Photo-spintronics of spin-orbit active electric weak links
We show that a carbon nanotube can serve as a functional electric weak link performing photo-spintronic transduction. A spin current, facilitated by strong spin-orbit interactions in the nanotube and not accompanied by a charge current, is induced in a device containing the nanotube weak link by cir...
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Shekhter, R.I. Entin-Wohlman, O. Jonson, M. Aharony, A. 2021-01-26T07:49:05Z 2021-01-26T07:49:05Z 2017 Photo-spintronics of spin-orbit active electric weak links / R.I. Shekhter, O. Entin-Wohlman, M. Jonson, A. Aharony // Физика низких температур. — 2017. — Т. 43, № 8. — С. 1137-1140. — Бібліогр.: 7 назв. — англ. 0132-6414 PACS: 71.70.E, 75.70.Tj, 75.76.+j https://nasplib.isofts.kiev.ua/handle/123456789/174618 We show that a carbon nanotube can serve as a functional electric weak link performing photo-spintronic transduction. A spin current, facilitated by strong spin-orbit interactions in the nanotube and not accompanied by a charge current, is induced in a device containing the nanotube weak link by circularly polarized microwaves. Nanomechanical tuning of the photo-spintronic transduction can be achieved due to the sensitivity of the spinorbit interaction to geometrical deformations of the weak link. This work was partially supported by the Swedish Research Council (VR), by the Israel Science Foundation (ISF) and by the infrastructure program of Israel Ministry of Science and Technology under Contract No. 3-11173. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Low dimensionality and inhomogeneity effects in quantum matter Photo-spintronics of spin-orbit active electric weak links Article published earlier |
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Photo-spintronics of spin-orbit active electric weak links |
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Photo-spintronics of spin-orbit active electric weak links Shekhter, R.I. Entin-Wohlman, O. Jonson, M. Aharony, A. Low dimensionality and inhomogeneity effects in quantum matter |
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Photo-spintronics of spin-orbit active electric weak links |
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Photo-spintronics of spin-orbit active electric weak links |
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photo-spintronics of spin-orbit active electric weak links |
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Shekhter, R.I. Entin-Wohlman, O. Jonson, M. Aharony, A. |
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Shekhter, R.I. Entin-Wohlman, O. Jonson, M. Aharony, A. |
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Low dimensionality and inhomogeneity effects in quantum matter |
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Low dimensionality and inhomogeneity effects in quantum matter |
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Физика низких температур |
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We show that a carbon nanotube can serve as a functional electric weak link performing photo-spintronic transduction. A spin current, facilitated by strong spin-orbit interactions in the nanotube and not accompanied by a charge current, is induced in a device containing the nanotube weak link by circularly polarized microwaves. Nanomechanical tuning of the photo-spintronic transduction can be achieved due to the sensitivity of the spinorbit interaction to geometrical deformations of the weak link.
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Photo-spintronics of spin-orbit active electric weak links / R.I. Shekhter, O. Entin-Wohlman, M. Jonson, A. Aharony // Физика низких температур. — 2017. — Т. 43, № 8. — С. 1137-1140. — Бібліогр.: 7 назв. — англ. |
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AT shekhterri photospintronicsofspinorbitactiveelectricweaklinks AT entinwohlmano photospintronicsofspinorbitactiveelectricweaklinks AT jonsonm photospintronicsofspinorbitactiveelectricweaklinks AT aharonya photospintronicsofspinorbitactiveelectricweaklinks |
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Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 8, pp. 1137–1140
Photo-spintronics of spin-orbit active electric weak links
R.I. Shekhter1, O. Entin-Wohlman2,3, M. Jonson1,4, and A. Aharony2,3
1Department of Physics, University of Gothenburg, SE-412 96 Göteborg, Sweden
E-mail: mats.jonson@physics.gu.se
2Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
3Physics Department, Ben Gurion University, Beer Sheva 84105, Israel
4SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK
Received January 18, 2017, published online June 26, 2017
We show that a carbon nanotube can serve as a functional electric weak link performing photo-spintronic
transduction. A spin current, facilitated by strong spin-orbit interactions in the nanotube and not accompanied by
a charge current, is induced in a device containing the nanotube weak link by circularly polarized microwaves.
Nanomechanical tuning of the photo-spintronic transduction can be achieved due to the sensitivity of the spin-
orbit interaction to geometrical deformations of the weak link.
PACS: 71.70.Ej Spin-orbit coupling, Zeeman and Stark splitting, Jahn-Teller effect;
75.70.Tj Spin-orbit effects;
75.76.+j Spin transport effects.
