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Register a new userSNS junction of topological superconductors revisited: fractional Josephson current, fermion parity, and oscillating wavefunctions
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The fractional Josephson effect is known to be a characteristic phenomenon of topological Josephson junctions hosting Majorana zero modes (MZMs), where the Josephson current has a $4pi$ (rather than a $2pi$) periodicity in the phase difference between the two topological superconductors. We introduce a one-dimensional model of a topological superconductor/normal-metal/superconductor (SNS) junction with the normal-metal (N) region of finite length, which is intermediate regime between the short- and long-junction limits. Assuming weak tunneling at the SN interfaces, we investigate resonance and finite-size effects on the fractional Josephson effect due to the existence of several discrete energy levels in the N region in which wavefunctions have oscillating nodal structure. Through careful analysis of the sign change in the transmission amplitudes through the junction and the fermion parity of the two MZMs, we find that the fractional Josephson current is proportional to the parity of total fermion numbers including both filled normal levels and two MZMs. Furthermore, we elucidate drastic enhancement of the Josephson current due to the resonance between a discrete level in the N region and MZMs.
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Using tunneling spectroscopy, we have measured the local electron energy distribution function in the normal part of a superconductor-normal metal-superconductor (SNS) Josephson junction containing an extra lead to a normal reservoir. In the presence of simultaneous supercurrent and injected quasiparticle current, the distribution function exhibits a sharp feature at very low energy. The feature is odd in energy, and odd under reversal of either the supercurrent or the quasiparticle current direction. The feature represents an effective temperature gradient across the SNS Josephson junction that is controllable by the supercurrent.
We compute the current voltage characteristic of a chain of identical Josephson circuits characterized by a large ratio of Josephson to charging energy that are envisioned as the implementation of topologically protected qubits. We show that in the limit of small coupling to the environment it exhibits a non-monotonous behavior with a maximum voltage followed by a parametrically large region where $Vpropto 1/I$. We argue that its experimental measurement provides a direct probe of the amplitude of the quantum transitions in constituting Josephson circuits and thus allows their full characterization.
The Andreev bound states and charge transport in a Josephson junction between two superconductors with intrinsic exchange fields are studied. We find that for a parallel configuration of the exchange fields in the superconductors the discrete spectrum consists of two pairs of spin-split states. The Josephson current in this case is mainly carried by bound states. In contrast, for the antiparallel configuration we find that there is no spin-splitting of the bound states and that for phase differences smaller than certain critical value there are no bound states at all. Hence the supercurrent is only carried by states in the continuous part of the spectrum. Our predictions can be tested by performing a tunneling spectroscopy of a weak link between two spin-split superconductors.
Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4$pi$-periodic current-phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of dynamical properties of topological JJs using a modified resistively and capacitively shunted junction model and extensively investigated the progressive evolution of Shapiro steps as a function of the junction parameters and microwave power and frequency. Our calculation results indicate that the suppression of odd-integer Shapiro steps, i.e., evidence of the fractional ac Josephson effect, is enhanced significantly by the increase in the junction capacitance and IcRn product as well as the decrease in the microwave frequency even for the same portion of the 4$pi$-periodic supercurrent. Our study provides the optimal conditions for observing the fractional ac Josephson effect; furthermore, our new model can be used to precisely quantify the topological supercurrent from the experimental data of topological JJs.
We study the dynamics of current-biased Josephson-junction arrays with a magnetic penetration depth smaller than the lattice spacing. We compare the dynamics imaged by low-temperature scanning electron microscopy to the vortex dynamics obtained from model calculations based on the resistively-shunted junction model, in combination with Maxwells equations. We find three bias current regions with fundamentally different array dynamics. The first region is the subcritical region, i.e. below the array critical current I_c. The second, for currents I above I_c, is a vortex region, in which the response is determined by the vortex degrees of freedom. In this region, the dynamics is characterized by spatial domains where vortices and antivortices move across the array in opposite directions in adjacent rows and by transverse voltage fluctuations. In the third, for still higher currents, the dynamics is dominated by coherent-phase motion, and the current-voltage characteristics are linear.
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