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Physica E
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N.T. Bagraeva; ∗ , A.D. Bouravleuva , W. Gehlho*b , V.K. Ivanova , L.E. Klyachkina ,
A.M. Malyarenkoa , S.A. Rykova , I.A. Shelykha
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a A.F.
Ioe Physico-Technical Institute, Russian Academy of Sciences, 26 Polytechnicheskaya ul, 194021 St. Petersburg, Russia
b Institut f%
ur Festk%orperphysik, Technische Universit%at, Berlin, Germany
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Spin-dependent single-hole tunneling in self-assembled silicon
quantum rings
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We study the quantum conductance revealed by the quantum wire embedded within one of the arms of the Aharonov–
Bohm (AB) ring that exhibits a weak localisation regime. The AB ring is prepared inside self-assembled silicon quantum
well of the p-type between -barriers on the n-type Si(1 0 0) surface. The coherence of the single-hole transport and negative
magnetic resistance e*ect is demonstrated. The positive=negative transformation of the magnetoresistance is found by the
electrically detected NMR of the 29 Si nuclei in the weakest magnetic 8elds, which seems to be caused by the e*ect of the
nuclear spin polarisation on a weak antilocalisation. ? 2002 Published by Elsevier Science B.V.
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Abstract
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Keywords: Weak localisation; Negative magnetic resistance; Quantum conductance
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Recent applications of the split-gate technique
have enabled the fabrication of clean one-dimensional
(1D) constrictions, where if the mean free path is
longer than the channel length, ballistic conductance
plateaus de8ned by steps of 2e2 =h as a function of
the split-gate voltage are possible to be observed [1].
The fundamental property of 1D channel is the transmission phase shift (TPS), which can be measured
with the Aharonov–Bohm (AB) double-path interferometer [2]. Here we present the p-type AB ring that
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1. Introduction
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Corresponding author. Tel.: +007-812-247-9311; fax: +007812-247-1017.
E-mail address: [email protected]*e.rssi.ru
(N.T. Bagraev).
exhibits the weak localisation regime on the n-type
Si(1 0 0) surface. Using the split-gate technique, the
quantum wire is electrostatically embedded within one
of the AB ring’s arms to prove the coherence of the
single-hole transport and the negative magnetic resistance e*ect that is complementary attributable of a
weak localisation and antilocalisation. Since the AB
ring’s conductance has to be oscillated with a periodicity of a Fux quantum h=e when a variable magnetic
8eld threads its inner core, these AB oscillations seem
to be persisting, if transport through the quantum wire
embedded is coherent. The TPS of the quantum wire
(QW) is found to be equal to . Therefore, the oscillations of the magnetic resistance that are caused
by the gate voltage and the NMR of the 29 Si nuclei
in the weakest magnetic 8elds are of importance to
verify the e*ect of the spin polarisation on a weak
antilocalisation.
1386-9477/02/$ - see front matter ? 2002 Published by Elsevier Science B.V.
PII: S 1 3 8 6 - 9 4 7 7 ( 0 2 ) 0 0 2 7 8 - 3
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2. Methods
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Fig. 2. Schematic description of ultra-shallow boron di*usion
pro8le into Si wafer that contains the self-assembled quantum
well between -barriers heavily doped with boron (a). Equivalent
three-dimensional one electron band scheme (b).
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The AB double-path interferometer used is based on
the self-assembled quantum well (SQW) of the p-type
that was formed between -barriers by the short-time
di*usion of boron from the gas phase into the n-type
Si(1 0 0) surface (Figs. 1 and 2). The parameters of
the SQW were de8ned by the SIMS, STM, cyclotron
resonance (CR) and EPR methods [3]. The di*usion
pro8le depth is equal to 8 nm, whereas the thickness
of the -barriers heavily doped with boron that are
found to exhibit ferroelectrical properties is 3 nm
(Fig. 1b). The SQW, 2 nm, naturally formed between
-barriers contains the high-mobility 2D hole gas
with hole density 0:8 × 1013 m−2 and an elastic free
path L = 15 m at T = 4:2 K. The AB ring created
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Fig. 1. Schematic description of the Si-based double-path interferometer that is de8ned by the microdefect penetrating through
the self-assembled quantum well of the p-type between -barriers
heavily doped with boron.
Fig. 3. Temperature dependence of the resistivity that exhibits
the weak localisation mode of the 1D ring inside self-assembled
quantum well of the p-type which is formed by the -barriers
heavily doped with boron on the n-type Si (1 0 0) surface.