Keywords: spin-orbit interactions, spintronics.
1. Introduction
Spintronics is a rapidly developing research area of
modern solid state physics. In contrast to traditional elec-
tronics, where the electric charge of electrons is in focus,
the field of spintronics relies on another fundamental prop-
erty of electrons, viz. their magnetic moment, which is as-
sociated with their spin degree of freedom.
Issues related to the electrical control of spin currents as
well as to spin control of charge currents are at the heart of
spintronics research today, both from a fundamental and an
applied perspective [1]. Recently it has been suggested that
such controls may be effectively implemented in nano-
devices containing an electric weak link with strong spin-
orbit interactions (SOI) that bridges bulk electrodes [2–4].
In [2] it was demonstrated that a spin-orbit coupling results
in a “splitting” of the spin of electrons passing through
such a weak link (Rashba spin splitting), which under cer-
tain conditions may generate a spin current. This was
shown to occur if an imbalance of the population of spin
states in the electrodes is established by spin-flip assisted
electronic transitions due to the absorption (or emission) of
circularly polarized photons created by microwave pump-
ing [5]. The SOI-induced spin generation inside the weak
link makes it a point-like source of a spin current due to a
photo-spintronic effect on the nanometer length scale. Es-
timations show, however, that if the SOI is caused by an
external electric field, as implicitly assumed in [2], that
field has to be quite strong for the induced Rashba spin
splitting to be significant. The aim of the present work is to
demonstrate that a much stronger photo-spintronic trans-
duction effect can be achieved if a material with an intrin-
sic SOI, here assumed to be induced by stresses, is used for
the weak link.
The precise form of the stress-induced SOI depends on
the material used for the electric weak link and the type of
strains involved. In a single-wall carbon nanotube, which
will be considered here, the strain can be thought of as
occurring when a graphene ribbon is rolled up to form a
tube. The strain-induced SOI in a simple one-dimensional
model of such a nanotube is described by the Hamiltonian
strain strain
so so
ˆ ˆ= ,F k ⋅n v σ (1)
where Fv is the Fermi velocity, strain
sok is a phenomenolog-
ical parameter that gives the strength of the SOI in units of
inverse length, σ is a vector whose components are the
Pauli matrices , ,x y zσ , and n̂ is a unit vector pointing along
the longitudinal axis of the nanotube in the direction of
electron propagation ( ˆˆ =n k ). Equation (1), which was used
in Ref. 3, is a simplified form of the SOI Hamiltonian previ-
ously derived for a realistic model of such a nanotube [6].
© R.I. Shekhter, O. Entin-Wohlman, M. Jonson, and A. Aharony, 2017
mailto:mats.jonson@physics.gu.se
R.I. Shekhter, O. Entin-Wohlman, M. Jonson, and A. Aharony
The SOI active weak-link device shown in Fig. 1 com-
prises a nanowire that bridges two bulk electronic reser-
voirs. The spin-orbit interaction described by Eq. (1) is
restricted to the nanowire and has the effect of scattering
the spins of electrons that pass through the wire. Following
the approach developed in Refs. 2–4 we will describe the
transfer of electrons through the nanowire-based weak link
with the help of a spin-dependent tunnel Hamiltonian.
Hence, the total Hamiltonian of the system can be written
as a sum of three parts,
ˆ ˆ ˆ ˆ= ,L R T+ + (2)
where
†
( ) ( ) ( )( )
( )
ˆ =L R k p c c σσ
σ
ε∑ k pk p
k p
(3)
are Hamiltonians that describe the electrons in the left and
right leads. These electrons are characterized by the mo-
mentum quantum numbers k and p, respectively, and by
the spin projection on the ẑ -axis. We label the latter by
= 1σ ± , so that the spin projections are = /2s σ . The tun-
nel Hamiltonian is expressed in terms of the probability
amplitudes , ,[ ]W ′σ σp k for electron transmission through
the wire,
†
, ,
, ,
ˆ = ( [ ] h. .).T c W c c′σ σ σ′σ
′σ σ
+∑∑ p k kp
k p
(4)
These amplitudes have to be calculated taking the spin
dynamics given by Hamiltonian (1) into account.
2. Spin-biased electric weak link
Electronic transport through the weak link shown in
Fig. 1 can be induced in a number of different ways. The
standard method would be to apply a voltage bias V across
the link, so that the chemical potentials for electrons in the
left and right reservoirs are shifted by a small amount eV
with respect to each other. The result of such charge bias-
ing is that excess charge of opposite polarity is accumulat-
ed on either side of the link, which leads to an electrical
current through the link in a direction that counters the
bias-induced charge imbalance.
