Pairing-dependent superconductivity gap and nonholonomic Andreev reflection in Weyl semimetal/Weyl superconductor heterojunctions

Jun Fang, Wenye Duan, Junfeng Liu, Chao Zhang, and Zhongshui Ma

Phys. Rev. B 97, 165301 – Published 4 April 2018

Abstract

We study superconductivity states mediated by the BCS and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairings in superconducting Weyl semimetals. It is found that a mixture of BCS and FFLO pairings results in a distinctive double-gap structure for superconducting states. With a heterojunction of a Weyl semimetal and a superconducting Weyl semimetal, we demonstrate the nonholonomic Andreev reflection and show that the intra- and internode Andreev reflections increase at the edges of the effective gap. The influence of interface potentials on the Andreev reflections is investigated. The conductance spectra arising from the mixed superconducting pairings is also analyzed.

Received 16 March 2017

DOI:https://doi.org/10.1103/PhysRevB.97.165301

Physics Subject Headings (PhySH)

Andreev reflection FFLO Weyl fermions

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jun Fang¹, Wenye Duan¹, Junfeng Liu², Chao Zhang³, and Zhongshui Ma^1,4

¹School of Physics, Peking University, Beijing 100871, China
²Department of Physics, South University of Science and Technology of China, Shenzhen 518055, China
³School of Physics, University of Wollongong, New South Wales 2522, Australia
⁴Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

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Vol. 97, Iss. 16 — 15 April 2018

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Images

Figure 1
(a) The spectra of a SWSM with a mixture of BCS and FFLO pairings, in which the curved cerise and ultramarine surfaces are, respectively, for $β = + 1$ and $β = - 1$ . (b) and (c) The general view of the effective superconducting gaps $Δ_{eff}^{(+)}$ and $Δ_{eff}^{(-)}$ , where $Δ_{F} + Δ_{B} = 1.5 Δ_{0}$ is used in the calculation. (d) The cross-sectional views of $Δ_{eff}^{(\pm)}$ at the value $Δ_{0}$ . (e) Effective gap vs $θ$ at $Δ_{F} = 0.5 Δ_{0}$ .
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Figure 2
The energy dispersion of a BdG Hamiltonian. The red (blue) solid lines are the electron part of the Weyl nodes local at $K_{+}$ ( $K_{-}$ ), and the red (blue) dashed lines are the hole part of the Weyl nodes located at $K_{+}$ ( $K_{-}$ ). (a) and (b) are for the FFLO and the BCS pairings, respectively, where the directions of the group velocities of the reflected electrons or holes are marked by the arrows. For an electron incident from state $a$ , the normal reflected electron is reflected to state $b$ , while AR is reflected to $c$ (for a FFLO pairing) or $c^{'}$ (for a BCS pairing). (c) and (d) are the top views of the normal reflected electron and the Andreev reflected hole in the WSM region. The incidence angle and the normal reflection angle are $θ$ , and the AR angle is $θ^{'}$ .
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Figure 3
The transport coefficients as functions of the incident angle $θ$ and energy $E$ (in units of $Δ_{0}$ ). (a) $R_{+ +}^{e} = {|r_{+ +}^{e}|}^{2}$ , the normal reflection in $K_{+}$ ; (b) $R_{+ +}^{h} = {|r_{+ +}^{h}|}^{2}$ , AR in $K_{+}$ ; (c) $R_{- +}^{e} = {|r_{- +}^{e}|}^{2}$ , the normal reflection in $K_{-}$ ; and (d) $R_{- +}^{h} = {|r_{- +}^{h}|}^{2}$ , AR in $K_{-}$ . The parameters used in the calculations are $μ = 10 Δ_{0}, Δ_{F} = 0.5 Δ_{0}$ , and $Δ_{B} = Δ_{0}$ .
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Figure 4
The influence of the interface configurations on the transport coefficients (a)–(d) for the intra-SIP and (e)–(h) for the inter-SIP. (a) and (e) The normal reflection in $K_{+}$ , (b) and (f) AR in $K_{+}$ , (c) and (g) the normal reflection in $K_{-}$ , and (d) and (h) AR in $K_{-}$ . The parameters used in the calculations are $θ = π / 6, μ = 10 Δ_{0}, Δ_{F} = Δ_{0}, Δ_{B} = 0.5 Δ_{0}$ .
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Figure 5
The angle-resolved conductance. The parameters used in the calculations are $μ = 10 Δ_{0}, Δ_{F} = 0.5 Δ_{0}$ , and $Δ_{B} = Δ_{0}$ .
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Figure 6
Contour plot of the ratio $G^{tot} / G_{0}$ with different interface configurations (a)–(c) for the intra-SIP and (d)–(f) for the inter-SIP. (a) and (d) The co-occurrence of the BCS and FFLO superconducting pairings ( $Δ_{F} = Δ_{0}$ and $Δ_{B} = 0.5 Δ_{0}$ ), (b) and (e) the pure FFLO superconducting pairings ( $Δ_{F} = Δ_{0}$ and $Δ_{B} = 0$ ) and (c) and (f) the pure BCS superconducting pairings ( $Δ_{F} = 0$ and $Δ_{B} = Δ_{0}$ ). The chemical potential is taken as $μ = 10 Δ_{0}$ .
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