Conductance Anomaly in a Partially Open Adiabatic Quantum Point Contact

Abstract

We demonstrate that conductance anomalies can arise in a clean, adiabatic quantum point contact when a channel is partially open. Even for a smooth barrier potential, backscattering induces Friedel oscillations that, via electron interactions, generate a singular correction to the conductance. This correction is maximized when the channel is half-open, resulting in a reduction of conductance. In addition, a magnetic field applied perpendicular to the spin-orbit axis modifies the single-particle spectrum, resulting in conductance oscillations via Fabry-Pérot-type interference, as well as a non-monotonic field dependence of the anomaly. Our findings reveal a universal mechanism by which interactions modify the conductance of an ideal partially open channel and offer a possible explanation for the anomalous features observed in experiments.

Figures (12)

• Figure 1: Anomalous conductance $\delta G$ as a function of chemical potential at different temperatures. Inset: minimum $\delta G$ versus temperature. $V\left(0\right)$ is the maximum of the barrier potential in Eq. (\ref{['eq:Vx']}). Model parameters: $m_e^{*}=0.067m_e$ (with $m_e$ the electron mass), $l=25.8$, and $\alpha=3.95\times 10^{-3}\,\mathrm{nm}^{-1}$.
• Figure 2: Band dispersion away from the central scattering region with $\boldsymbol{B}\perp\boldsymbol{\gamma}$: (a) and (c) are the weak-field regime ($B<B_c$) and strong-field regime ($B>B_c$), respectively. $B_c$ is the value of magnetic field at which the chemical potential crosses the hump of the lower band, shown in (b). In (a) and (c), the Fermi points responsible for Friedel oscillations are indicated.
• Figure 3: Noninteracting conductance $G_0$ as a function of $B$, $\tilde{B}=g\mu_B B$, $\boldsymbol{B}\perp\boldsymbol{\gamma}$ for $\hbar\gamma=4\mathrm{meV\cdot nm}$. As $B$ increases, the first channel opens and $G_0$ exhibits oscillations. The chemical potential is a constant, and other parameters are the same as in Fig. \ref{['fig:AnomalyVsChemicalPotential']}. Inset: The single-particle spectrum. The blue dashed line marks the chemical potential. Far from the barrier, it intersects the bands at two Fermi points, corresponding to a single transport channel. At the barrier top $V\left(0\right)$, the red dashed line marks the kinetic energy $\mu-V\left(0\right)$, which defines four local Fermi points. The boundaries between the regions with four and two Fermi-points form Fabry-Pérot-type interference, giving rise to conductance oscillations.
• Figure 4: Anomalous conductance $\delta G$ and spin overlap $S(k_1^+,k_1^-)$ as a function of magnetic field. The set up and parameters are the same as in Fig. \ref{['fig:AnomalyVsChemicalPotential']} and \ref{['fig:NoninteractingG']}, except that the chemical potential is always tuned to be at the barrier maximum $V\left(0\right)$ so that the channel of the lower subband is kept half open. The red arrow marks the critical field $B_c$. $N$ is the number of channels contributing to the transport.
• Figure S1: (a) The density as a function of $x$. $\delta\rho$ is obtained by Eq. (\ref{['SIeq:densitykF']}). $\delta\rho_{\text{origin}}$ is obtained directly by substituting the wavefunctions in Eqs. (\ref{['LegendreL']}) and (\ref{['LegendreR']}) into Eq. (\ref{['SIeq:densityNoSOC']}). (b) shows the corresponding barrier potential $V\left(x\right)$ with the model parameter set by $\lambda=1/2+il$, $l=25.8$, and $\alpha=3.95\times 10^{-3}\,\mathrm{nm}^{-1}$.