Another method, which will be in focus here and which
is illustrated in Fig. 1, is to arrange for the chemical poten-
tial to be different for the two possible projections of the
electron spin along a certain axis. Such spin biasing can be
achieved by illuminating the entire device with circularly-
polarized microwave radiation of a frequency that enables
electron spin-flip assisted photon absorption. This photonic
pumping of the electronic spin creates an imbalance be-
tween the number of electrons with opposite spin projec-
tions on an axis defined by the direction of the radiation
and leads to a spin-dependent shift in the chemical poten-
tials for electrons with opposite spin projections. The mag-
nitude of the shift, which extends throughout the device,
depends on the intensity of the radiation and on the spin
relaxation rate. If we assume that the SOI, which is re-
stricted to the weak link, is the dominant spin relaxation
mechanism the SOI becomes a source of a spin current,
which flows out of the weak link into the two reservoirs and
which counteracts the spin pumping. Referring to Fig. 1, we
note that both the orientation of the plane that contains the
weak link with respect to the pumped spin orientation and
the bending angle of the link can be used to tune the gener-
ated spin current.
The spin bias U can be defined by noting that for
ˆ = 0T the electron spin reservoirs are described by Fer-
mi–Dirac distributions with different chemical potentials,
†
ˆ( ) ( ) ( )( ) =0= = ( ),FT
f c c nσ
σ σσ〈 〉 ε −µk p k p k pk p (5)
where
= /2, = 1,Uσµ µ −σ σ ± (6)
and µ is the chemical potential of both leads at equilibri-
um. The spin current generated by electrons tunneling out
of the SOI-active weak link can be obtained as the time
derivative of the total spin, Ŝ〈 〉 , of the electrons,
spin
= 1
ˆˆ
= = ,
2
dd SJ
dt dt
σ
σ ±
〈 〉 σ
〈 〉∑
(7)
where
†
( ) ( )( )
( )
ˆ ˆ ˆ ˆ= , = .L R L R c cσ σ σ σ σσ+ ∑ k pk p
k p
(8)
Fig. 1. (Сolor online) Schematic picture of the device considered.
A bent nanowire with a strong spin-orbit interaction bridges two
bulk reservoirs. The bent nanowire is modeled by two equal-
length straight wire segments which form angles θ and −θ with
the x̂ -axis, respectively, while the plane that contains the nan-
owire is tilted by an angle γ away from the ŷ -axis towards the ẑ-
axis. The device is irradiated by circularly-polarized microwave
radiation (wavy arrows) that creates a difference in the population
of spin-up and spin-down electrons (thick vertical arrows) corre-
sponding to a “spin biasing” of the device. Spin-flip transitions
induced by the spin-orbit interaction in the nanowire create a spin
current spin spin spin= L RJ J J+ traveling out from the wire with a
magnitude that depends on the angles θ and γ .
1138 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 8
Photo-spintronics of spin-orbit active electric weak links
A straightforward calculation of the spin current (7) can be
done using the tunnel Hamiltonian (1) to lowest order in
perturbation theory [2]. Then, one finds for the spin con-
ductance spinG (defined in analogy with the electrical con-
ductance G) the relation
spin spin= / for 0.G J U U → (9)
3. Rashba spin splitting as a source of spin generation
in an SOI active weak link
In order to calculate the spin current given by Eq. (7) one
needs to evaluate the electronic transmission amplitudes
, ,[ ]W ′σ σp k , which appear in the tunnel Hamiltonian (4), and
specifically their dependence on the spin-orbit interaction as
given by Eq. (1). In our simple model the weak link consists
of two straight parts of equal length | |=| | = /2L R dR R
joined by a bend. Neglecting the momentum (but not the spin)
dependence, the probability amplitude for an electron of ener-
gy E to pass from, say, the left to the right lead can be written
as a product of five factors,
= ( , ) ( , ) .R R L LW T G E G E TR R (10)
Here W is a 2×2 matrix in spin space, ( )L RT is the proba-
bility amplitude to tunnel from the wire to the left (right)
lead and is the transfer matrix through the bend in the
wire. In Ref. 4 the Green’s function ( )( ; )L RG ER for the
straight segments of the wire, in which the SOI interaction
takes place, was evaluated for a Hamiltonian of the form
2 2
*
ˆ = ( ) .
