Correlated-state magnetization and microscopic NMR detection in quantum point contacts: is the no-bound-state interpretation of the 0.7 anomaly robust?

The conductance of a quantum point contact (QPC) exhibits a long-unexplained '0.7 anomaly', variously attributed to spontaneous spin polarization, a quasi-bound state whose localized moment is Kondo-screened, or van-Hove-enhanced spin fluctuations in a smooth potential barrier. Kawamura, Ono, Stano, Kono, and Aono (Phys. Rev. Lett. 115, 036601 (2015)) reported the only direct measurement of a QPC's electronic magnetization, extracting it from resistively detected nuclear magnetic resonance (NMR) Knight shifts of arsenic nuclei in a single GaAs QPC at 20 mK in in-plane fields up to 6 T. The magnetization varies smoothly with gate voltage, peaks on the half-plateau at $0.5\times 2e^2/h$, and is quantitatively captured by a mean-field tight-binding model of a smooth barrier without a bound state; the authors concluded against a quasi-bound state in their device. That conclusion rests on three uncontrolled elements: interactions were treated at mean-field level, neglecting spin fluctuations and Kondo correlations; the Knight-shift-to-magnetization inversion used a phenomenological hard-wall transverse wave function and an unknown proportionality coefficient $A$ linking nuclear depolarization to the conductance change; and only one device was measured. The open problem is to replace these elements by controlled theory: compute the local magnetization profile and its NMR response including beyond-mean-field correlations, and derive the microscopic conductance response to nuclear polarization, so that the absence of a bound state inferred from the measurement can be assessed microscopically. A 2018 theory follow-up by three of the same authors explicitly leaves the microscopic detection link open.

Background

A quantum point contact (QPC) is a short, gate-defined quasi-one-dimensional channel connecting two electron reservoirs in a semiconductor heterostructure. Because transverse momentum is quantized, its two-terminal conductance rises in steps of $2e^2/h$ as the channel is opened. Shortly after this quantization was discovered, a shoulder near $0.7\times 2e^2/h$ — the 0.7 anomaly — was reported (Thomas et al., 1996) and became one of the longest-standing puzzles of mesoscopic transport. The proposed mechanisms differ most sharply in their predictions for the electron spin arrangement in the channel: spontaneous spin polarization, an antiferromagnetic Wigner crystal (a quasi-periodic arrangement of electrons dominated by repulsion), Kondo screening of a localized moment formed in a quasi-bound state (an electron state trapped near the barrier top, whose spin is screened by lead electrons), or local spin fluctuations enhanced by a van Hove singularity (a peak in the electronic density of states produced by the smooth barrier itself). In the Kondo and related quasi-bound-state scenarios a localized magnetic moment in the QPC is unavoidable; Fano-resonance experiments (Yoon et al., 2007) — conductance spectra showing asymmetric resonances characteristic of interference between direct transmission and a localized level — supported such a trapped spin, while a compressibility study of quasi-one-dimensional wires (Smith et al., 2011) reached the opposite conclusion. Most experiments probe only transmission, so the degree of QPC spin polarization became a central, directly untested issue.

