Abstract:It is well established that density reconstruction at the edge of a two-dimensional electron gas takes place for hole-conjugate states in the fractional quantum Hall effect (such as v=2/3, 3/5, etc.). Such reconstruction leads, after equilibration between counterpropagating edge channels, to a downstream chiral current edge mode accompanied by upstream chiral neutral modes (carrying energy without net charge). Short equilibration length prevented thus far observation of the counterpropagating current channels-… Show more
“…This conclusion, however, seems to be at odds with the presence of QH plateaus (Fig. S5b), since no conductance quantization is expected in absence of channel equilibration [6,21,37,[45][46][47]. The above observation that the inner nontopological channels "cut" the corners and protrusions can resolve the puzzle by noting that the ohmic contacts (and voltage contacts in particular, Figs.…”
Section: Si6 Movie M3 -Plunger Gate Dependencementioning
Topology is a powerful recent concept asserting that quantum states could be globally protected against local perturbations [1,2]. Dissipationless topologically protected states are thus of major fundamental interest as well as of practical importance in metrology and quantum information technology. Although topological protection can be robust theoretically, in realistic devices it is often fragile against various dissipative mechanisms, which are difficult to probe directly because of their microscopic origins. By utilizing scanning nanothermometry [3], we visualize and investigate microscopic mechanisms undermining the apparent topological protection in the quantum Hall state in graphene. Our simultaneous nanoscale thermal and scanning gate microscopy shows that the dissipation is governed by crosstalk between counterpropagating pairs of downstream and upstream channels that appear at graphene boundaries because of edge reconstruction. Instead of local Joule heating, however, the dissipation mechanism comprises two distinct and spatially separated processes. The work generating process that we image directly and which involves elastic tunneling of charge carriers between the quantum channels, determines the transport properties but does not generate local heat. The independently visualized heat and entropy generation process, in contrast, occurs nonlocally upon inelastic resonant scattering off single atomic defects at graphene edges, while not affecting the transport. Our findings offer a crucial insight into the mechanisms concealing the true topological protection and suggest venues for engineering more robust quantum states for device applications. (E.Z.) 2 In recent years, major progress has been made in identifying new topological states of matter [1,2] but the extent to which the topological protection is manifested in realistic systems and the microscopic mechanisms leading to its apparent breakdown remain poorly understood. The quantum Hall (QH) effect is a prime example of a topologically protected state exhibiting quantized dissipationless electron transport. While an extremely high degree of conductance quantization has been achieved in engineered systems in GaAs and in graphene [4], QH devices commonly exhibit small but fundamentally important deviations from the ideal quantized conductance. Various mechanisms undermining the topological protection were explored, including imperfect contacts [5], current-induced breakdown [4], absence of edge equilibration [6], and edge reconstruction [7,8]. Nonetheless, how exactly the dissipation in the QH regime occurs on a microscopic level has eluded direct identification. Here we provide nanoscale imaging of the dissipation processes in the QH state in graphene and reveal the intricate mechanisms compromising the apparent global topological protection.A superconducting quantum interference device, SQUID-on-tip (SOT) [9] acting as nanothermometer (tSOT) with µK sensitivity [3] and effective diameter of ~50 nm was scanned ~50 nm above high-mobility hBN-encapsu...
