Distinguishing between non-abelian topological orders in a quantum Hall system

Dutta, Bivas; Yang, Wenmin; Melcer, Ron; Kundu, Hemanta Kumar; Heiblum, Moty; Umansky, V.; Oreg, Yuval; Stern, Ady; Mross, David F.

doi:10.1126/science.abg6116

Cited by 51 publications

(17 citation statements)

References 50 publications

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“…Nonetheless, a detailed understanding of thermal equilibration on the edge is crucial for interpreting [13][14][15][16][17] the recent observation 11 of κ 2T % 2:5κ 0 at filling ν ¼ 5 2 . As both the topological order and the extent of thermal equilibration are not known, two contradicting explanations were proposed: (i) full thermal equilibration 11 , which implies ν Q ¼ 2:5, indicating a topological order known as the PH-Pfaffian, which is further supported by a recent experiment 18 , (ii) partial thermal equilibration 15 and ν Q ¼ 1:5, indicating the anti-Pfaffian order, which is supported by numerical simulations 19,20 . Our present work paves the way towards the solution, by combining local thermometry with thermal conductance measurements to study thermal equilibration in Abelian fractional states, for which the topological order is known.…”

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confidence: 93%

Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale

et al. 2022

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Two-dimensional topological insulators, and in particular quantum Hall states, are characterized by an insulating bulk and a conducting edge. Fractional states may host both downstream (dictated by the magnetic field) and upstream propagating edge modes, which leads to complex transport behavior. Here, we combine two measurement techniques, local noise thermometry and thermal conductance, to study thermal properties of states with counter-propagating edge modes. We find that, while charge equilibration between counter-propagating edge modes is very fast, the equilibration of heat is extremely inefficient, leading to an almost ballistic heat transport over macroscopic distances. Moreover, we observe an emergent quantization of the heat conductance associated with a strong interaction fixed point of the edge modes. Such understanding of the thermal equilibration on edges with counter-propagating modes is a natural route towards extracting the topological order of the exotic 5/2 state.

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confidence: 93%

Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale

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“…The statistical phase of excitations is defined as that generated upon exchanging vertex operators at different locations. Applying (39) to the vertex operator (35) and using the commutation relations (31), we find…”

Section: A Tunneling Operators Quantum Statistics and Scaling Dimensionsmentioning

confidence: 99%

“…In recent decades, partition noise has successfully been used as a sensitive tool [2] to probe collective properties in systems of strongly correlated electrons. Examples include shot-noise measurements of fractional charges and nontrivial scaling dimensions in the fractional quantum Hall (FQH) [3][4][5][6][7][8][9][10] and Kondo [11][12][13][14][15][16][17][18] effects, observation of anyonic statistics via noise correlations [19][20][21][22][23][24][25][26][27][28][29][30][31], and detecting neutral modes in complex FQH states [32][33][34][35][36][37][38][39][40].…”

Section: Introduction a Background And Motivationmentioning

confidence: 99%

Does delta-$T$ noise probe quantum statistics?

Z¹,

Gornyi²,

Spånslätt³

2022

Preprint

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We study delta-T noise-excess charge noise at zero voltage but finite temperature bias-for weak tunneling in one-dimensional interacting systems. We show that the sign of the delta-T noise is generically determined by the nature of the dominating tunneling process. More specifically, the sign is governed by the leading charge-tunneling operator's scaling dimension. We clarify the relation between the sign of delta-T noise and the quantum exchange statistics of tunneling quasiparticles. We find that, for infinite systems hosting chiral channels with local interactions (e.g., quantum Hall or quantum spin Hall edges), when the delta-T noise is negative, the tunneling particles are boson-like, revealing their tendency towards bunching. However, the opposite is not true: Bosonlike particles do not necessarily produce negative delta-T noise. Importantly, the bosonic nature of particles generating the negative delta-T is not necessarily intrinsic, but can be induced by the interactions. This, in particular, implies that negative delta-T noise for tunneling between the edge states cannot serve as a smoking gun for detecting "intrinsic anyons". We also establish a connection between the delta-T noise and the temperature derivative of the Nyquist-Johnson (thermal) noise in interacting systems, both governed by the same scaling dimensions. As a demonstration of the above statements, we study tunneling between two interacting quantum spin Hall edges. With bosonization and renormalization-group techniques, we find that many-body interactions can generate negative delta-T noise for both direct tunneling through a point contact and in Kondo exchange tunneling via a localized spin. In both these setups, we show that the noise can become negative at sufficiently low temperatures, when interactions renormalize the tunneling to favor boson-like pair-tunneling of electrons rather than single-electron tunneling. Our findings show that delta-T noise can be used to probe the nature of collective excitations in interacting one-dimensional systems.

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“…This allows us to learn about the bulk by probing the edge of the system [39]. Comparatively speaking, interfaces between a pair of FQH states are explored much less [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. The physics of interfaces is much richer than simple edges [57].…”

Section: Introductionmentioning

confidence: 99%

Simple analog of the black-hole information paradox in quantum Hall interfaces

Ma,

Yang

2021

Preprint

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The black hole information paradox has been hotly debated for the last few decades, without full resolution. This makes it desirable to find analogs of this paradox in simple and experimentally accessible systems, whose resolutions may shed light on this long-standing and fundamental problem.Here we identify and resolve an apparent "information paradox" in a quantum Hall interface between the Halperin-331 and Pfaffian states. Information carried by pseudospin degree of freedom of the Abelian 331 quasiparticles gets scrambled when they cross the interface to enter non-Abelian Pfaffian state, and becomes inaccessible to local measurements; in this sense the Pfaffian region is an analog of black hole interior while the interface plays a role similar to its horizon. We demonstrate that the "lost" information gets recovered once the "black hole" evaporates and the quasiparticles return to the 331 region, albeit in a highly entangled form. Such recovery is quantified by the Page curve of the entropy carried by these quasiparticles, which are analogs of Hawking radiation.

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Distinguishing between non-abelian topological orders in a quantum Hall system

Cited by 51 publications

References 50 publications

Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale

Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale

Does delta-$T$ noise probe quantum statistics?

Simple analog of the black-hole information paradox in quantum Hall interfaces

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