Nucleation of merons in double quantum dots with spontaneous interlayer phase coherence

We have investigated how merons nucleate in the spontaneous interlayer phase coherent state of double quantum dots when a distortion with a reflection symmetry is present in the lateral confinement potential. When the lateral confinement strength is large enough merons with a negative topological charge nucleate in the ground state. For weaker values of the lateral confinement strength both density depletions and positively charged merons are present. These density depletions form an ordered structure. When the strength of the distortion increases some of these density depletions can transform into merons. In the presence of merons the resulting electron density in one of the layers is the mirror image of the electron density of the other layer. Even when a random disorder potential is present both density depletions and merons can coexist.

Figure 1

Spin texture (a) and total electron density (b) of the MDD in parabolic double quantum dots. Length unit is a magnetic length $\ell$ and the electron density unit is $1∕{\ell }^2$. In the spin texture the arrows are projections of $\vec{\tau }$ on the $xy$ plane. The area with maximum positive (negative) ${\tau }_z$ is white (black) (${\tau }_z=2s_z∕\hslash$ is dimensionless). In the right column the white area has the higher density than the black one. Here $N=26$ and $\gamma =0.085$.

Figure 2

Displays how the spin texture changes as the strength of the lateral distortion with the center at the coordinate $(-5,5)\ell$ increases. (The center is indicated by a cross in the figure.) Results in (a), (b), and (c) correspond, respectively, to $(u_{1s},u_{1d})=(1.2,0.2),(1.5,0.25),(1.8,0.3)(e^2∕\epsilon \ell )$. Here $N=26$, $\gamma =0.085$, and $a=3\ell$ are used. The total electron density corresponding to (c) is displayed in (d).

Figure 3

Spin textures (a) and (c) and total electron densities (b) and (c) of reconstructed MDDs at $\gamma =0.070$ when a lateral distortion is present at the coordinate $(-5,5)\ell$. The strengths of the distortion are $(u_{1s},u_{1d})=(0.24,0.04)(e^2∕\epsilon \ell )$ in (a) and (b), $(u_{1s},u_{1d})=(0.42,0.07)(e^2∕\epsilon \ell )$ in (c) and (d). Here $N=26$, $\gamma =0.070$, and $a=3\ell$.

Figure 4

Spin textures (a) and (c) and total electron densities (b) and (d) of reconstructed MDDs at $\gamma =0.066$ when a lateral distortion is present at the coordinate $(-5,5)\ell$. The following parameters are used: $(u_{1s},u_{1d})=(0.24,0.04)(e^2∕\epsilon \ell )$ in (a) and (b), $(u_{1s},u_{1d})=(0.42,0.07)(e^2∕\epsilon \ell )$ in (c) and (d), $N=26$, and $a=3\ell$.

Figure 5

Electron densities in each dot for the case shown in 4(c).

Figure 6

Spin texture (a), total electron density (b), and electron densities in the left (c) and right (d) dots when random impurities are present. The following parameters are chosen: $(u_{1s},u_{1d})=(1.728\times {10}^{-1},8.64\times {10}^{-2})(e^2∕\epsilon \ell )$, $(u_{2s},u_{2d})=(2.94\times {10}^{-2},1.47\times {10}^{-2})(e^2∕\epsilon \ell )$, $(u_{3s},u_{3d})=(-9.78\times {10}^{-2},-4.89\times {10}^{-2})(e^2∕\epsilon \ell )$, $(u_{4s},u_{4d})=(3.654\times {10}^{-1},1.827\times {10}^{-1})(e^2∕\epsilon \ell )$, $(u_{5s},u_{5d})=(-6.90\times {10}^{-2},-3.45\times {10}^{-2})(e^2∕\epsilon \ell )$, $N=26$, $\gamma =0.066$, and $a=5\ell$.

Figure 7

Occupation numbers for the case shown in Fig. 6.