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Register a new userProtocol to identify a topological superconducting phase in a three-terminal device
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We develop a protocol to determine the presence and extent of a topological phase with Majorana zero modes in a hybrid superconductor-semiconductor device. The protocol is based on conductance measurements in a three-terminal device with two normal leads and one superconducting lead. A radio-frequency technique acts as a proxy for the measurement of local conductance, allowing a rapid, systematic scan of the large experimental phase space of the device. Majorana zero modes cause zero bias conductance peaks at each end of the wire, so we identify promising regions of the phase space by filtering for this condition. To validate the presence of a topological phase, a subsequent measurement of the non-local conductance in these regions is used to detect a topological transition via the closing and reopening of the bulk energy gap. We define data analysis routines that allow for an automated and unbiased execution of the protocol. Our protocol is designed to screen out false positives, especially trivial Andreev bound states that mimic Majorana zero modes in local conductance. We apply the protocol to several examples of simulated data illustrating the detection of topological phases and the screening of false positives.
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We present an exhaustive theoretical analysis of a double-loop Josephson proximity interferometer, as the one recently realized by Strambini et al. for the control of the Andreev spectrum via an external magnetic field. This system, called $omega$-SQUIPT, consists of a T-shaped diffusive normal metal (N) attached to three superconductors (S) forming a double loop configuration. By using the quasiclassical Green function formalism, we calculate the local normalized density of states, the Josephson currents through the device and the dependence of the former on the length of the junction arms, the applied magnetic field and the S/N interface transparencies. We show that by tuning the fluxes through the double loop, the system undergoes transitions from a gapped to a gapless state. We also evaluate the Josephson currents flowing in the different arms as a function of magnetic fluxes and explore the quasi-particle transport, by considering a metallic probe tunnel-coupled to the Josephson junction and calculating its I-V characteristics. Finally, we study the performances of the $omega$-SQUIPT and its potential applications, by investigating its electrical and magnetometric properties.
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.
Recently Baselmans et al. [Nature, 397, 43 (1999)] showed that the direction of the supercurrent in a superconductor/normal/superconductor Josephson junction can be reversed by applying, perpendicularly to the supercurrent, a sufficiently large control current between two normal reservoirs. The novel behavior of their 4-terminal device (called a controllable PI-junction) arises from the nonequilibrium electron energy distribution established in the normal wire between the two superconductors. We have observed a similar supercurrent reversal in a 3-terminal device, where the control current passes from a single normal reservoir into the two superconductors. We show theoretically that this behavior, although intuitively less obvious, arises from the same nonequilibrium physics present in the 4-terminal device. Moreover, we argue that the amplitude of the PI-state critical current should be at least as large in the 3-terminal device as in a comparable 4-terminal device.
Josephson junctions with three or more superconducting leads have been predicted to exhibit topological effects in the presence of few conducting modes within the interstitial normal material. Such behavior, of relevance for topologically-protected quantum bits, would lead to specific transport features measured between terminals, with topological phase transitions occurring as a function of phase and voltage bias. Although conventional, two-terminal Josephson junctions have been studied extensively, multi-terminal devices have received relatively little attention to date. Motivated in part by the possibility to ultimately observe topological phenomena in multi-terminal Josephson devices, as well as their potential for coupling gatemon qubits, here we describe the superconducting features of a top-gated mesoscopic three-terminal Josephson device. The device is based on an InAs two-dimensional electron gas (2DEG) proximitized by epitaxial aluminum. We map out the transport properties of the device as a function of bias currents, top gate voltage and magnetic field. We find a very good agreement between the zero-field experimental phase diagram and a resistively and capacitively shunted junction (RCSJ) computational model.
We propose a protocol to locally detect the Berry curvature of a three terminal Josephson junction with a quantum dot based on a synchronic detection when an AC modulation is applied in the device. This local gauge invariant quantity is expressed in terms of the instantaneous Green function of the Bogoliubov-de Gennes Hamiltonian. We analyze the contribution to the Berry curvature from both the quasi-particle excitations and the Andreev bound state levels by introducing an effective low-energy model. In addition, we propose to induce topological properties in the junction by breaking time-reversal symmetry with a microwave field in the non-resonant regime. In the last case, the Floquet-Andreev levels are the ones that determine the topological structure of the junction, which is formally equivalent to a 2D-honeycomb Haldane lattice. A relation between the Floquet Berry curvature and the transconductance of the driven system is derived.
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