“…This conclusion, however, seems to be at odds with the presence of QH plateaus (Fig. S5b), since no conductance quantization is expected in absence of channel equilibration [6,21,37,[45][46][47]. The above observation that the inner nontopological channels "cut" the corners and protrusions can resolve the puzzle by noting that the ohmic contacts (and voltage contacts in particular, Figs.…”
Section: Si6 Movie M3 -Plunger Gate Dependencementioning
Topology is a powerful recent concept asserting that quantum states could be globally protected against local perturbations [1,2]. Dissipationless topologically protected states are thus of major fundamental interest as well as of practical importance in metrology and quantum information technology. Although topological protection can be robust theoretically, in realistic devices it is often fragile against various dissipative mechanisms, which are difficult to probe directly because of their microscopic origins. By utilizing scanning nanothermometry [3], we visualize and investigate microscopic mechanisms undermining the apparent topological protection in the quantum Hall state in graphene. Our simultaneous nanoscale thermal and scanning gate microscopy shows that the dissipation is governed by crosstalk between counterpropagating pairs of downstream and upstream channels that appear at graphene boundaries because of edge reconstruction. Instead of local Joule heating, however, the dissipation mechanism comprises two distinct and spatially separated processes. The work generating process that we image directly and which involves elastic tunneling of charge carriers between the quantum channels, determines the transport properties but does not generate local heat. The independently visualized heat and entropy generation process, in contrast, occurs nonlocally upon inelastic resonant scattering off single atomic defects at graphene edges, while not affecting the transport. Our findings offer a crucial insight into the mechanisms concealing the true topological protection and suggest venues for engineering more robust quantum states for device applications. (E.Z.) 2 In recent years, major progress has been made in identifying new topological states of matter [1,2] but the extent to which the topological protection is manifested in realistic systems and the microscopic mechanisms leading to its apparent breakdown remain poorly understood. The quantum Hall (QH) effect is a prime example of a topologically protected state exhibiting quantized dissipationless electron transport. While an extremely high degree of conductance quantization has been achieved in engineered systems in GaAs and in graphene [4], QH devices commonly exhibit small but fundamentally important deviations from the ideal quantized conductance. Various mechanisms undermining the topological protection were explored, including imperfect contacts [5], current-induced breakdown [4], absence of edge equilibration [6], and edge reconstruction [7,8]. Nonetheless, how exactly the dissipation in the QH regime occurs on a microscopic level has eluded direct identification. Here we provide nanoscale imaging of the dissipation processes in the QH state in graphene and reveal the intricate mechanisms compromising the apparent global topological protection.A superconducting quantum interference device, SQUID-on-tip (SOT) [9] acting as nanothermometer (tSOT) with µK sensitivity [3] and effective diameter of ~50 nm was scanned ~50 nm above high-mobility hBN-encapsu...
“…In practice, however, the measured conductance is always G 2T = 2 e 2 /3 h —supporting a single downstream v = 2/3 charge mode and an upstream neutral mode. The experimental ubiquity of the latter conductance value becomes even more remarkable if one recalls that the v = 2/3 edge profile may involve a more complicated edge reconstruction, as was shown theoretically 6,7 and experimentally 8–10 .Fig. 1The 2/3 hole-conjugate state and its synthetized form.…”
Topological edge-reconstruction occurs in hole-conjugate states of the fractional quantum Hall effect. The frequently studied filling factor,
ν
= 2/3, was originally proposed to harbor two counter-propagating modes: a downstream
v
= 1 and an upstream
v
= 1/3. However, charge equilibration between these two modes always led to an observed downstream
v
= 2/3 charge mode accompanied by an upstream neutral mode. Here, we present an approach to synthetize a
v
= 2/3 edge mode from its basic counter-propagating charged constituents, allowing a controlled equilibration between the two counter-propagating charge modes. This platform is based on a carefully designed double-quantum-well, which hosts two populated electronic sub-bands (lower and upper), with corresponding filling factors,
v
l
and
v
u
. By separating the 2D plane to two gated intersecting halves, each with different fillings, counter-propagating chiral modes can be formed along the intersection line. Equilibration between these modes can be controlled with the top gates’ voltage and the magnetic field.
“…Discussion.-We expect our noise classification to be applicable not only for conventional edge structures, but also for experimentally engineered edge structures with equal G but different G Q [8,[40][41][42]. For instance, an interface between ν = 4/3 and ν = 2/3 FQH states is expected to host two co-propagating 1/3 channels.…”
Electrical and thermal transport on a fractional quantum Hall edge are determined by topological quantities inherited by the corresponding bulk state. While electrical transport is the standard method for studying edges, thermal transport appears more challenging. Here, we show that the shot noise generated on the edge provides a fully electrical method to probe the edge structure. In the incoherent regime, the noise falls into three topologically distinct universality classes: charge transport is always ballistic while thermal transport is either ballistic, diffusive, or "anti-ballistic". Correspondingly, the noise either vanishes, decays algebraically or is constant up to exponentially small corrections in the edge length.Electrical and thermal transport on fractional quantum Hall (FQH) edges are quantized, reflecting the bulk topological order [1][2][3]. In particular, the electrical Hall and two-terminal conductances, G H and G,are determined by the bulk filling factor ν ∈ Q. Furthermore, the thermal Hall and two-terminal conductances, G Q H and G Q , arXiv:1906.05623v1 [cond-mat.mes-hall]
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