Bloch diode

Abstract

In a SQUID tuned away from half-integer flux (in units of the superconducting flux quantum), the concurrence of multiple Josephson harmonics and an asymmetry between the junctions leads to the Josephson diode effect -- a nonreciprocal current-voltage characteristic manifested as an asymmetry of critical currents at opposite polarities. We predict a dual version of this effect in a gate-tunable Cooper pair transistor placed in series with a highly resistive environment. When tuned away from half-integer gate charge (in units of the Cooper pair charge) it shows an asymmetry of critical voltages at opposite polarities -- a dual diode effect we refer to as the Bloch diode effect. It arises from an asymmetry in the dispersion of the transistor's Bloch bands. A highly resistive environment can be realized with a Josephson junction array, suggesting that such a diode could be implemented using conventional superconducting quantum circuits.

Figures (5)

• Figure 1: The Bloch diode effect is predicted in a voltage-biased asymmetric Cooper pair transistor connected in series with a highly-resistive environment, $R\gg R_Q$.
• Figure 2: Duality between the Josephson diode effect in a SQUID at $R\ll R_Q$ (left) and the Bloch diode effect in a Cooper pair transistor at $R\gg R_Q$ (right). The double cross represents a Josephson junction with multiple harmonics in its current-phase relation; the hatched diamond represents a quantum phase-slip junction with multiple harmonics in its voltage-charge relation. Time-reversal symmetry enforces $U(-\varphi,-\Phi)=U(\varphi,\Phi)$ for the Josephson potential of the SQUID, where $\Phi$ is the flux piercing the loop. Thus nonreciprocity is realized if $\Phi$ is tuned away from a half-integer flux (in units of the superconducting flux quantum) and the SQUID is asymmetric, such that $U(-\varphi,\Phi)\neq U(\varphi,\Phi)$. In the Cooper pair transistor, inversion symmetry enforces ${\cal E}_0(-{\cal N},-{\cal N}_g)={\cal E}_0({\cal N},{\cal N}_g)$ with ${\cal N}_g=-C_gV_g/2e$. Thus nonreciprocity is realized for two unequal phase-slip junctions if the gate charge is tuned away from a multiple of $e$, such that ${\cal E}_0(-{\cal N},{\cal N}_g)\neq{\cal E}_0({\cal N},{\cal N}_g)$.
• Figure 3: Ratchet potential (blue) and voltage-charge relation (red) associated with a Bloch diode with efficiency $\eta=1/3$ in the Josephson-dominated regime, cf. Eq. \ref{['eq:ratchet']}.
• Figure 4: Ratchet potential (blue) and voltage-charge relation (red) associated with a Bloch diode with efficiency $\eta=(\sqrt{2}-1)^2$ in the Coulomb-dominated regime. Dashed and dotted lines are metastable energies at fixed charge and $\sigma_z=\mp 1$, respectively, cf. Eq. \ref{['eq:E0-CB']}. The gaps of the order $E_J\ll E_C$ when charging energies cross each other, and associated smearing of the charge-voltage relation, are not shown.
• Figure 5: Nonreciprocal current-voltage characteristics of the Bloch diode described by the ratchet potential of Fig. \ref{['F:2']} (purple) and Fig. \ref{['F:4']} (green).