H/T Scaling of the Magnetoconductance in Two Dimensions near the Conductor-Insulator Transition

3 Pages·0.12 MB·English

by  D. Simonian

H/T Scaling of the Magnetoconductance near the Conductor-Insulator Transition
in Two Dimensions.
D. Simonian, S. V. Kravchenko,and M. P. Sarachik
City College of the City University of New York, New York, New York 10031
8 V. M. Pudalov
9 Institute for High Pressure Physics, Troitsk, 142092 Moscow District, Russia
9 (February 1, 2008)
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ForanelectrondensityneartheH =0insulator-to-conductortransition,themagnetoconductiv-
n
ity of the low-temperature conducting phase in high-mobility silicon MOSFETs is consistent with
a
theform∆σ(H ,T)≡σ(H ,T)−σ(0,T)=f(H /T)formagneticfieldsH appliedparalleltothe
J || || || ||
planeoftheelectronsystem. Thissetsavaluableconstraintontheoryandprovidesfurtherevidence
2
that theelectron spin is central to theanomalous H =0 conducting phase in two dimensions.
1

PACS numbers: 71.30.+h, 73.40.Qv
]
n
n
0.0
- Recent experiments [1,2] have demonstrated that the
s
i anomalous conducting phase [3] found in the absence of
d
a magnetic field in two-dimensional electron systems in
.
t silicon metal-oxide-semiconductor field-effect transistors
a
m (MOSFETs) is strongly suppressed by an in-plane mag-
- netic field, H||. For electron densities near the H = 0 -0.5
d transition (i.e. for δn ≡ (ns − nc)/nc << 1, nc ∼
n 1011cm−2),anexternalparallelfieldaslowasH ∼4kOe
||
o )
causes an increase in the resistivity, changing the sign h
c 2/
[ of dρ(T)/dT at low temperatures from positive (metal- (e 2.0
lic) to negative (insulating behavior); the resistivity sat- T)
v2 urates to a constant value for fields H|| above ