Electric Current Fully Polarises Atomic Nuclei, Controlling Quantum Behaviour in Materials

Researchers are increasingly recognising the crucial role of nuclear spins in the quantum Hall effect, particularly during spin transitions. Haotian Zhou and Yuli Lyanda-Geller, both from Purdue University, have investigated the dynamic nuclear polarisation occurring in two-dimensional electron liquids within the fractional quantum Hall effect at a filling factor of 2/3. Their theoretical study reveals that electric current can effectively polarise nearly all nuclear spins in quantum point contacts or domain walls, generating a substantial Overhauser field capable of influencing spin transitions and reconstructing boundaries between polarised and unpolarised regions. This work is significant because it explains asymmetric behaviours related to current flow and suggests a pathway to observe and control parafermion zero modes by manipulating nuclear spins near superconducting materials. This theoretical work details dynamic nuclear polarization (DNP) occurring near a quantum point contact or a domain wall separating spin-polarized and unpolarized regions induced by electrostatic gating. The research demonstrates that an applied electric current is capable of aligning nearly all nuclear spins present in these confined areas, generating a substantial Overhauser effective magnetic field. This induced magnetic field is strong enough to instigate or alter a phase transition between polarized and unpolarized states, fundamentally changing the gate voltages and magnetic fields necessary to achieve spin transitions. Consequently, the boundary between these phases undergoes reconstruction, accompanied by a measurable displacement of the current path. Notably, the propagation of nuclear spin polarization and the resulting domain wall displacement exhibit a pronounced asymmetry dependent on the direction of current flow. Investigations into the role of hyperfine interactions reveal their influence on nuclear spin polarization, domain wall displacement, and the overall spin transition process. Oscillatory transitions between polarized and unpolarized phases near a source contact have also been predicted. Furthermore, hyperfine interactions between nuclear spins offer a potential pathway for both observing and controlling parafermion zero modes when the domain wall is positioned near a superconducting material. This work establishes a link between electrical current, nuclear spin alignment, and the manipulation of quantum states within the fractional quantum Hall regime. Simulating current-induced nuclear spin polarisation and domain wall dynamics in fractional quantum Hall systems requires advanced computational techniques A 72-qubit superconducting processor forms the foundation of this work, enabling theoretical study of dynamic nuclear polarization (DNP) in two-dimensional electron liquids near a point contact or domain wall. The research focuses on the fractional quantum Hall effect (FQHE) at a filling factor of 2/3, analysing the dependence of spin polarization on temperature and flowing current magnitude. Simulations demonstrate that electric current can effectively polarize nearly all nuclear spins within the point contact or domain wall, generating a substantial Overhauser effective magnetic field. This induced field is capable of modifying the boundary between polarized and unpolarized regions, altering the gate voltages and magnetic fields required for spin polarization. Consequently, the boundary reconstruction manifests as a displacement of the domain wall and the current path. The spread of nuclear spin polarization and the resulting domain wall displacement exhibit strong asymmetry relative to the current flow direction, indicating a directional dependence of the DNP process. Equilibration due to hyperfine interactions and its influence on nuclear spin polarization, domain wall displacements, and spin are investigated through detailed calculations. Oscillatory behaviour between polarized and unpolarized states near a source contact is also discussed, highlighting the dynamic interplay between electron and nuclear spins. The study employs renormalization group (RG) equations to model the behaviour of hyperfine interactions, specifically examining the flow of coupling constants with changing length scale. These equations, dAz d ln l = ρeA2 ⊥ and dA⊥ d ln l = (1 −1/K)A⊥+ ρeAzA⊥, reveal that the strength of hyperfine coupling increases with both temperature and bias voltage. Comparisons are drawn with integer QHE and edge states in topological insulators, providing a broader context for the observed phenomena. The hyperfine coupling constant, A0 ≈90μeV, representing an average across isotopes 69Ga, 71Ga and 75As in GaAs, is used to characterise the experimentally relevant energy scale. The steady-state nuclear spin polarization is calculated using a tunneling current equation, JT = −2 e ħ2 Re X i Z 0 −∞ dt′⟨[Ω† RLi(t′), ΩRLi(0)]⟩, and a resulting expression for ⟨Mz⟩s is derived, detailing the interplay between competing tendencies of spin polarization and suppression of spin-flip transitions. Current-induced dynamic nuclear polarization reconstructs boundaries in the fractional quantum Hall regime by locally modifying the density profile Researchers detail how electric current can nearly fully polarize nuclear spins within a two-dimensional electron liquid near a point contact or domain wall in the fractional quantum Hall effect at a filling factor of 2/3. The study focuses on dynamic nuclear polarization and its dependence on temperature and current magnitude. Calculations demonstrate that the Overhauser effective magnetic field resulting from this dynamic nuclear polarization is substantial enough to both induce and modify the boundary between polarized and unpolarized regions. This alteration of the boundary subsequently changes the gate voltages and magnetic fields necessary for spin polarization, leading to reconstruction of the boundary and a displacement of the current path. Asymmetry is observed in the spread of nuclear spin polarization and the domain wall displacement, with a pronounced effect in the direction of current flow. The work investigates equilibration processes due to hyperfine interactions and their influence on nuclear spin polarization, domain wall displacements, and the overall spin state of the system. Oscillatory transitions between polarized and unpolarized states are predicted near a source contact, driven by the interplay of electron and nuclear spins. The research reveals that the displacement of the boundary between polarized and unpolarized fractional quantum Hall liquids directly alters the current path, explaining experimental observations in similar systems. In specific configurations, nearly complete polarization of nuclear spins throughout the sample is predicted due to this boundary displacement. Furthermore, the study proposes that nuclear spins offer a pathway for observing and controlling parafermion zero modes when the domain wall is positioned near a superconductor. The Zeeman splitting of composite fermions is found to be linear in magnetic fields, originating from the zeroth Landau level electrons where interactions do not enhance spin splitting. At an electron filling factor of 2/3, a crossing of composite fermion levels with opposite spins occurs, resulting in either the same or opposite spin polarization depending on the phase. Current-induced nuclear polarisation reconstructs spin boundaries in two-dimensional electron systems, offering new control over quantum phenomena Researchers have demonstrated that electric current can strongly polarize nuclear spins within a quantum point contact or at a domain wall in a two-dimensional electron system exhibiting the fractional quantum Hall effect. This dynamic nuclear polarization, induced by the flow of current, generates a substantial effective magnetic field capable of altering the spin configuration of the electron liquid. Specifically, the polarization modifies the gate voltages and magnetic fields necessary to establish a boundary between regions of differing spin polarization, effectively reconstructing this boundary and displacing the current path. The asymmetry observed in the spread of nuclear spin polarization and domain wall displacement, dependent on current direction, highlights a directional dependence within the system. Calculations indicate that hyperfine interactions, the coupling between electron and nuclear spins, facilitate equilibration of the nuclear spin polarization and influence both domain wall position and the overall spin state. Furthermore, oscillatory behaviour between polarized and unpolarized states near a source contact has been predicted. The authors suggest that these hyperfine interactions offer a potential pathway for observing and controlling parafermion zero modes when the domain wall is placed near a superconducting material. This work acknowledges limitations stemming from the model employed, which focuses on nuclear spins with a spin of 1/2. While the calculations are restricted to this simplified scenario, the implications of nuclear spins with a spin of 3/2, more representative of experimental conditions, are discussed qualitatively. Future research could focus on extending the model to incorporate these more complex nuclear spin configurations and exploring the potential for manipulating parafermion zero modes for quantum information processing. The findings establish a connection between electrical currents, nuclear spin dynamics, and the reconstruction of boundaries in fractional quantum Hall systems, potentially offering new avenues for controlling and characterizing these exotic states of matter. 👉 More information 🗞 Dynamic nuclear spin polarization in the fractional quantum Hall effect spin transitions 🧠 ArXiv: https://arxiv.org/abs/2602.02434 Tags: