Theory of the nonequilibrium electronic Mach-Zehnder interferometer

Schneider, Martin; Bagrets, Dmitry; Mirlin, A. D.

doi:10.1103/physrevb.84.075401

Cited by 22 publications

(55 citation statements)

References 66 publications

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“…In particular, experiments that revealed striking non-equilibrium effects in Mach Zehnder interferometers [6] have stimulated extensive theoretical research, [25,[30][31][32][33][34][35][36][37] including calculations [33] of interferometer dephasing based on the same bosonized model [16] for edge states at ν = 2 with contact interactions that we adopt in the following. In the context of edge state relaxation a parallel development to the present paper, described in Ref.…”

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confidence: 99%

Relaxation in Driven Integer Quantum Hall Edge States

Kovrizhin

Chalker

2012

Phys. Rev. Lett.

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A highly non-thermal electron distribution is generated when quantum Hall edge states originating from sources at different potentials meet at a quantum point contact. The relaxation of this distribution to a stationary form as a function of distance downstream from the contact has been observed in recent experiments [C. Altimiras et al. Phys. Rev. Lett. 105, 056803 (2010)]. Here we present an exact treatment of a minimal model for the system at filling factor ν=2, with results that account well for the observations. PACS numbers: 71.10. Pm, 42.25.Hz Introduction. The importance of understanding nonequilibrium dynamics and relaxation in many-body quantum systems has been recognised since the early years of quantum mechanics [1, 2]. Settings in which such problems are of high current interest include, among others, cold atomic gases [2] and nanoscale electronic devices. [3-14] As a particular example, recent experiments [3] on quantum Hall (QH) edge states driven out of equilibrium at a quantum point contact (QPC) provide very detailed information on the approach to a steady state in an electron system that appears to be wellisolated from other degrees of freedom. In this paper we describe the exact solution of a simple model for these experiments and compare our results with the measurements.In outline, the experiments we are concerned with [3] involve two sets of integer QH edge states, which meet at a QPC. When a bias voltage is applied to the QPC, tunneling between the edge states generates a non-equilibrium electron distribution. The form of this distribution in energy and its evolution as a function of distance downstream from the QPC are probed by monitoring the tunneling current from a point on the edge, through a quantum dot that has an isolated level of controllable energy. Close to the QPC, the measured distribution has two steps, reflecting the different energies of Fermi steps in each of the incident edges. With increasing distance from the QPC, the distribution relaxes to a single, broad step. The theoretical challenge presented by these observations is to understand and model this relaxation process.The relationship between these edge state experiments and other recent work on many-body quantum dynamics far from equilibrium has several aspects worth emphasising. First, in the context of QH edge states, these are the most recent of a series of striking observations of non-equilibrium effects in interferometers [6] and in thermal transport [7]. They are also the equivalent for a ballistic system of earlier studies [8] of local distributions in diffusive wires. Second, the measurements stand apart from earlier theory [13] and experiment [14] on non-equilibrium transport between fractional QH edge states, because they probe local distribution functions, rather than the global non-linear current-voltage characteristic. Third, and more broadly, the system studied is different in important ways from quantum impurity problems [9][10][11][12], as there is no impurity degree of freedom and interactions ...

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confidence: 99%

Relaxation in Driven Integer Quantum Hall Edge States

Kovrizhin

Chalker

2012

Phys. Rev. Lett.

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“…Experiments on the interferometer have revealed nontrivial interaction-induced dephasing effects such as the so-called lobe structure 2-6 of the interference visibility under nonequilibrium. Different aspects of the dephasing effects have been theoretically studied in various ways of a bosonization approach, [8][9][10][11][12][13][14][15] a shot-noise argument, 11,16 an interedge interaction model, 10,11 and an exactly solvable model. 13,14 Whereas most previous studies dealt with the dephasing effects in the case that electrons are continuously injected, by dc bias voltage, into the Mach-Zehnder interferometer, here we examine a simpler problem where a single isolated electron wave packet is injected to the interferometer.…”

Section: Introductionmentioning

confidence: 99%

Visibility recovery by strong interaction in an electronic Mach-Zehnder interferometer

Lee

Sim

2012

Phys. Rev. B

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We study the evolution of a single-electron packet of Lorentzian shape along an edge of the integer quantum Hall regime or in a Mach-Zehnder interferometer, considering a capacitive Coulomb interaction and using a bosonization approach. When the packet propagates along a chiral quantum Hall edge, we find that its electron density profile becomes more distorted from Lorentzian due to the generation of electron-hole excitations, as the interaction strength increases yet stays in a weak-interaction regime. However, as the interaction strength becomes larger and enters a strong-interaction regime, the distortion becomes weaker and eventually the Lorentzian packet shape is recovered. The recovery of the packet shape leads to an interesting feature of the interference visibility of the symmetric Mach-Zehnder interferometer whose two arms have the same interaction strength. As the interaction strength increases, the visibility decreases from the maximum value in the weak-interaction regime and then increases to the maximum value in the strong-interaction regime. We argue that this counterintuitive result also occurs under other types of interactions.

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“…In these circuits, mixing between edge states has so far been achieved using beam splitters (BSs) based on quantum point contacts (QPCs). Fascinating but still puzzling phenomena have been highlighted in these devices 11 , in particular in relation to finite-bias visibility and edge reconstruction phenomena. While the QPC approach has proven successful, the intrinsic geometry of this BS implementation makes it necessary to adopt non-simply connected 2D electron gases (EGs) and limits the complexity and size of the achievable 2D QH circuits.…”

Section: Introductionmentioning

confidence: 99%

Coherent edge mixing and interferometry in quantum Hall bilayers

et al. 2013

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We discuss the implementation of a beam splitter for electron waves in a quantum Hall bilayer. Our architecture exploits inter-layer tunneling to mix edge states belonging to different layers. We discuss the basic working principle of the proposed coherent edge mixer, possible interferometric implementations based on existing semiconductor-heterojunction technologies, and advantages with respect to canonical quantum Hall interferometers based on quantum point contacts.

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Theory of the nonequilibrium electronic Mach-Zehnder interferometer

Cited by 22 publications

References 66 publications

Relaxation in Driven Integer Quantum Hall Edge States

Relaxation in Driven Integer Quantum Hall Edge States

Visibility recovery by strong interaction in an electronic Mach-Zehnder interferometer

Coherent edge mixing and interferometry in quantum Hall bilayers

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