Local thermometry of neutral modes on the quantum Hall edge

Abstract

Summary: Quantum dots, used as local thermometers, detect upstream heat transport in a ν = 2/3 fractional quantum Hall edge state, even when the state is carrying no net charge. AbstractA system of electrons in two dimensions and strong magnetic fields can be tuned to create a gapped 2D system with one dimensional channels along the edge. Interactions among these edge modes can lead to independent transport of charge and heat, even in opposite directions. Measuring the chirality and transport properties of these charge and heat modes can reveal otherwise hidden structure in the edge. Here, we heat the outer edge of such a quantum Hall system using a quantum point contact. By placing quantum dots upstream and downstream along the edge of the heater, we can measure both the chemical potential and temperature of that edge to study charge and heat transport, respectively. We find that charge is transported exclusively downstream, but heat can be transported upstream when the edge has additional structure related to fractional quantum Hall physics.When a two-dimensional electron system (2DES) is subject to a strong perpendicular magnetic field and tuned such that the ratio of electrons to magnetic flux quanta in the system (ν) is near certain integer or fractional values, the bulk of the system develops a gap due to either quantization of kinetic energy (the integer quantum Hall, or IQH, effect) or strong correlations arising from non-perturbative Coulomb interactions (the fractional quantum Hall, or FQH, effect) [1]. While the bulk (2D) is gapped and incompressible, the edge (1D) of the system contains compressible regions with gapless excitations that carry charge chirally around the system, in a direction determined by the external magnetic field. Compressible edge states have gained more attention recently due to their ability to serve as a bus for quasiparticles that exist in exotic FQH phases [2,3]. These edges, however, can have considerable internal structure that is not apparent from bulk transport measurements.The spatial structure of edges is dictated by the interplay between the external confining potential which defines the edge, an additional harmonic confinement from the magnetic field, and Coulomb interactions. It was predicted [4] and verified [5, 6, 7] that for a smooth, topgate-defined confining potential, it is energetically favorable for the electron density to redistribute slightly to create alternating compressible and incompressible strips. This has the effect of spatially separating edges corresponding to different filling factors. Such an effect is not present in sharper edges [8].Perhaps more surprising than this spatial structure is the possibility of modes that carry energy (or heat) upstream, even as the magnetic field carries the injected charge downstream. The edge of the ν = 2/3 FQH state was originally predicted to consist of a ν = 1 edge of electrons going downstream with a ν = 1/3 edge of holes going upstream [9,10] would be allowed to travel diffusively upstream and downstream, l...

Edge reconstruction in fractional quantum Hall states

“…In that model, depicted in Fig. 1a III, the inner three edge channels were expected to renormalize to a single downstream charge mode with conductance 1 On the experimental front, recent observations of upstream neutral modes [6,7,14,15,16] supported the KFP model of the = 2 3 state [5]. However, Bid et al [17], while studying partitioning of the downstream charge channel for = 2 3 in a quantum point contact (QPC), ) with strong noise.…”

Extracting net current from an upstream neutral mode in the fractional quantum Hall regime

“…These modes, which carry energy without net charge [2][3][4][5][6][7][8][9][10] , are at the focus of recent experimental and theoretical studies, and are encouraged by the advent of the search for Majorana quasiparticles 11,12 . Certain fractional states, dubbed as holeconjugate states 13,14 , with the most prominent one v ¼ 2/3, support reconstructed chiral edge modes, which due to interaction and disorder, give birth to counter propagating neutral modes [2][3][4] .…”

“…In a recent work by Gross et al 7 , a few new features of these modes were reported: first, that a standard (non-ideal) ohmic contact can detect neutral modes, very much like a QPC; second, injecting charge onto a QPC also excites upstream neutral modes; and third, a simple model of classical heating was found to explain much of the observed data. Moreover, quantum dots (QDs) were used as thermometers to detect temperature increase due to neutral modes 8,9 . The results, shown in these precursory works, support energy propagation via upstream chiral neutral modes, and exclude transport of lattice phonons.…”

Fluctuation theorem for heat transport probed by a thermal probe electrode

“…[3][4][5] Recent efforts are focused on thermoelectric transport in coherent quantumconductors coupled to local vibrational modes, 6 or to temperature and/or potential-probing electrodes, 7 in the linear-response regime and also beyond it. [8][9][10] An intriguing question raised in these investigations is the symmetry of the various transport coefficients with respect to time-reversal breaking, in particular under the effect of inelastic interactions induced by probing electrodes.…”