Platform for engineering topological superconductors: Superlattices on Rashba superconductors

Yao Lu, Wen-Yu He, Dong-Hui Xu, Nian Lin, and K. T. Law

Phys. Rev. B 94, 024507 – Published 11 July 2016

Abstract

The search for topological superconductors which support Majorana fermion excitations has been an important topic in condensed matter physics. In this work, we propose an experimental scheme for engineering topological superconductors. In this scheme, by manipulating the superlattice structure of organic molecules placed on top of a superconductor with Rashba spin-orbit coupling, topological superconducting phases can be achieved without or with little fine tuning of the chemical potential. Moreover, superconductors with different Chern numbers can be obtained by changing the superlattice structure of the organic molecules.

Received 31 March 2016
Revised 22 June 2016

DOI:https://doi.org/10.1103/PhysRevB.94.024507

Physics Subject Headings (PhySH)

Majorana fermions Rashba coupling Spin-orbit coupling

Superlattices Topological superconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yao Lu¹, Wen-Yu He¹, Dong-Hui Xu¹, Nian Lin¹, and K. T. Law^1,2,*

¹Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
²Center for 2D and 1D Quantum Materials, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China

^*Corresponding author: phlaw@ust.hk

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Issue

Vol. 94, Iss. 2 — 1 July 2016

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Images

Figure 1
Schematic 1D band structures (a) in the presence of Rashba SOC and a Zeeman field. When the chemical potential $μ$ is in the Zeeman gap, one subband is partially filled and (b) in the presence of a Zeeman field, small Rashba SOC, and an infinitesimal superlattice potential. The superlattice potential with period $π / k_{F}$ reduces the Brillouin zone to $[- k_{F}, k_{F}]$ . (c) With finite superlattice potential, an energy gap opens at the Brillouin zone boundary and results in a single partially occupied band at the Fermi energy. Inducing superconductivity at the Fermi energy will result in an effective $p$ -wave superconductor.
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Figure 2
(a) The schematic illustration of a 1D wire with the potential of every third site is modified. (b) The normal state band structure with $t = 1, α_{R} = 0.01 t$ , and $V_{x} = 0.05 t$ . (c) The spectral function $A (ω)$ with parameters as in (b) except $Δ = 0.015 t$ . (d) The topological invariant $N_{BDI}$ of $H_{1D TB}$ . The topological regimes in (c) and (d) coincide.
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Figure 3
(a) Energy spectrum of the 1D system without disorder. The parameters are the same as those in Fig. 2. (b) Energy spectrum of the 1D system with on-site disorder. The disorder strength is uniformly distributed from $- 10 Δ$ to $10 Δ$ , where $Δ$ is the superconducting gap. It is evident that the topological phase with higher chemical potential is more robust against disorder than the topological phase with lower chemical potential.
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Figure 4
(a) Organic molecules on the top of the Au(111) surface where Au is grown on top of an $s$ -wave superconductor. (b) The outer (green) and inner Fermi (blue) circles in the superlattice Brillouin zone. The square indicates in reduced Brillouin zone due to superlattice potential. (c) The band closing and reopening at the $X$ point, as a function of $V_{z}$ . The chemical potential $μ = - 3.3 t$ and $V_{z c} = 0.026 t$ denotes the critical value of $V_{z}$ at which the band gap closes. (d) The energy spectrum of the Au surface with the square superlattice potential. The tight-binding model $H_{2D TB}$ used is described in Appendix pp2 with $α_{R} = 0.2 t, Δ = 0.02 t$ , and $V_{z} = 0.05 t$ . The superlattice is chosen such that the $N_{Chern}$ is $- 2$ . It is evident that there are two crossings at zero energy corresponding to the two zero-energy Majorana modes at each edge. (e) $N_{Chern}$ of $H_{2D TB}$ as a function of the chemical potential for a fixed superlattice configuration.
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Figure 5
(a) The schematic illustration of organic molecules, denoted by the disks, on the Au(111) surface. The local potential energy of the Au under the molecules is modified. A hexagonal unit cell with 16 Au sites, used in the tight-binding model, is shown. (b) The hexagon denotes the reduced Brillouin zone due to the superlattice potential. The superlattice is chosen such that the $M$ points touch the Fermi surface of the outer Rashba band. (c) The energy spectrum of a superconductor with $N_{Chern} = 3$ . The superconductor is obtained by adding superconductivity $Δ = 0.03 t$ and a Zeeman field $V_{z} = 0.1 t$ to a system with reduced Brillouin zone given in (b). (d) $N_{Chern}$ as a function of the chemical potential for a fixed superlattice configuration.
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