Interedge Strong-to-Weak Scattering Evolution at a Constriction in the Fractional Quantum Hall Regime

Abstract

Gate-voltage control of interedge tunneling at a split-gate constriction in the fractional quantum Hall regime is reported. Quantitative agreement with the behavior predicted for out-of-equilibrium quasiparticle transport between chiral Luttinger liquids is shown at low temperatures at specific values of the backscattering strength. When the latter is lowered by changing the gate voltage, the zero-bias peak of the tunneling conductance evolves into a minimum, and a nonlinear quasiholelike characteristic emerges. Our analysis emphasizes the role of the local filling factor in the split-gate constriction region.

Particle-Hole Symmetric Luttinger Liquids in a Quantum Hall Circuit

“…When g = ν = 1, the edge channel should behave like a Fermi liquid and linear tunneling is expected. The observed non-linear behavior indicates that the relevant interaction g is not equal to 1 but is determined by the SG voltage, confirming similar results obtained in the fractional QH regime [12,16]. We now show that the effective interaction is determined by the SG voltage through the creation of a region in which a fractional QH state emerges.…”

“…These edge excitations at the fractional filling factor ν = 1/m, with m odd integer, form a onedimensional liquid that was predicted to be equivalent to a CLL [2] with interaction parameter g = ν [3, 4, 5]. These predictions were tested by a large number of experiments [6,7,8,9,10,11,12] even if many open issues remain, in particular for the case of the edge states at ν = 1/m.A split-gate (SG) technique [13] can be exploited to define a nanofabricated constriction in order to induce a controllable scattering between counter-propagating edge channels that are locally brought in close proximity (see Fig.1a). The constriction thus realizes an artificial impurity and can be used to test one of the most significant manifestations of CLL behavior: the complete suppression of the (low-temperature, low-bias) transmission through the impurity and its related power-law behavior [3,4,5].…”

“…These edge excitations at the fractional filling factor ν = 1/m, with m odd integer, form a onedimensional liquid that was predicted to be equivalent to a CLL [2] with interaction parameter g = ν [3, 4, 5]. These predictions were tested by a large number of experiments [6,7,8,9,10,11,12] even if many open issues remain, in particular for the case of the edge states at ν = 1/m.…”

Imaging Fractional Incompressible Stripes in Integer Quantum Hall Systems

“…Despite a number of experimental and theoretical studies, the issue of fractional order within integer QH systems is still an open question. A number of experiments showed clear indications of fractional phases in constrictions, either in terms of fractional quantization of conductance [2,3] or Luttinger-like non-linear features [6][7][8][9], although even the simple problem of how an ideal integer edge can "branch" and give rise to fractional edges remains unclear. On the other hand, recent interferometry experiments [10] and out-of-equilibrium energy spectroscopy data [11] indicate that an integer edge can behave as a monolithic object and shows no clear evidence of an inner structure.…”

AC conductivity of a quantum Hall line junction

“…A LJ is formed by using a gate voltage to create a narrow barrier which divides a fractional QH state such that there are two chiral edges flowing in opposite directions (counter propagating) on the two sides of the barrier [13,14,15,16,17]. For a QH system corresponding to a filling fraction which is the inverse of an odd integer such as 1, 3, 5, · · · , the edge consists of a single mode which can be described by a chiral bosonic theory [18].…”