Optically Imaged Striped Domains of Nonequilibrium Electronic and Nuclear Spins in a Fractional Quantum Hall Liquid

Using photoluminescence microscopy enhanced by magnetic resonance, we visualize in real space both electron and nuclear polarization occurring in nonequilibrium fraction quantum Hall (FQH) liquids. We observe stripelike domain regions comprising FQH excited states which discretely form when the FQH liquid is excited by a source-drain current. These regions are deformable and give rise to bidirectionally polarized nuclear spins as spin-resolved electrons flow across their boundaries.

Figure 1

(a) Longitudinal resistance $R_{xx}$ as function of $\nu$: green, $I_{\mathrm{SD}}=2$; blue and red, 120 nA. $\nu$ is scanned over 0.5–1.02 with $3.15\times {10}^{-4}/\mathrm{s}$ (green and blue) and $6.18\times {10}^{-6}/\mathrm{s}$ (red) scan speed. (b)–(f) $38\times 68–\mu {\mathrm{m}}^2$ spatial images showing PL intensity of charged exciton singlet peak (PL intensity), at $\nu =0.660$ with $I_{\mathrm{SD}}$ (Hall voltage $V_H=(3/2G_0)I_{\mathrm{SD}}$, with $G_0$ as quantized conductance) of (b) 0 (0), (c) 30 (1.16), (d) 60 (2.32), (e) 90 (3.48), and (f) 120 nA (4.65 meV). $B=B_C=6.8\mathrm{T}$, and excitation current frequency is 13 Hz throughout. $T\sim 60\mathrm{mK}$ throughout unless otherwise specified. (g) Energy diagram of singlet and triplet trions and their optical transitions for PL. (h) Example $\mu \text{−}\mathrm{PL}$ spectrum. (i) Schematic of observed images. The microscopic internal structure of the $2/3$ edge state is not shown here, because it remains unclear [22, 31].

Figure 2

(a)–(e) $38\times 68\text{−}\mu {\mathrm{m}}^2$ PL-intensity spatial images at $\nu$ of (a) 0.647, (b) 0.653, (c) 0.660, (d) 0.666, and (e) 0.672, with $I_{\mathrm{SD}}=120\mathrm{nA}$. (f) Critical current at which first stripe becomes visible ($I_C$) as function of $\nu$. Error in $I_C$ determined by step size of applied current. Error in $\nu$ calculated from uncertainty in electron density. Right $y$ axis: potential difference between sample edges, $e{V}_H$.

Figure 3

(a) $\mathrm{OD}\text{−}\mu \text{−}\mathrm{NMR}$ spectra. (b) $15\times 7.5\text{−}\mu {\mathrm{m}}^2$ OD-MRI. PL-intensity spatial images under (c) off-resonant (49.84 MHz) and (d) on-resonant rf (49.7717 MHz). Data were obtained at $\nu =0.660$ and $T=\sim 80\mathrm{mK}$. The rf power at the generator for both methods was $-3.8\mathrm{dBm}$.

Figure 4

Pump-probe images and $\mu \text{−}\mathrm{PL}$ intensity time evolution. (a)–(c) $15\times 7.5\text{−}\mu {\mathrm{m}}^2$ PL-intensity spatial images at (a) $\nu =0.660$ during pumping, $I_{\mathrm{SD}}=120\mathrm{nA}$, (b) $\nu =0.5$ 3 s after pumping, and (c) $\nu =0.5$, $I_{\mathrm{SD}}=0\mathrm{nA}$. (d) PL intensity from two fixed points at (red) nonmagnetic and (blue) ferromagnetic phases. $t=0$ represents the time when $\nu$, $I_{\mathrm{SD}}$ were adjusted from pumping (0.660, 120 nA) to probing (0.5, 0 nA) conditions. Each data point in panel (d) was fitted using $a\exp (t/T_1)+b$, where $a=-2.7138$ (1.2165), $T_1=2.059$ (1.127) min, and $b=5.2096$ (4.9388) for the ferromagnetic (nonmagnetic) phase.