Fluctuation-dissipation theorem for chiral systems in nonequilibrium steady states

Wang, Chenjie; Feldman, D. E.

doi:10.1103/physrevb.84.235315

Cited by 22 publications

(23 citation statements)

References 21 publications

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“…Other methods that could show unique signatures of Abelian and nonAbelian states include thermopower measurements 28,37 and Mach-Zehnder interferometry 18,52,[58][59][60][61][62][63][64] . The nonequilibrium fluctuation-dissipation theorem 65,66 would provide an independent test of the existence of upstream modes.…”

Section: Discussionmentioning

confidence: 99%

Influence of device geometry on tunneling in theν=52quantum Hall liquid

Yang

Feldman

2013

Phys. Rev. B

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Two recent experiments [I. P. Radu et al., Science 320, 899 (2008) and X. Lin et al., Phys. Rev. B 85, 165321 (2012)] measured the temperature and voltage dependence of the quasiparticle tunneling through a quantum point contact in the ν = 5/2 quantum Hall liquid. The results led to conflicting conclusions about the nature of the quantum Hall state. In this paper, we show that the conflict can be resolved by recognizing different geometries of the devices in the experiments. We argue that in some of those geometries there is significant unscreened electrostatic interaction between the segments of the quantum Hall edge on the opposite sides of the point contact. Coulomb interaction affects the tunneling current. We compare experimental results with theoretical predictions for the Pfaffian, SU (2)2, 331 and K = 8 states and their particle-hole conjugates. After Coulomb corrections are taken into account, measurements in all geometries agree with the spin-polarized and spin-unpolarized Halperin 331 states.

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Section: Discussionmentioning

confidence: 99%

Influence of device geometry on tunneling in theν=52quantum Hall liquid

Yang

Feldman

2013

Phys. Rev. B

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“…The result for the chiral Luttinger liquid model follows from its technically difficult exact solution [7]. A more general result [8] was obtained with a simpler but still rather subtle method, generalizing the equilibrium Kubo formalism. In this paper we use a completely different trick based on fluctuation relations [9,10].…”

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confidence: 97%

“…The simplest relation [5][6][7] of such sort was derived for the exactly-solvable chiral Luttinger liquid model with a single impurity. We have recently found an FDT-type relation between the current noise and nonlinear conductance in a general chiral system in a non-equilibrium steady state in a three-terminal geometry [8]. In this paper we prove a much more general result: we express nonlinear responses of the currents of various conserved quantities, such as the electric current and thermal current, in terms of the second and higher order cumulants of the statistical distributions of the currents in a nonequilibrium steady state in a multi-terminal system with an arbitrary number of terminals.…”

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confidence: 99%

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Chirality, Causality, and Fluctuation-Dissipation Theorems in Nonequilibrium Steady States

Wang

Feldman

2013

Phys. Rev. Lett.

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Edges of some quantum Hall liquids and a number of other systems exhibit chiral transport: excitations can propagate in one direction only, e.g., clockwise. We derive a family of fluctuationdissipation relations in non-equilibrium steady states of such chiral systems. The theorems connect nonlinear response with fluctuations far from thermal equilibrium and hold only in case of chiral transport. They can be used to test chiral or non-chiral character of the system. PACS numbers: 05.70. Ln, 05.40.Ca, 73.43.Cd According to the causality principle, past events influence the future but the future has no effect on the past. This principle has no general counterpart in terms of the spatial separation of events: consequences of some events can be felt in every point after a sufficient wait time. A spatial version of the causality principle emerges in low-energy effective theories of some many-body systems. The best known example is the integer quantum Hall effect (QHE): low-energy excitations are confined to the edges and can propagate only clockwise or counterclockwise [1]. This can lead to a situation in which earlier events affect only those future events that occur "downstream". Similar chiral transport is possible in a number of other systems: some fractional quantum Hall liquids [1], interfaces of topological insulators, superconductors and ferromagnets [2,3], surface states in 3D QHE and so on. The simplest example comes from the statistical mechanics models of traffic [4]: chiral transport is possible on a network of one-way roads as long as no traffic jams form.In this paper we explore consequences of the extended causality principle in chiral systems. Causality is crucial for linear response theory. One of its celebrated results is the fluctuation-dissipation theorem (FDT). We show that a family of generalized FDTs holds in chiral sys-(a) tems. While the usual FDT applies in thermal equilibrium only, our theorems are also valid in non-equilibrium steady states. The simplest relation [5][6][7] of such sort was derived for the exactly-solvable chiral Luttinger liquid model with a single impurity. We have recently found an FDT-type relation between the current noise and nonlinear conductance in a general chiral system in a non-equilibrium steady state in a three-terminal geometry [8]. In this paper we prove a much more general result: we express nonlinear responses of the currents of various conserved quantities, such as the electric current and thermal current, in terms of the second and higher order cumulants of the statistical distributions of the currents in a nonequilibrium steady state in a multi-terminal system with an arbitrary number of terminals. The generalization is achieved due to a much simpler approach. The result for the chiral Luttinger liquid model follows from its technically difficult exact solution [7]. A more general result [8] was obtained with a simpler but still rather subtle method, generalizing the equilibrium Kubo formalism. In this paper we use a completely different trick based o...

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“…24,33 The existence of an upstream neutral edge mode favors the 113 state and the anti-Pfaffian state over the 331 state and the Pfaffian state. However, more experimental effort based on a variety of methods [34][35][36][37][38][39] is needed before one can draw a definite conclusion about the existence of upstream mode. Thus, it is necessary to have an alternative approach which offers additional data to test the proposal of the 113 topological order.…”

Section: Introductionmentioning

confidence: 99%

Probing theν=52quantum Hall state with electronic Mach-Zehnder interferometry

Yang

2015

Phys. Rev. B

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It was recently pointed out that Halperin's 113 topological order explains the transport experiments in the quantum Hall liquid at filling factor ν = 5/2. The 113 order, however, cannot be easily distinguished from other likely topological orders at ν = 5/2 such as the non-Abelian Pfaffian and anti-Pfaffian states and the Abelian Halperin 331 state in Fabry-Perot interferometry. In this paper, we show that an electronic Mach-Zehnder interferometer provides a clear identification of these candidate ν = 5/2 states. Specifically, the I-V curve for the tunneling current through the interferometer is more asymmetric in the 113 state than in other ν = 5/2 states. Moreover, the Fano factor for the shot noise in the interferometer can reach 13.6 in the 113 state, much greater than the maximum Fano factors 3.2 in the Pfaffian and anti-Pfaffian states and 2.3 in the 331 state.

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Fluctuation-dissipation theorem for chiral systems in nonequilibrium steady states

Cited by 22 publications

References 21 publications

Influence of device geometry on tunneling in theν=52quantum Hall liquid

Influence of device geometry on tunneling in theν=52quantum Hall liquid

Chirality, Causality, and Fluctuation-Dissipation Theorems in Nonequilibrium Steady States

Probing theν=52quantum Hall state with electronic Mach-Zehnder interferometry

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