Barrier-curvature dependence of the low-energy scales of the 0.7 anomaly in quantum point contacts: a program to discriminate the van Hove-ridge, spontaneous-spin-polarization, and Kondo-like scenarios

Experiments on 98 multiplexed split-gate quantum wires established that the 0.7 anomaly in quantum point contacts grows stronger and shifts to lower conductance as the longitudinal barrier curvature $\hbar\omega_x$ decreases, and proposed a concrete program to settle the anomaly's microscopic origin: measure $G_e/G_0$ versus $\hbar\omega_x$ under controlled variation of temperature $T$, in-plane magnetic field $B$, and dc source-drain bias $V_{sd}$; extract the model-specific crossover scales $\tilde{T}_*$, $\tilde{B}_*$, and $\tilde{V}_{sd*}$ as functions of curvature; test the van Hove-ridge prediction for $\tilde{B}_*(\Omega_x)$; and supply the then-missing finite-temperature conductance calculations within the van Hove framework for quantitative comparison. The program remains open: finite-temperature van Hove conductance theory now exists qualitatively, and ensemble statistics at two temperatures favor the van Hove scenario, but the curvature-resolved extraction of the low-energy scales and the decisive $\tilde{B}_*(\Omega_x)$ test remain unperformed.

Background

A quantum point contact (QPC) is a narrow constriction, patterned electrostatically by split gates in a two-dimensional electron gas, whose width is comparable to the electron Fermi wavelength. Its linear conductance is quantized in units of $G_0=2e^2/h$ as transverse modes are opened one by one. Shortly after this quantization was discovered, Thomas et al. (Phys. Rev. Lett. 77, 135 (1996)) reported an unexplained shoulder near $0.7G_0$ below the first plateau — the "0.7 anomaly" — which strengthens with temperature and evolves smoothly into the spin-split plateau in an in-plane magnetic field. Three families of microscopic explanations dominate the literature. (i) Spontaneous spin polarization: exchange interactions split the lowest 1D subband even at zero field, as advocated by Wang and Berggren (Phys. Rev. B 54, R14257 (1996)). (ii) Kondo-like physics: Cronenwett et al. (Phys. Rev. Lett. 88, 226805 (2002)) argued from the anomaly's temperature, field, and bias dependence that a quasi-bound state near the QPC top produces a Kondo-correlated open system. (iii) The van Hove-ridge scenario: Bauer et al. (Nature 501, 73 (2013)) combined functional renormalization group (fRG, a controlled scheme integrating momentum-shell flow equations for the effective interaction vertex) with detailed experiments to attribute the anomaly to a smeared van Hove singularity — a ridge of enhanced local density of states at the bottom of the lowest 1D subband at the barrier top — which amplifies interaction effects and produces an inelastic-scattering spin structure without static magnetization. This framework introduces model-specific low-energy scales $\tilde{T}_*$, $\tilde{B}_*$, and $\tilde{V}_{sd*}$: the crossover temperatures, fields, and biases below which the 0.7 structure appears, with a parameter-free prediction for how $\tilde{B}_*$ grows with the bare barrier curvature $\Omega_x$ (Eq. 35a and Fig. S13 of that paper's supplement). Smith et al. (Phys. Rev. B 91, 235402 (2015)) measured 98 lithographically identical split gates in a single cooldown using cryogenic on-chip multiplexing, fitted each conductance trace with a saddle-point model (a parabolic approximation to the barrier top whose longitudinal curvature $\hbar\omega_{x,1}\in 1.3$–$3$ meV sets the effective device length), and found that the anomaly's strength grows while its conductance value falls as $\hbar\omega_{x,1}$ decreases, with carrier density a secondary factor; traces showing strong evidence of disorder at conductances below $3G_0$ were excluded from the ensemble. Because those data were taken at base temperature ($kT/\hbar\omega_{x,1}<0.1$), the curvature dependence of the low-energy scales could not be accessed; spontaneous-polarization and Kondo scenarios also predict reduced conductance at lower curvature, so the scenarios could not be separated. The paper therefore posed the discrimination program stated below. Related earlier van Hove-type analyses of the finite-temperature conductance include Sloggett, Milstein, and Sushkov (Eur. Phys. J. B 61, 427 (2008)).

Problem Statement

Determine how the barrier-curvature dependence of the 0.7 anomaly in GaAs (gallium arsenide) split-gate quantum point contacts evolves with the low-energy control variables, and use this to discriminate the candidate microscopic mechanisms. Concretely, building on the ensemble result that the anomaly strengthens and shifts to lower conductance as the longitudinal barrier curvature $\hbar\omega_{x,1}$ decreases (observed over roughly 1.3–3 meV): (1) measure $G_e/G_0$ versus $\hbar\omega_{x,1}$ under controlled, systematic variation of temperature $T$, in-plane magnetic field $B$, and dc source-drain bias $V_{sd}$, on ensembles (or continuously retunable devices) large and clean enough to separate curvature effects from device-to-device disorder; (2) extract the model-specific crossover scales $\tilde{T}_*$, $\tilde{B}_*$, and $\tilde{V}_{sd*}$ as functions of the bare barrier curvature, in particular testing the van Hove-ridge prediction that $\tilde{B}_*$ scales with $\Omega_x$ — Bauer et al.'s notation for the bare longitudinal barrier curvature, unmodified by electron interactions, which is operationally extracted per device as $\hbar\omega_{x,1}$ from the saddle-point fits — (Eq. 35a and Fig. S13 of Bauer et al., Nature 501, 73 (2013)); (3) perform finite-temperature conductance calculations within the van Hove-ridge framework — going beyond the existing qualitative results — that are quantitatively comparable to these measured trends, alongside the corresponding predictions of the spontaneous-spin-polarization and Kondo-like scenarios; and (4) establish whether the extracted scale dependences discriminate among these scenarios decisively. Components (1) and (2) require new measurements and are outside the scope of a submission, which consists of components (3) and (4); component (4) is to be carried out not with measured crossover scales but with the crossover scales predicted by each of the three scenarios as functions of $\hbar\omega_{x,1}$, compared quantitatively against the curvature trend already established in the existing ensemble data (Smith et al. 2015; Ma et al. 2024) and against the van Hove-ridge $\tilde{B}_*(\Omega_x)$ prediction. A submission that finds the existing data insufficient for a decisive discrimination must establish what the comparison does resolve, what remains open, and which curvature-resolved measurements would settle it. The single objective uniting these components is the identification of the microscopic mechanism governing the 0.7 anomaly via the curvature dependence of its low-energy scales.

References

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