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An odd-occupied quantum dot in a Josephson junction can flip transmission phase, creating a {pi}-junction. When the junction couples topological superconductors, no phase flip is expected. We investigate this and related effects in a full-shell hybrid interferometer, using gate voltage to control dot-junction parity and axial magnetic flux to control the transition from trivial to topological superconductivity. Enhanced zero-bias conductance and critical current for odd parity in the topological phase reflects hybridization of the confined spin with zero-energy modes in the leads.
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We study the spin transport through a 1D quantum Ising-XY-Ising spin link that emulates a topological superconducting-normal-superconducting structure via Jordan-Wigner (JW) transformation. We calculate, both analytically and numerically, the spectrum of spin Andreev bound states and the resulting $mathbb{Z}_2$ fractional spin Josephson effect (JE) pertaining to the emerging Majorana JW fermions. Deep in the topological regime, we identify an effective time-reversal symmetry that leads to $mathbb{Z}_4$ fractional spin JE in the $textit{presence}$ of interactions within the junction. Moreover, we uncover a hidden inversion time-reversal symmetry that protects the $mathbb{Z}_4$ periodicity in chains with an odd number of spins, even in the $textit{absence}$ of interactions. We also analyze the entanglement between pairs of spins by evaluating the concurrence in the presence of spin current and highlight the effects of the JW Majorana states. We propose to use a microwave cavity setup for detecting the aforementioned JEs by dispersive readout methods and show that, surprisingly, the $mathbb{Z}_2$ periodicity is immune to $textit{any}$ local magnetic perturbations. Our results are relevant for a plethora of spin systems, such as trapped ions, photonic lattices, electron spins in quantum dots, or magnetic impurities on surfaces.
We study the emergent band topology of subgap Andreev bound states in the three-terminal Josephson junctions. We scrutinize the symmetry constraints of the scattering matrix in the normal region connecting superconducting leads that enable the topological nodal points in the spectrum of Andreev states. When the scattering matrix possesses time-reversal symmetry, the gap closing occurs at special stationary points that are topologically trivial as they carry vanishing Berry fluxes. In contrast, for the time-reversal broken case we find topological monopoles of the Berry curvature and corresponding phase transition between states with different Chern numbers. The latter is controlled by the structure of the scattering matrix that can be tuned by a magnetic flux piercing through the junction area in a three-terminal geometry. The topological regime of the system can be identified by nonlocal conductance quantization that we compute explicitly for a particular parametrization of the scattering matrix in the case where each reservoir is connected by a single channel.
Majorana zero modes are quasiparticle states localized at the boundaries of topological superconductors that are expected to be ideal building blocks for fault-tolerant quantum computing. Several observations of zero-bias conductance peaks measured in tunneling spectroscopy above a critical magnetic field have been reported as experimental indications of Majorana zero modes in superconductor/semiconductor nanowires. On the other hand, two dimensional systems offer the alternative approach to confine Ma jorana channels within planar Josephson junctions, in which the phase difference {phi} between the superconducting leads represents an additional tuning knob predicted to drive the system into the topological phase at lower magnetic fields. Here, we report the observation of phase-dependent zero-bias conductance peaks measured by tunneling spectroscopy at the end of Josephson junctions realized on a InAs/Al heterostructure. Biasing the junction to {phi} ~ {pi} significantly reduces the critical field at which the zero-bias peak appears, with respect to {phi} = 0. The phase and magnetic field dependence of the zero-energy states is consistent with a model of Majorana zero modes in finite-size Josephson junctions. Besides providing experimental evidence of phase-tuned topological superconductivity, our devices are compatible with superconducting quantum electrodynamics architectures and scalable to complex geometries needed for topological quantum computing.
The thermoelectric performance of a topological Josephson nonlocal heat engine is thoroughly investigated. The nonlocal response is obtained by using a normal metal probe coupled with only one of the proximized helical edges in the middle of the junction. In this configuration, we investigate how the flux bias and the phase bias trigger the nonlocal thermoelectric effects under the application of a thermal difference between the superconducting terminals. Possible experimental nonidealities such as asymmetric proximized superconducting gaps are considered showing how the nonlocal response can be affected. The interplay between Doppler-shift, which tends to close gaps, and Andreev interferometry, which affects particle-hole resonant transport, are clearly identified for different operating regimes. Finally, we discuss the power and the efficiency of the topological thermoelectric engine which reaches maximum power at maximal efficiency for a well coupled normal probe. We find quite high nonlocal Seebeck coefficient of the order of tenths of $mu$V/K at a few kelvin, a signal that would be clearly detectable also against any spurious local effect even with moderate asymmetry of the gaps.
Topological Josephson junctions designed on the surface of a 3D-topological insulator (TI) harbor Majorana bound states (MBSs) among a continuum of conventional Andreev bound states. The distinct feature of these MBSs lies in the $4pi$-periodicity of their energy-phase relation that yields a fractional ac Josephson effect and a suppression of odd Shapiro steps under $r!f$ irradiation. Yet, recent experiments showed that a few, or only the first, odd Shapiro steps are missing, casting doubts on the interpretation. Here, we show that Josephson junctions tailored on the large bandgap 3D TI Bi$_2$Se$_3$ exhibit a fractional ac Josephson effect acting on the first Shapiro step only. With a modified resistively shunted junction model, we demonstrate that the resilience of higher order odd Shapiro steps can be accounted for by thermal poisoning driven by Joule overheating. Furthermore, we uncover a residual supercurrent at the nodes between Shapiro lobes, which provides a direct and novel signature of the current carried by the MBS. Our findings showcase the crucial role of thermal effects in topological Josephson junctions and lend support to the Majorana origin of the partial suppression of odd Shapiro steps.
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