2
k
m
+ ⋅Q k
σ (11)
A comparison with Eq. (1) shows that in the present case
strain
so ˆ( ) = F kQ k nv . Hence, from Eqs. (A12) and (A13) of
Ref. 4 we conclude that
( ) 0 ( )( , ) = ( , )L R L RG E G E ×R R
( )ˆ[cos( ) sin( ) ],L Ri× α − α ⋅n σ (12)
where we have used the short-hand notation strain
so /2k d ≡ α,
which is a measure of the strength of the SOI, and where
2*
0 ( ) 0 0 ( )( , ) = ( / ) exp[ | |],L R L RG E i m k ikπR R (13)
with 2 1/2*
0 = (2 / )k m E , is the propagator on the left
(right) segment in the absence of SOI. It follows that we
can factor out the dependence on the SOI and write the
amplitude given by Eq. (10) as
0= ,W W (14)
where
0 0 0= (| |, ) (| |, )R R L LW T G E G E TR R (15)
is the SOI-independent part and
ˆ ˆ= [cos( ) sin( ) ][cos( ) sin( ) ]R Li iα − α ⋅ α − α ⋅n n σ σ (16)
contains the effect of the SOI.
In our geometry the ẑ -axis is the spin quantization ax-
is, and the bent wire lies in a plane that (i) contains the
x̂-axis and (ii) is rotated by an angle γ away from the ŷ-axis
towards the ẑ -axis. In the plane of the wire, the left
(right) straight leg of the wire forms an angle θ (−θ) with
the x̂-axis. In other words,
ˆ ˆ ˆ ˆ= cos( ) sin( )[cos( ) sin( ) ],L θ + θ γ + γn x y z
ˆ ˆ ˆ ˆ= cos( ) sin( )[cos( ) sin( ) ] ,R θ − θ γ + γn x y z (17)
which means that we can write Eq. (16) in a matrix form,
= ,W A i− ⋅B σ (18)
where
2 2 ˆ ˆ= ( ) ( )cos sin R LA α − α ⋅ =n n
2 2= ( ) ( ) cos(2 ) ,cos sinα − α θ (19)
and
2ˆ ˆ ˆ ˆ= sin( ) cos( )( ) ( )sinR L R Lα α + + α × =B n n n n
2ˆ ˆ= sin(2 )cos( ) sin ( )sin(2 )sin( )α θ − α θ γ +x y
2ˆ sin ( )sin(2 )cos( ) .+ α θ γz (20)
Hence, the probability for a SOI-induced spin-flip transi-
tion is
2 2 2| | = | | | |x yw B B↑↓ ↑↓≡ + =
2 2 4 2 2= sin (2 )cos ( ) sin ( )sin (2 )sin ( ) .α θ + α θ γ (21)
The spin conductance can now be expressed in terms of the
spin-flip probability w↑↓ as
spin 2= ( , ).
/
GG w
e ↑↓ θ γ
(22)
Equations (21) and (22) represent the main results of the
paper. The strength of the SOI, characterized by the di-
mensionless parameter strain
so= /2k dα , determines the
amount of photo-spintronic transduction that can be
achieved by the studied Rashba spin-splitter device. The
sensitivity of the effect to the geometry of the experimental
set-up opens the possibility for tuning the device nano-
mechanically, by varying the angles γ and θ. The depend-
ence of the spin conductance on these experimentally ac-
cessible device parameters is illustrated in Figs. 2 and 3.
The photo-spintronic transduction occurs even for a
straight wire (i.e., when = 0θ ). However, wire deformation
provides a tool for a nanomechanical control of the gener-
ated spin current. Depending on the strength of SOI cou-
pling α, both a monotonic and a non-monotonic depend-
ence of the dimensionless spin-conductance w↑↓ on
mechanical deformations can be achieved.
Figure 2 illustrates that the dimensionless conductance,
w↑↓ , is an oscillatory function of the angle γ . As is clear
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 8 1139
R.I. Shekhter, O. Entin-Wohlman, M. Jonson, and A. Aharony
from Eq. (21), the maximal [minimal] value, m ( )axwα θ
m[ ( )]inwα θ , of = ( )w w↑↓ ↑↓ γ is achieved when the normal
to the plane containing the nanowire weak link is perpendicu-
lar [parallel] to the spin quantization axis, i.e. when = / 2γ ±π
[ = 0γ or π] and therefore 2( ) = 1sin γ 2[ ( ) = 0]sin γ , inde-
pendent of the values of α and θ.
