Aharonov-Bohm oscillations and electron gas transitions in hexagonal core-shell nanowires with an axial magnetic field

We use spin-density-functional theory within an envelope function approach to calculate electronic states in a GaAs/InAs core-shell nanowire pierced by an axial magnetic field. Our fully three-dimensional quantum modeling includes explicitly a description of the realistic cross section and composition of the sample, and the electrostatic field induced by external gates in two different device geometries: gate-all-around and back-gate. At low magnetic fields, we investigate Aharonov-Bohm oscillations and signatures therein of the discrete symmetry of the electronic system, and we critically analyze recent magnetoconductance observations. At high magnetic fields, we find that several charge and spin transitions occur. We discuss the origin of these transitions in terms of different localization and Coulomb regimes, and we predict their signatures in magnetoconductance experiments.

Figure 1

Schematics of a core-shell NW in the (a) gate-all-around and (b) back-gate device configurations.

Figure 2

(a) Magnetic spin-subbands (MSS) in the low-field regime. Red and blue dots indicate ↓- MSSs and ↑-MSSs, respectively. The horizontal black line is set at $E_F$. (b) Self-consistent electron density distribution, $n\left(\mathbf{r}\right)$, for the InAs/GaAs NW at $B=0$. (c) Spin-projected magnetoconductances $G_{\downarrow }$ (red) and $G_{\uparrow }$ (blue), and total magnetoconductance (black).

Figure 3

(a) Total magnetoconductance at selected gate-all-around voltages, $V_g$, as indicated by labels [the $V_g=0$ curve is the same as the black line in Fig. 2]. (b) MSSs at $V_g=-60\text{mV}$. (c) MSSs at $V_g=80\text{mV}$. Insets in (b) and (c) show the corresponding $n\left(\mathbf{r}\right)$.

Figure 4

(a) Same as in Fig. 3 but for a back-gate device. (b) MSSs at $V_g=-80\text{mV}$, (c) MSSs at $V_g=200\text{mV}$.

Figure 5

(a) MSSs up to complete charge depletion. Blue (red) dots are used for ↑-MSSs (↓-MSSs). The horizontal line indicates the position of $E_F$. Vertical dashed arrows indicate fields at which different spin/charge transitions occur (see text). (b)–(f) Self-consistent electron density distributions $n\left(\mathbf{r}\right)$ at selected magnetic fields.

Figure 6

(a) Total density $\widehat{n}$ (black lines) and spin-projected densities ${\overline{n}}_{\uparrow }$ (blue lines) and ${\overline{n}}_{\downarrow }$ (red lines) as a function of the field intensity $B$. Vertical dashed lines illustrate the transition fields in Fig. 5. (b) Spin polarization as a function of the magnetic field. Inset: spin susceptibility.

Figure 7

(a) Total free energy per electron and (b) Hartree (solid), exchange (dashed), and correlation (dotted) energies per electron as a function of the field $B$. Vertical dashed lines indicate the transition fields in Fig. 5.

Figure 8

Noninteracting MSS edges with respect to the InAs conduction-band edge. Blue (red) dots are used for ↑-MSSs (↓-MSSs).

Figure 9

(a) Total magnetoconductance $G=G_{\uparrow }+G_{\downarrow }$ (black) and spin-resolved magnetoconductances, $G_{\uparrow }$ (blue) and $G_{\downarrow }$ (red). (b) Total magnetoresistance. Vertical dashed lines indicate the transition fields in Fig. 5.