around semi-insulator microdefect, R ≈ 2:5 m, is
formed by electrostatic forces caused by ferroelectrical properties for heavily doped -barriers. The
quantum wire is embedded in the right arm of the
1D ring using the split-gate technique. The additional plunger gate is used to change the concentration of the 2D holes by varying the p+ –n junction
bias (Fig. 1a). The source and drain constrictions
represent QPC, while the number of the highest
occupied mode of the QW inserted in the right-side
arm is controlled by varying the split-gate voltage
(Vg ). The logarithmic temperature dependence of
resistivity has revealed a weak localisation regime
(Fig. 3), which is also veri8ed by the measurements
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of a negative magnetic resistance (Fig. 4). The quantum staircase observed at 77 K is evidence of the
heavy hole’s tunneling through the QW embedded in
the AB ring (Fig. 5a). The high-temperature measurements of the quantum conductance are provided by
the channel length, 1:0 m, and the QW cross-section,
2 nm × 2 nm, which is determined by the SQW width
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Fig. 4. The variations of the resistance with an magnetic 8eld
B applied to the 1D ring inside self-assembled silicon quantum well of the p-type: (a) under di*erent gate voltage applied
to the quantum wire embedded into one arm of the 1D ring;
1 − Ug = 7:5 mV; 2–13 mV; 3–22 mV; (b) by varying the NMR
saturation of the 29 Si nuclei determined by the strength of the microwave 8eld B1 ; Ug = 7:5 mV; B0 = 0:02 mT; f0 = 545 Hz; B1 : 1–
0, 2–0:4 × 10−4 mT, 3–1 × 10−5 mT, 4 –5 × 10−5 mT. The inset
depicts the electrically detected NMR spectrum of the 29 Si nuclei.
Fig. 5. The quantum staircase in zero-magnetic 8eld that is revealed
by heavy holes tunneling through the quantum wire embedded
into one arm of the 1D silicon ring (a). The phase of the AB
oscillations that are taken at speci8ed positions on the quantum
staircase (b). The negative magnetic resistance which is measured
under di*erent gate voltage in magnetic 8eld B = 0:055 mT (c).
and the lateral con8nement due to ferroelectric properties for the -barriers heavily doped with boron.
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3. Results
A weak localisation e*ect is due to the interferences along a closed coherent path between two propagating waves + (R) and − (R), one being the time
reversed of the other increase the back scattering probability by a factor of 2, because these waves come back
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4. Conclusions
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The single-hole transport and the negative magnetic
resistance have been found to be coherent in the studies of the quantum conductance revealed by the quantum wire embedded in the Si-based AB ring in a weak
localisation regime. The e*ect of the hyper8ne interaction between the 29 Si nuclei and the holes inside
the AB ring on the antilocalisation processes has been
revealed by the positive=negative transformation of the
magnetic resistance in weak magnetic 8elds using the
electrically detected NMR technique.
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speci8ed points on the staircase gives rise to the TPS of
the QW. Fig. 5b shows the phase for successive steps
of the quantum staircase, which demonstrates a rise by
near the origin of ballistic plateaus. The single-hole
transport and the negative magnetic resistance e*ect
are seen to be coherent, because the characteristics
shown in Figs. 5b and c correlate with the number of
occupied 1D subbands (Fig. 5a).
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in phase. Therefore, the conductivity along SQW is
decreased (Fig. 3). When a transverse magnetic 8eld
is applied, the time-reversal invariance is broken. The
phase of the two waves around a closed loop is modi8ed by ±2=0 = S=(lB )2 in the same way as in the
A–B experiment, where = BS is the enclosed Fux,
0 = h=e is the Fux quantum, and lB = (h=eB)1=2 is the
magnetic length, and a negative magnetic resistance
is observed (Fig. 4a). However, if a weak antilocalisation that is due to the spin inFuence caused by the
spin–orbit coupling will be taken into account, a positive magnetic resistance seems to be veri8ed in the
weakest magnetic 8elds (Fig. 4a).
Besides, the spin nuclear polarisation can be induced in the weak localisation regime as a result of
the hyper8ne interaction between 29 Si nuclei and the
holes in quantum wells, which decreases additionally
the mobility of holes. The experimental test on the
contribution of this e*ect to the antilocalisation phenomenon represents the magnetic resistance measurements under the NMR saturation of the 29 Si nuclei,
which demonstrate the positive=negative transformation of its value in weak magnetic 8elds (Fig. 4b). The
electrically detected NMR of the 29 Si nuclei exhibits
also the nuclear spin polarisation by the corresponding
shift of the resonance frequency Mf; Mf = 385 Hz,
from well-known value in the weakest magnetic
8elds [4].
Since a magnetic Fux threading the AB ring
with double slit results in an AB phase di*erence
M’=2=0 ; 0 =h=e, between the interfering paths,
the AB oscillations are revealed by the drain–source
current when the QW is being tuned to conduct.
The phase shift of the AB oscillations measured at
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References
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Mace, D.A. Ritchie, Phys. Rev. Lett. 77 (1996) 135.
[2] Schuster, E. Buks, M. Heiblum, D. Mahalu, V. Umansky, H.
Shtrikman, Nature 385 (1997) 417.
[3] N.T. Bagraev, A.D. Bouravleuv, W. Gehlho*, L.E. Klyachkin,
A.M. Malyarenko, S.A. Rykov, Defect and Di*usion Forum
194 –199 (2001) 673.
[4] N.T. Bagraev, L.S. Vlasenko, R.A. Zhitnikov, Zh. Tekh. Fiz.
Pis’ma 4 (1978) 1033.
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