Electrically-detected single-spin resonance with Quantum Spin Hall edge states F. Delgado1and J. Fern andez-Rossier23 1Instituto de estudios avanzados IUDEA Departamento de F sica

2025-05-03 0 0 900.66KB 5 页 10玖币

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Electrically-detected single-spin resonance with Quantum Spin Hall edge states

F. Delgado1and J. Fern´andez-Rossier2,3

1Instituto de estudios avanzados IUDEA, Departamento de F´ısica,

Universidad de La Laguna, C/Astrof´ısico Francisco S´anchez, s/n. 38203, La Laguna and

2International Iberian Nanotechnology Laboratory (INL),

Av. Mestre Jos´e Veiga, 4715-310 Braga, Portugal ,

(Dated: October 7, 2022)

Detection is most often the main impediment to reduce the number of spins in paramagnetic

resonance experiments. Here we propose a new route to carry out electrically-detected spin resonance

of an individual spin, placed at the edge of a quantum spin Hall insulator (QSHI). The edges of

a QSHI host a one dimensional electron gas with perfect spin-momentum locking. Therefore, the

spin relaxation induced by emission of an electron-hole pair at the edge state of the QSHI can

generate current. Here we demonstrate that driving the system with an AC signal, a nonequilibrium

occupation can be induced in the absence of applied bias voltage, resulting in a DC measurable

current. We compute the DC current as a function of the Rabi frequency Ω, the spin relaxation

and decoherence times, T1and we discuss the feasibility of this experiment with state of the art

instrumentation.

PACS numbers: 73.22.Pr, 73.43.Cd, 76.30.-v

I. INTRODUCTION

The sensitivity limit of commonly available electron

paramagnetic resonance (EPR) spectrometers is in the

range of 1013 spins1. This number can be dramatically

reduced in taylored set-ups2. In some special systems,

such as NV-centers, permit one to carry out single-spin

resonance using optical readout, made possible both by

the fact that NV centers are very good single-photon

emitters and their photon yield is spin dependent.3Us-

ing spin-to-charge conversion, electrically detected single

spin resonance has been demonstrated for defects in ﬁeld

eﬀect-transistors,4quantum dots5,6 and single dopants in

silicon.7Electrically detected single spin resonance with

subatomic spatial resolution has been also demonstrated8

using scanning tunneling microscopy (ESR-STM).

Here we explore the spin-locked edges states of a two

dimensional Quantum Spin Hall insulator9,10 (QSHI) to

accomplish the electrical readout of the spin resonance of

an individual spin sitting on the edge. The edge states of

QSHI are predicted to have a one-to-one relation between

the propagation direction and the spin orientation along

a system-dependent spin quantization axis, see Fig. 1.

As a result, pumping spin along this axis entails elec-

trical current ﬂow. As we discuss below, if a externally

pumped localized spin is exchange coupled to the spin-

locked edges, it will generate a DC current.

Experimental evidences of the spin-locked edge states

in QSHI are indirect. In the absence of magnetic impuri-

ties, edge states should have no backscattering and there-

fore a quantized conductance is expected.11–13 Values of

conductance close to 2e2/h were reported in HgTe/CdTe

quantum wells14 and 1T’ WTe2.15,16 In addition, coher-

ent propagation along the edge with scattering proper-

ties consistent with strong suppression of backscatter-

ing have been observed in bismuth bilayers,17,18 and in

bismuth nanocontacts19. Very relevant for the ensuing

Driving Frequency w

DC Current

Bac(t)

e- h+

FIG. 1. Scheme of the device proposed for the electrically-

detected single spin detection. A local spin Sis exchange

coupled to one edge state of a QSHI, where momentum di-

rection and spin orientation are locked, see left inset. When

the system is under the action of an external AC magnetic

ﬁeld with frequency ωand intensity determined by the Rabi

rate Ω, a frequency-dependent non-equilibrium steady state

occupation is established (see right inset), where one of the

spin transitions ∆Szis favored. This, in turns, leads to a net

DC electrical current along the QSHI edge.

discussion, experiments where magnetic atoms interact

with edge states in bismuth bilayer and produced back-

scattering have been demonstrated20.

The interplay between local spins and the spin-locked

edge states of a QSHI has been widely studied theo-

retically 21–37. Several physical realizations of the lo-

cal spin have been considered, including a conﬁned elec-

tron in a quantum dot29,35, nanomagnets,28 magnetic

atoms,26,27 spin chains36, nuclear spins,25,33,37 and mag-

netic molecules32. Early works focused on the Kondo

eﬀect,21,24 and the inﬂuence of magnetic impurities on

conductance22. More recent works have addressed spin-

pumping of local moments at the edges by the helical-

electron spin current.26–29,31,32,34 The reverse problem,

pumping DC current by an external AC excitation of

arXiv:2210.02917v1 [cond-mat.mes-hall] 6 Oct 2022

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Electrically-detectedsingle-spinresonancewithQuantumSpinHalledgestatesF.Delgado1andJ.Fernandez-Rossier2;31InstitutodeestudiosavanzadosIUDEA,DepartamentodeFsica,UniversidaddeLaLaguna,C/AstrofsicoFranciscoSanchez,s/n.38203,LaLagunaand2InternationalIberianNanotechnologyLaboratory(INL),Av.MestreJo...

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Electrically-detected single-spin resonance with Quantum Spin Hall edge states F. Delgado1and J. Fern andez-Rossier23 1Instituto de estudios avanzados IUDEA Departamento de F sica

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