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

Abstract

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.

Pump-probe nuclear spin relaxation study of the quantum Hall ferromagnet at filling factor ν = 2

“…The quantum Hall ferromagnet (QHF) formed at two energetically-degenerate spin-resolved Landau levels (LLs) in a two-dimensional electron gas (2DEG) has provided an ideal system for understanding itinerant electron ferromagnetism, spin interactions, and domain dynamics [1][2][3][4][5][6][7][8][9][10][11][12][13]. In particular, a resistively detected nuclear magnetic resonance (RDNMR) technique developed in the QHF of GaAs 2DEGs at filling factor ν=2/ 3 (corresponding to a composite-fermion (CF) filling factor ν CF =2) has been widely used to investigate the dynamic nuclear polarization (DNP) in semiconductors [14,15], to coherently control the nuclear spins in the 2DEG [16], and to discover exotic electron phases in quantum Hall systems [17][18][19].…”

Scanning nuclear resonance imaging of a hyperfine-coupled quantum Hall system

“…However, to fully understand its microscopic origins, there is a strong demand for direct observation of the spin distribution. A recent imaging technique based on scanning photoluminescence microscopy within the particular QH v = 2/3 domain system visualised the electron spin distributions of the domains 15 , the NR response of which provided spatial information of the DNP 16 . The optical measurement, however, provides the influence of photo-excited carriers and has a limited spatial resolution.…”

Role of chiral quantum Hall edge states in nuclear spin polarization

“…Figure 2d depicts the domain structures of QHF in the Hall bar, where the edge states become part of an array of domains. It is seen that the two edges of the sample are connected by channels along domain boundaries, which is supported by optically detected magnetic resonance imaging of the ν =2/3 QHF of GaAs 2DEGs20. The edge transport will affect the bulk mode of the Hall bar as follows: the chiral nature of edge states determines that electrons feeding into the sample from one side (for example, point A) either go back to the same side (point C) by travelling along the DW without spin flip or reach the other side (point B) by passing across the DW with spin flip36.…”

“…However, the detailed mechanism is still poorly understood. In particular, the above-mentioned studies of the ν =2/3 QHF are performed on the Hall bar where contributions from both bulk and edge states to DNP16171819 coexist and also the edge physics at ν =2/3 remains unclear20, which may complicate its interpretation.…”