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Register a new userPersistent current and zero-energy Majorana modes in a p-wave disordered superconducting ring
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We discuss the emergence of zero-energy Majorana modes in a disordered finite-length p-wave one-dimensional superconducting ring, pierced by a magnetic flux $Phi$ tuned at an appropriate value $Phi=Phi_*$. In the absence of fermion parity conservation, we evidence the emergence of the Majorana modes by looking at the discontinuities in the persistent current $I[Phi]$ at $Phi=Phi_*$. By monitoring the discontinuities in $I[Phi]$, we map out the region in parameter space characterized by the emergence of Majorana modes in the disordered ring.
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Majorana zero modes are fractional quantum excitations appearing in pairs, each pair being a building block for quantum computation . Some possible signatures of these excitations have been reported as zero bias peaks at endpoints of one-dimensional semiconducting wires and magnetic chains. However, 1D systems are by nature fragile to a small amount of disorder that induces low-energy excitations, hence obtaining Majorana zero modes well isolated in a hard gap requires extremely clean systems. Two-dimensional systems offer an alternative route to get robust Majorana zero modes. Indeed, it was shown recently that Pb/Co/Si(111) could be used as a platform for generating 2D topological superconductivity with a strong immunity to local disorder. While 2D systems exhibit dispersive chiral edge states, they can also host Majorana zero modes located on local topological defects. According to predictions, if an odd number of zero modes are located in a topological domain an additional zero mode should appear all around the domains edge. Here we use scanning tunneling spectroscopy to characterize a disordered superconducting monolayer of Pb coupled to underlying Co-Si magnetic islands meant to induce a topological transition. We show that pairs of zero modes are stabilized: one zero mode positioned at a point in the middle of the magnetic domain and its zero mode partner extended all around the domain. The zero mode pair is remarkably robust, it is isolated within a hard superconducting energy gap and it appears totally immune to the strong disorder present in the Pb monolayer. Our theoretical scenario supports the protected Majorana nature of this zero mode pair, highlighting the role of magnetic or spin-orbit coupling textures. This robust pair of Majorana zero modes offers a new platform for theoretical and experimental study of quantum computing.
We provide a current perspective on the rapidly developing field of Majorana zero modes in solid state systems. We emphasize the theoretical prediction, experimental realization, and potential use of Majorana zero modes in future information processing devices through braiding-based topological quantum computation. Well-separated Majorana zero modes should manifest non-Abelian braiding statistics suitable for unitary gate operations for topological quantum computation. Recent experimental work, following earlier theoretical predictions, has shown specific signatures consistent with the existence of Majorana modes localized at the ends of semiconductor nanowires in the presence of superconducting proximity effect. We discuss the experimental findings and their theoretical analyses, and provide a perspective on the extent to which the observations indicate the existence of anyonic Majorana zero modes in solid state systems. We also discuss fractional quantum Hall systems (the 5/2 state) in this context. We describe proposed schemes for carrying out braiding with Majorana zero modes as well as the necessary steps for implementing topological quantum computation.
We show that long-ranged superconducting order is not necessary to guarantee the existence of Majorana fermion zero modes at the ends of a quantum wire. We formulate a concrete model which applies, for instance, to a semiconducting quantum wire with strong spin-orbit coupling and Zeeman splitting coupled to a wire with algebraically-decaying superconducting fluctuations. We solve this model by bosonization and show that it supports Majorana fermion zero modes. We argue that a large class of models will also show the same phenomenon. We discuss the implications for experiments on spin-orbit coupled nanowires coated with superconducting film and for LaAlO3/SrTiO3 interfaces.
We describe the occurrence and physical role of zero-energy modes in the Dirac equation with a topologically non-trivial background.
We study theoretically the contribution of fluctuating Cooper pairs to the persistent current in superconducting rings threaded by a magnetic flux. For sufficiently small rings, in which the coherence length $xi$ exceeds the radius $R$, mean field theory predicts a full reduction of the transition temperature to zero near half-integer flux. We find that nevertheless a very large current is expected to persist in the ring as a consequence of Cooper pair fluctuations that do not condense. For larger rings with $Rgg xi$ we calculate analytically the susceptibility in the critical region of strong fluctuations and show that it reflects competition of two interacting complex order parameters.
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