Nuclear magnetic resonance offers a direct magnetization probe. Through the hyperfine interaction, an electronic magnetization shifts the nuclear resonance frequency by the Knight shift, proportional to the local electronic spin density; because the QPC contains only a few spins, Kawamura et al. (2015) detected the NMR resistively (RD-NMR): after dynamical nuclear spin polarization (DNSP) was built up by a source-drain bias, the nuclear polarization and its Overhauser field (the effective magnetic field the polarized nuclei exert on electrons) were probed by measuring the small change of QPC conductance while sweeping an applied radio frequency. The paper's model treats the QPC as a one-dimensional tight-binding chain (electrons hopping between discrete sites) with a smooth parabolic barrier, treating the on-site interaction $U_j n_{j,\uparrow}n_{j,\downarrow}$ in a mean-field approximation that explicitly neglects spin fluctuations; the measured frequency-dependent conductance change was related to the magnetization through $\delta G(f)=A\int dy\,dz\, e^{-\delta f^2/2\gamma^2}|\psi(y,z)|^2$ with $A$ an unknown proportionality coefficient and $\psi(y,z)$ a hard-wall transverse wave function with widths $w_y=(65\pm 5)$ nm and $w_z=(18\pm 3)$ nm. The maximum Knight shift, $K=(11.7\pm 0.5)$ kHz, corresponds to a one-dimensional magnetization density $m_z=(16.5\pm 4.5)\times 10^{6}\,\mathrm{m}^{-1}$ (where $m_z\equiv n_\uparrow-n_\downarrow$ is the spin density per unit length) and a total magnetic moment of $(1.65\pm 0.45)$ in units of the single-electron-spin moment, exceeding what a bound state could support. The smooth, non-saturating field dependence agreed with no-bound-state models (Sloggett et al., 2008; Bauer et al., 2013) and contradicted the trapped-spin interpretation of Yoon et al. Notably, Tripathi and Cooper (2008) had proposed NMR — Knight shift combined with nuclear relaxation rates — precisely as a test of the Kondo scenario; only the Knight-shift leg has been realized. Beyond-mean-field many-body methods for QPCs exist — functional renormalization group treatments of the conductance (resumming fluctuations by successively integrating out high-energy modes) and density-matrix-renormalization-group treatments of the local density of states (a variational method that truncates many-body entanglement to simulate long one-dimensional chains) — but none has addressed the magnetization observable that this experiment measures.

Problem Statement

Determine whether the no-bound-state interpretation of the quantum point contact's local electronic magnetization — the conclusion drawn by Kawamura et al. (2015) from resistively detected NMR Knight shifts — is correct and robust. The single common objective is to bring the QPC magnetization and its NMR detection under microscopic control, so that the measured Knight shifts become a controlled discriminator between the quasi-bound-state (Kondo) and no-bound-state (spin-fluctuation/van Hove) scenarios of the 0.7 anomaly. Two jointly supporting results are required. (1) Correlated magnetization: compute the local spin-resolved magnetization profile of a realistic QPC (smooth confining potential, finite-range interactions, open leads) including correlation effects beyond mean field — spin fluctuations and Kondo-type screening — and from it the predicted gate-voltage dependence of the Knight shift, the NMR line shapes, and the total magnetic moment, for quantitative comparison with the measured values ($K_{\max}=(11.7\pm 0.5)$ kHz, $m_z=(16.5\pm 4.5)\times 10^{6}\,\mathrm{m}^{-1}$, total moment $(1.65\pm 0.45)$ in single-electron-spin units) and with the observed smooth, non-saturating magnetic-field dependence. (2) Microscopic detection theory: derive, rather than fit, the relation between nuclear spin polarization and the QPC conductance change — the coefficient $A$ in $\delta G(f)=A\int dy\,dz\,e^{-\delta f^2/2\gamma^2}|\psi(y,z)|^2$ or its beyond-linear-response replacement, including the backaction of dynamical nuclear spin polarization on transport and the sign and magnitude discrepancy of the predicted conductance change that Stano, Aono, and Kawamura (Phys. Rev. B 97, 075440 (2018)) explicitly left as an open question for further experimental and numerical investigations — so that the inversion from measured spectra to magnetization rests on controlled theory. Result (2) validates what is measured and (1) validates how it is interpreted; the problem is complete when both strands are settled: strand (1) is settled by a beyond-mean-field treatment that captures the correlation regime scoped by spin fluctuations and Kondo-type screening and confronts the predicted gate-voltage dependence of the Knight shift, the NMR line shapes, and the total magnetic moment with the measured values ($K_{\max}$, $m_z$, and the total moment within the quoted errors) and with the observed smooth, non-saturating magnetic-field dependence; either outcome of that confrontation settles the strand, a treatment that reproduces the measured features supporting the no-bound-state reading and one that contradicts them counting against it; and strand (2) is settled by a controlled derivation, rather than a fit, of the coefficient $A$ (or its beyond-linear-response replacement) whose sign and magnitude are compared with the prediction of Stano, Aono, and Kawamura (2018) — so that the NMR magnetization can be accepted or rejected as evidence in the 0.7-anomaly mechanism debate.

References

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