### Abstract

Using a recently developed crystal growth technique (see Fig. 1), we have succeeded in creating a two-dimensional (2D) electron system that is bent at an atomically sharp angle of 90° 1. Naming the two 2D systems after their substrate (S) and precleave (P) facets, we can measure their densities n
_{s}
and n
_{p}
. In the presence of a tilted magnetic field, this system realizes an abrupt junction between two quantum Hall effect (QH) systems with arbitrary filling factors
^{2}
v
_{s}
= n
_{s}
h/eBcos(θ) and v
_{p}
= n
_{p}
h/eBsin(θ). When the two filling factors are equal v
_{s}
= v
_{p}
, the corner junction represents a multimode wire with the maximum number of forward & reverse moving modes equalling the filling factor v plus two spin degenerate modes from corner-accumulation wire. The conductance of this bent QH system dI/dV(V) or G(T) can be characterized with four-point measurements. As long as the excitation energy (V or T, respectively) is smaller than the QH gap energy, there is no scattering of electrons away from the wire system to the 2D bulk and the transport is truly one-dimensional. The devices studied here are from 0.4 - 4 mm long with ohmic contacts alloyed on both facets away from the junction. The resulting ID wire at the corner junction has exhibited metallic, insulating, and critical phases depending on filling factor, with all ID conductances of order 0.02e
^{2}
/A or below. The insulating ID behavior occurs for v = 1 and v = 2, and is manifest in a vanishing ID conductance at low temperatures and low dc voltage biases. Metallic ID behavior occurs for v = 1/3 where the conductance rises with decreasing temperature and the dc bias shows a large zero-bias peak in the differential conductivity. The so-called critical behavior has only weak temperature dependence and a weak zerobias dip in the dc bias voltage dependence. The conductance G at v = 3 and v = 4 goes inversely with the wire length L indicating that scattering is distributed equally along the wire length. These observations can be partly explained with Hartree calculations of the bent quantum Hall junction. Low magnetic fields (y = 3 and 4) are expected to manifest a multimode wire, which provides a basis for understanding the critical phase. Higher magnetic fields (v = 1 and 2) are expected to open up a gap in the ID energy spectrum at the corner, resulting in the experimentally observed insulating phase. Alternatively, disorder may also explain the ID insulating behavior via scaling theory of localization. The highest magnetic fields for the fractional state v = 1/3 show the remarkable metallic phase which might be explained in terms of an antiwire between counterpropagating v = 1/3 Luttinger liquid edges which are randomly coupled by electron back-scattering events
^{3}
.

Original language | English (US) |
---|---|

Pages (from-to) | 1207-1208 |

Number of pages | 2 |

Journal | International Journal of Modern Physics B |

Volume | 21 |

Issue number | 8-9 |

State | Published - Apr 10 2007 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Condensed Matter Physics

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## Cite this

*International Journal of Modern Physics B*,

*21*(8-9), 1207-1208.