate the emergence of robust edge states protected by the winding number for one- and two-dimensional systems. These topological edge states can be experimentally accessible by measuring diffusive dynamics at edges. Furthermore, we discover a novel diffusion phenomenon by numerically simulating the distribution of temperatures for a honeycomb lattice system; the temperature field with wavenumber $$\pi $$ π cannot diffuse to the bulk, which is attributed to the complete localization of the edge state.

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Random-walk topological transition revealed via electron counting

Cited by 12 publications

References 47 publications

Tuning the Aharonov-Bohm effect with dephasing in nonequilibrium transport

Tuning the Aharonov-Bohm effect with dephasing in nonequilibrium transport

Fractional charges in conventional sequential electron tunneling

Bulk-edge correspondence of classical diffusion phenomena

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