Magnetic-field asymmetry of mesoscopic $\mathit{dc}$ rectification in Aharonov-Bohm rings

Fundamental Casimir-Onsager symmetry rules for linear response do not apply to nonlinear transport. This motivates the investigation of nonlinear $\mathit{dc}$ conductance of mesoscopic $\mathrm{Ga}\mathrm{As}∕\mathrm{Ga}\mathrm{Al}\mathrm{As}$ rings in a two-wire configuration. The second-order current response to a potential bias is of particular interest. It is related to the sensitivity of conductance fluctuations to this bias and contains information on electron interactions not included in the linear response. In contrast with the linear response, which is a symmetric function of magnetic field, we find that this second-order response exhibits a field dependence, which contains an antisymmetric part. We analyze the flux periodic and aperiodic components of this asymmetry and find that they only depend on the conductance of the rings, which is varied by more than an order of magnitude. These results are in good agreement with recent theoretical predictions relating this asymmetric response to the electron interactions.

Figure 1

(Color online) Field dependence of $G_1^{S,AS}$ and $G_2^{S,AS}$ ($G_1^{\mathit{AS}}$ shifted). These data were obtained on ring 1 in its initial state for a current of $10\mathrm{nA}$. Inset: micrograph of ring 1.

Figure 2

(Color online) (a) Amplitudes of the UCF and AB components of $G_1$ in units of $e^2∕h$, and $G_2^S$ and $G_2^{\mathit{AS}}$ in ${\left(\Omega \mathrm{V}\right)}^{-1}$ as a function of the conductance of the rings. The open and closed symbols correspond to UCF and AB integrated peaks (straight lines are guides to the eyes). (b) Fourier transforms of $G_2$ and $G_1$ renormalized so that the amplitude of the AB peaks are identical. (c) Conductance dependence of the ratio $\delta G_2^{\mathit{AS}}∕\delta G_2^S$ for UCF (open stars) in comparison with Eq. (2) (diamonds), where ${\gamma }_{\mathit{int}}=0.85$ for ring 1 and 0.94 for ring 2.

Figure 3

(Color online) (a) Temperature dependence of the amplitude of the AB oscillations in $G_1$, $G_2^S$, and $G_2^{\mathit{AS}}$ (ring 2). Continuous lines are the fits corresponding to the regions (1) $k_{B}T⪡E_c$ and (2) $k_{B}T⪢E_c$ but $L⪡L_{\varphi }$ (3) $L>L_{\varphi }$. (b) Examples of temperature dependence of $G_2$ in ring 2 for different values of the magnetic field between $-1000$ and $1000\mathrm{G}$.

Figure 4

(Color online) (a) Low-field dependence of $G_2$ on ring 1 for different temperatures. (b) Field dependence of $G_2^{\mathit{AS}}$ after low-pass (light line) and high-pass (bold line) filtering on ring 1 and ring 2, respectively, lower and upper curves (shifted for clarity). Note the extinction of AB oscillations in the vicinity of $B=0$.