Majorana zero mode assisted spin pumping

doi:10.1007/s11467-024-1407-6

Front. Phys.

2024, Vol. 19

Issue (5) : 53207 https://doi.org/10.1007/s11467-024-1407-6

Majorana zero mode assisted spin pumping

Mingzhou Cai¹, Zhaoqi Chu¹, Zhen-Hua Wang², Yunjing Yu¹, Bin Wang¹(

), Jian Wang^1,³(

)

¹. State Key Laboratory of Radio Frequency Heterogeneous Integration, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
². College of Physics and Electronic Engineering, and Center for Computational Sciences, Sichuan Normal University, Chengdu 610068, China
³. Department of Physics, The University of Hong Kong, Hong Kong, China

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Abstract

We present a theoretical investigation of Majorana zero mode (MZM) assisted spin pumping which consists of a quantum dot (QD) and two normal leads. When the coupling between the MZM and the QD is absent, d.c. pure spin current can be excited by a rotating magnetic field where low energy spin down electrons are flipped to high energy spin up electrons by absorbing photons. However, when the coupling is turned on, the d.c. pure spin current vanishes, and an a.c. charge current emerges with its magnitude independent of the coupling strength. We reveal that this change is due to the formation of a highly localized MZM assisted topological Andreev state at the Fermi level, which allows only the injection of electron pairs with opposite spin into the QD. By absorbing or emitting photons, the electron pairs are separated to opposite spin electrons, and then return back to the lead again, generating an a.c. charge current without spin polarization. We demonstrate the switching from d.c. pure spin current to a.c. charge current based on both Kitaev model and a more realistic topological superconductor nanowire. Although this switching can also be induced by partially separated Andreev bound state (ps-ABS) in the topological trivial phase, it is extremely unstable and highly sensitive to the Zeeman field, which is different from the switching induced by MZM. Our result suggests that quantum spin pumping may be a feasible local transport method for detecting the presence of MZMs at the ends of a superconducting nanowire.

Keywords Majorana zero mode spin pumping

Corresponding Author(s): Bin Wang,Jian Wang

Issue Date: 22 May 2024

Cite this article:

Mingzhou Cai,Zhaoqi Chu,Zhen-Hua Wang, et al. Majorana zero mode assisted spin pumping[J]. Front. Phys. , 2024, 19(5): 53207.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-024-1407-6
https://academic.hep.com.cn/fop/EN/Y2024/V19/I5/53207

Fig.1 Schematic structure of topological superconducting nanowire assisted spin pumping system. A rotating magnetic field (

B

) is applied to the QD, and spin resolved quantum transport is measured through left (

L

) and right (

R

) semi-infinite metallic leads which are Ohmic-contacted to the QD. The QD is also coupled to one end of a topological superconducting nanowire with coupling strength equal to

λ

. MZMs indicate two zero energy modes located at both ends of the wire, and

? M

is the coupling strength between the two MZMs.

Fig.2 (a)

I ↑

(solid curves) and

I ↓

(dash curves) versus

μ

with different

λ

when

? M = 0

. The other parameters are

? d

= 0,

ω = 0.1

θ

π / 2

and

Γ L = Γ R = 0.1

. (b)

I c

versus time in one period of rotating magnetic field with different

B 0

when

λ ≠ 0

and

? M = 0

. (c)

I ↑

(solid curves) and

I ↓

(dash curves) versus

μ

with different

λ

when

? M ≠ 0

. Peaks appear at

μ = ± ? M / 2

. (d) Ordinary fermion assisted

I c

(black dashed line) and

I s

(black solid curve) with

λ = 0.005

and

β = 0

;

I s

(blue solid curve) with

λ = 0.005

and

β = 0.001

;

I s

(red solid curve) with

λ = 0.01

and

β = 0.001

. For (b?d), the other used parameters are the same as those in (a).

Fig.3 DOS of the QD (left panels) and the corresponding schematic plot of MZM assisted spin pumping (right panels) when

λ = 0

for (a) and (b);

λ = 0.001

and

? M = 0

for (c) and (d);

λ = 0.001

and

? M = 0.01

for (e) and (f).

Fig.4

I s

and

I c

of the spin pumping device coupled by a TSC nanowire when

V Z > Δ

or an ordinary superconducting nanowire when

V Z < Δ

. The fixed parameters are

Δ = 0.04

θ = π / 2

ω = 0.1

Γ L = Γ R = 0.1

? d = 0

α R = 0.02

, and

λ = 0.002

. In (a) and (b),

B 0

is fixed to 0.05, and

V Z

is changed to 0.06 (red curve), 0.05 (blue curve) and 0.03 (black curve). The dash line in (a) indicates the zero value. In (c) and (d), both

V Z

and

B 0

are changed. In (c), (

V Z, B 0

) is assumed to be the following values (0.05, 0.03) (red curve); (0.05, 0.05) (blue curve); (0.03, 0.05) (black curve). In (d), (

V Z, B 0

) is assumed to be the following values (0.05, 0.05) (red curve); (0.03, 0.05) (blue curve); (0.03, 0.03) (black curve).

Fig.5 ps-ABSs assisted spin pumping. (a) Energy spectrum of a superconducting nanowire with a long-range parabolic potential versus

V z / Δ

; (b) zoom in of (a) near the quasi-zero modes; (c) distribution of a pair of ps-ABSs

ξ A

and

ξ B

V Z / Δ = 1.475

; (d) distribution of a pair of MZMs

ξ A

and

ξ B

V Z / Δ = 3.0

. In (c) and (d), the light-yellow covered region from left to right describes the parabolic potential with maximum value equal to

Δ

. (e)

I s

and

I c

of the spin pumping device coupled by one end of superconducting nanowire with

V Z / Δ

; (f)

I s

and

I c

at one of the sharp peak in (e). The black dash line indicates the zero value. The parameters are

V Z / Δ = 1.472

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