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Register a new userEngineering 1D topological phases on $p$-wave superconductors
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In this work, we study how, with the aid of impurity engineering, two-dimensional $p$-wave superconductors can be employed as a platform for one-dimensional topological phases. We discover that, while chiral and helical parent states themselves are topologically nontrivial, a chain of scalar impurities on both systems support multiple topological phases and Majorana end states. We develop an approach which allows us to extract the topological invariants and subgap spectrum, even away from the center of the gap, for the representative cases of spinless, chiral and helical superconductors. We find that the magnitude of the topological gaps protecting the nontrivial phases may be a significant fraction of the gap of the underlying superconductor.
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In this work we consider the influence of potential impurities deposited on top of two-dimensional chiral superconductors. As discovered recently, magnetic impurity lattices on an $s$-wave superconductor may give rise to a rich topological phase diagram. We show that similar mechanism takes place in chiral superconductors decorated by non-magnetic impurities, thus avoiding the delicate issue of magnetic ordering of adatoms. We illustrate the method by presenting the theory of potential impurity lattices embedded on chiral $p$-wave superconductors. While a prerequisite for the topological state engineering is a chiral superconductor, the proposed procedure results in vistas of nontrivial descendant phases with different Chern numbers.
Topological phases of matter that depend for their existence on interactions are fundamentally interesting and potentially useful as platforms for future quantum computers. Despite the multitude of theoretical proposals the only interaction-enabled topological phase experimentally observed is the fractional quantum Hall liquid. To help identify other systems that can give rise to such phases we present in this work a detailed study of the effect of interactions on Majorana zero modes bound to vortices in a superconducting surface of a 3D topological insulator. This system is of interest because, as was recently pointed out, it can be tuned into the regime of strong interactions. We start with a 0D system suggesting an experimental realization of the interaction-induced $mathbb{Z}_8$ ground state periodicity previously discussed by Fidkowski and Kitaev. We argue that the periodicity is experimentally observable using a tunnel probe. We then focus on interaction-enabled crystalline topological phases that can be built with the Majoranas in a vortex lattice in higher dimensions. In 1D we identify an interesting exactly solvable model which is related to a previously discussed one that exhibits an interaction-enabled topological phase. We study these models using analytical techniques, exact numerical diagonalization (ED) and density matrix renormalization group (DMRG). Our results confirm the existence of the interaction-enabled topological phase and clarify the nature of the quantum phase transition that leads to it. We finish with a discussion of models in dimensions 2 and 3 that produce similar interaction-enabled topological phases.
We investigate the topological properties of a Kitaev chain in the shape of a legged-ring, which is here referred to as Kitaev tie. We demonstrate that the Kitaev tie is a frustrated system in which topological properties are determined by the position of the movable bond (the tie knot). We determine the phase diagram of the system as a function of the knot position and chemical potential, also discussing the effects of topological frustration. The stability of the topological Kitaev tie is addressed by a careful analysis of the system free energy.
In condensed matter systems, zero-dimensional or one-dimensional Majorana modes can be realized respectively as the end and edge states of one-dimensional and two-dimensional topological superconductors. In this $textit{top-down}$ approach, $(d-1)$-dimensional Majorana modes are obtained as the boundary states of a topologically nontrivial $d$-dimensional bulk. In a $textit{bottom-up}$ approach instead, $d$-dimensional Majorana modes in a $d$-dimensional system can be realized as the continuous limit of a periodic lattice of coupled $(d-1)$-dimensional Majorana modes. We illustrate this idea by considering one-dimensional proximitized superconductors with spatially-modulated potential or magnetic fields. The ensuing inhomogenous topological state exhibits one-dimensional counterpropagating Majorana modes with finite dispersion, and with a Majorana gap which can be controlled by external fields. In the massless case, the Majorana modes have opposite Majorana polarizations and pseudospins, are conformally invariant, and realize centrally extended quantum mechanical supersymmetry. The supersymmetry exhibits spontaneous partial breaking. Consequently, the massless Majorana fermion can be identified as a Goldstino, i.e., the Nambu-Goldstone fermion associated with the spontaneously broken supersymmetry.
We show that a two-dimensional semiconductor with Rashba spin-orbit coupling could be driven into the second-order topological superconducting phase when a mixed-pairing state is introduced. The superconducting order we consider involves only even-parity components and meanwhile breaks time-reversal symmetry. As a result, each corner of a square-shaped Rashba semiconductor would host one single Majorana zero mode in the second-order nontrivial phase. Starting from edge physics, we are able to determine the phase boundaries accurately. A simple criterion for the second-order phase is further established, which concerns the relative position between Fermi surfaces and nodal points of the superconducting order parameter. In the end, we propose two setups that may bring this mixed-pairing state into the Rashba semiconductor, followed by a brief discussion on the experimental feasibility of the two platforms.
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