Effects of electron interactions at crossings of Zeeman-split subbands in quantum wires

Recent experimental studies of Zeeman-split one-dimensional subbands in ballistic quantum wires in an in-plane magnetic field show that additional nonquantized conductance structures occur as subbands cross at low electron densities [A. C. Graham et al., Phys. Rev.Lett. 91, 136404 (2003)]. These structures are called 0.7 analogs. We analyze the experimental transconductance data within the Kohn-Sham spin-density-functional method, including exchange and correlation effects for an infinite split-gate quantum wire in a parallel, in-plane magnetic field $B_{\parallel }$. Energy levels are found to rearrange abruptly as they cross due to polarization effects driven by exchange and Coulomb interactions. Experimental qualitative features are explained well by this model.

Figure 1

Typical gray scale of experimental transconductance data $dG∕dV$ at 50 mK as a function of gate voltage $V$ in volts and magnetic field $B_{\Vert }$ in T (adapted from Ref. 24). The structures at ${\alpha }_1,{\alpha }_2,{\beta }_1\mathrm{\dots }$ are referred to as 0.7 conduction analogs. The splitting at ${\alpha }_0$ is the usual low/zero field 0.7 conduction anomaly (Ref. 1).

Figure 2

(Color online) Calculated Zeeman-split sublevels in meV as function a parallel magnetic field $B_{\Vert }$ in Tesla for noninteracting electrons in a parabolic well with $\hslash {\omega }_y=1.85$ and $\hslash {\omega }_z=15\mathrm{meV}$, and a $g$-factor of 1.9. The GaAs effective mass is $m^{*}∕m_e=0.067$.

Figure 3

Schematic picture of the split gate wire used in the modeling. There is an undoped GaAs cap layer (24 nm) followed by a doped AlGaAs layer (36 nm, doping density ${\rho }_D=6\times {10}^{17}{\mathrm{cm}}^{-3}$), and a spacer layer of AlGaAs (10 nm). The electron gas resides at the interface between the GaAs substrate and the spacer layer; $z_0=70\mathrm{nm}$ is the distance to the metallic gate. The electron density is controlled by an applied voltage $V$ between the gate and the substrate. The width $w$ of the gate opening is 700 nm.

Figure 4

(Color online) Onset of subband fillings as function of magnetic field $B_{\Vert }$ and gate voltage $V$ in the Hartree approximation.

Figure 5

(Color online) Onset of subband fillings as function of magnetic field $B_{\Vert }$ and gate voltage $V$ according to the spin-dependent Kohn-Sham equations with exchange and correlation included.

Figure 6

(Color online) Electron density corresponding to Fig. 5 as function of magnetic field $B_{\Vert }$ and gate voltage $V$. Curves show the occupation onset of the different Zeeman-split subbands.