For a strong enough SOI, i.e., when 2sin ( ) 1/2α ≥ , the
largest possible value, max ( ) = 1wα θ , is reached when the
bending angle is = αθ θ , where 2 2cos ( ) = 1/[2sin ( )]αθ α ,
as illustrated in Fig. 3. On the other hand, for 2sin ( ) < 1/2α
the effect is smaller since then 2
max ( ) < sin (2 ) < 1wα θ α .
4. Conclusions
In this paper we have shown that a nanowire, in which
the electrons are subjected to a spin-orbit interaction (SOI),
can be used as a functional electric weak link between
SOI-inactive leads and serve as an essentially point-like
source of a spin-current induced by circularly-polarized
microwave radiation. This spin current is not accompanied
by a charge current. The possibility to concentrate such
“pure” spin-currents at the nanometer length scale suggests
novel spintronic devices.
Whether realistic applications are feasible crucially de-
pends on how strong a photo-spintronic effect can be real-
ized in practice, which in turn depends on the strength of
the SOI that can be achieved. Consider, for instance, a sin-
gle-wall carbon nanotube. Its strain-induced SO energy
gap strain
so∆ has been measured to be around 0.4 meV [7].
Since strain strain
so so= 2 F k∆ v , this value corresponds to
strain 6
so 0.4 10k ≈ ⋅ m–1 for 60.5 10F ≈ ⋅v m/s. For nanowire
lengths d of the order of a µm, strain
sok d can therefore be of
order 1, which is large enough to allow the dimensionless
spin conductance to be tuned near to its maximal value
= 1w↑↓ .
This work was partially supported by the Swedish Re-
search Council (VR), by the Israel Science Foundation
(ISF) and by the infrastructure program of Israel Ministry
of Science and Technology under contract 3-11173.
1. D.D. Awschalom, L.C. Bassett, A.S. Dzurak, E.L. Hu, and
J.R. Petta, Science 339, 1174 (2013).
2. R.I. Shekhter, O. Entin-Wohlman, and A. Aharony, Phys.
Rev. Lett. 111, 176602 (2013); R.I. Shekhter, O. Entin-
Wohlman, and A. Aharony, Phys. Rev. B 90, 045401 (2014).
3. R.I. Shekhter, O. Entin-Wohlman, M. Jonson, and A.
Aharony, Phys. Rev. Lett. 116, 217001 (2016).
4. R.I. Shekhter, O. Entin-Wohlman, M. Jonson, and A.
Aharony, Fiz. Niz. Temp. 43, 368 (2017) [Low Temp. Phys.
43, 309 (2017)].
5. K. Koyama and H. Merz, Z. Physik B 20, 131 (1975); M.
Wohlecke and G. Borstel, Phys. Status Solidi B 106, 593
(1981).
6. M.S. Rudner and E.I. Rashba, Phys. Rev. B 81, 125426
(2010); K. Flensberg and C.M. Marcus, Phys. Rev. B 81,
195418 (2010).
7. F. Kuemmeth, S. Ilani, D.C. Ralph, and P.L. McEuen,
Nature 452, 448 (2008).
Fig. 2. The dimensionless spin conductance ( , )w↑↓ θ γ defined in
Eqs. (21) and (22), plotted as a function of the tilt angle γ of the
plane that contains the nanowire weak link (see Fig. 1). The spin
conductance oscillates between a maximal value max ( )wα θ and a
minimal value min ( )wα θ , which both depend on the bend angle θ
and the strength α of the spin-orbit interaction in the wire. Here
= = /4α θ π for which max ( ) = 0.75wα θ and min ( ) = 0.50wα θ .
Fig. 3. The maximal value max ( )wα θ of the dimensionless spin
conductance ( , )w↑↓ θ γ [obtained for 2sin ( ) = 1γ ] and the minimal
value min ( )wα θ of ( , )w↑↓ θ γ [obtained for 2sin ( ) = 0γ ] plotted as
functions of the nanowire bend angle θ defined in Fig. 1. The two
pairs of curves are for two different values of the spin-orbit inter-
action strength α in the nanowire: the upper pair pertains for
= /3α π , for which 2sin > 1/2α , and the lower one pertains for
= /8α π , for which 2sin ( ) < 1/2α . Note that when 2sin ( ) 1/2α ≥
the maximal spin conductance max ( )wα θ reaches the value 1 for
2 2cos ( ) = 1/[2sin ( )]θ α . When 2sin ( ) < 1/2α both max ( )wα θ and
min ( )wα θ decrease monotonically from 2sin (2 )α to 0.
1140 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 8
1. Introduction
2. Spin-biased electric weak link
3. Rashba spin splitting as a source of spin generation in an SOI active weak link
4. Conclusions
|