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Register a new userNodal Andreev Spectra in Multi-Majorana Three-Terminal Josephson Junctions
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Maria Teresa Mercaldo
Publication date
2020
fields
Physics
and research's language is
English
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We investigate the Andreev-bound-state (ABS) spectra of three-terminal Josephson junctions which consist of 1D topological superconductors (TSCs) harboring multiple zero-energy edge Majorana bound states (MBSs) protected by chiral symmetry. Our theoretical analysis relies on the exact numerical diagonalization of the Bogoliubov-de Gennes (BdG) Hamiltonian describing the three interfaced TSCs, complemented by an effective low-energy description solely based on the coupling of the interfacial MBSs arising before the leads get contacted. Considering the 2D synthetic space spanned by the two independent superconducting phase differences, we demonstrate that the ABS spectra may contain either point or line nodes, and identify $mathbb{Z}_2$ topological invariants to classify them. We show that the resulting type of nodes depends on the number of preexisting interfacial MBSs, with nodal lines necessarily appearing when two TSCs harbor an unequal number of MBSs. Specifically, the precise number of interfacial MBSs determines the periodicity of the spectrum under $2pi$-slidings of the phase differences and, as a result, also controls the shape of the nodal lines in synthetic space. When chiral symmetry is preserved, the lines are open and coincide with high-symmetry lines of synthetic space, while when it is violated the lines can also transform into loops and chains. The nodal spectra are robust by virtue of the inherent particle-hole symmetry of the BdG Hamiltonian, and give rise to distinctive experimental signatures that we identify.
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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.
Establishment of phase-coherence and a non-dissipative (super)current between two weakly coupled superconductors, known as the Josephson effect, plays a foundational role in basic physics and applications to metrology, precision sensing, high-speed digital electronics, and quantum computing. The junction ranges from planar insulating oxides to single atoms, molecules, semiconductor nanowires, and generally to any finite-size coherent conductor. Recently, junctions of more than two superconducting terminals gained broad attention in the context of braiding of Majorana fermions in the solid state for fault-tolerant quantum computing, and accessing physics and topology in dimensions higher than three. Here we report the first observation of Josephson effect in 3- and 4-terminal junctions, fabricated in a top-down fashion from a semiconductor/superconductor (InAs/Al) epitaxial two-dimensional heterostructure. Due to interactions, the critical current of an N-terminal junction becomes the boundary of an (N-1)-dimensional manifold of simultaneously allowed supercurrents. The measured shapes of such manifolds are explained by the scattering theory of mesoscopic superconductivity, and they can be remarkably sensitive to the junctions symmetry class. Furthermore, we observed a notably high-order (up to 8) multiple Andreev reflections simultaneously across every terminals pair, which verifies the multi-terminal nature of normal scattering and a high interface quality in our devices. Given the previously shown gate-control of carrier density and evidence of spin-orbit scattering in InAs/Al heterostructures, and device compatibility with other 2D materials, the multi-terminal Josephson effect reported here can become a testbed for physics and applications of topological superconductivity.
We demonstrate how the boundary-driven reconstruction of the superconducting order parameter can be employed to manipulate the zero-energy Majorana bound states (MBSs) occurring in a topological Josephson junction. We focus on an interface of two p-wave superconductors, which are described by a spin-vector order parameter $bf{d}$. Apart from the sensitivity of $bf{d}$ to external Zeeman/exchange fields, here, we show that the orientation of $bf{d}$ throughout the junction can be controlled by electrically gating the weak link. The remarkable local character of this knob is a manifestation of the edge reconstruction of the order parameter, which takes place whenever different $bf{d}$-vector configurations in each superconductor compete and are close in energy. As a consequence, the spin-dependent superconducting-phase difference across the junction is switchable from $0$ to $pi$. Moreover, in the regime where multiple edge MBSs occur for each superconductor, the Andreev-bound-state (ABS) spectra can be twisted by the application of either a charge- or spin-phase difference across the interface, and give rise to a rich diversity of nonstandard ABS dispersions. Interestingly, some of these dispersions show band crossings protected by fermion parity, despite their $2pi$-periodic character. These crossings additionally unlock the possibility of nontrivial topology in synthetic spaces, when considering networks of such 1D junctions. Lastly, the interface MBSs induce a distinct elecronic spin polarization near the junction, which possesses a characteristic spatial pattern that allows the detection of MBSs using spin-polarized scanning tunneling microscopy. These findings unveil novel paths to mechanisms for ABS engineering and single-out signatures relevant for the experimental detection and manipulation of MBSs.
We consider mesoscopic four-terminal Josephson junctions and study emergent topological properties of the Andreev subgap bands. We use symmetry-constrained analysis for Wigner-Dyson classes of scattering matrices to derive band dispersions. When scattering matrix of the normal region connecting superconducting leads is energy-independent, the determinant formula for Andreev spectrum can be reduced to a palindromic equation that admits a complete analytical solution. Band topology manifests with an appearance of the Weyl nodes which serve as monopoles of finite Berry curvature. The corresponding fluxes are quantified by Chern numbers that translate into a quantized nonlocal conductance that we compute explicitly for the time-reversal-symmetric scattering matrix. The topological regime can be also identified by supercurrents as Josephson current-phase relationships exhibit pronounced nonanalytic behavior and discontinuities near Weyl points that can be controllably accessed in experiments.
We demonstrate how to design various nonstandard types of Andreev-bound-state (ABS) dispersions, via a composite construction relying on Majorana bound states (MBSs). Here, the MBSs appear at the interface of a Josephson junction consisting of two topological superconductors (TSCs). Each TSC harbors multiple MBSs per edge by virtue of a chiral or unitary symmetry. We find that, while the ABS dispersions are $2pi$-periodic, they still contain multiple crossings which are protected by the conservation of fermion parity. A single junction with four interface MBSs and all MBS couplings fully controllable, or, networks of such coupled junctions with partial coupling tunability, open the door for topological bandstructures with Weyl points or nodes in synthetic dimensions, which in turn allow for fermion-parity (FP) pumping with a cycle set by the ABS-dispersion details. In fact, in the case of nodes, the FP pumping is a manifestation of chiral anomaly in 2D synthetic spacetime. The possible experimental demonstration of ABS engineering in these devices, further promises to unveil new paths for the detection of MBSs and higher-dimensional chiral anomaly.
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