Conductance anomalies in quantum wires

We study the conductance threshold of clean nearly straight quantum wires in which an electron is bound. We show that such a system exhibits spin-dependent conductance structures on the rising edge to the first conductance plateau, one near 0.25(2e 2 /h), related to a singlet resonance, and one near 0.75(2e 2 /h), related to a triplet resonance. As a quantitative example we solve exactly the scattering problem for two-electrons in a wire with planar geometry and a weak bulge. From the scattering matrix we determine conductance via the Landauer-Büttiker formalism. The conductance anomalies are robust and survive to temperatures of a few degrees. With increasing in-plane magnetic field the conductance exhibits a plateau at e 2 /h, consistent with recent experiments. Following the pioneering work in Refs. [1, 2] many groups have now observed conductance steps in various types of quantum wire. These first experiments were performed on gated two-dimensional electron gas (2DEG) structures, while similar behaviour of conductance are shown in " hard-confined " quantum wire structures, produced by cleaved edge over-growth [3], epitaxial growth on ridges [4], heteroepitaxial growth on " v "-groove surfaces [5] and most recently in GaAs/Al δ Ga 1−δ As narrow " v "-groove [6] and low-disorder [7] quantum wires. These experiments strongly support the idea of ballistic conductance in quantum wires and are in surprising agreement with now the standard Landauer-Büttiker formalism [8, 9] neglecting electron interactions [10]. However, there are certain anomalies, some of which are believed to be related to electron-electron interactions and appear to be spin-dependent. In particular, already in early experiments a structure is seen in the rising edge of the conductance curve [1], starting at around 0.7G 0 with G 0 = 2e 2 /h and merging with the first conductance plateau with increasing energy. Under increasing in-plane magnetic field, the structure moves down, eventually merging with a new conductance plateau at e 2 /h in very high fields [11, 12]. Theoretically this anomaly has not been adequately explained, despite several scenarios, including spin-polarised sub-bands [13], conductance suppression in a Luttinger liquid with repulsive interaction and disorder [14] or local spin-polarised density-functional theory [15]. Recently we have shown that these conductance anomalies near 0.7G 0 and 0.25G 0 are consistent with an electron being weakly bound in wires of circular cross section, giving rise to spin-dependent scattering resonances [16].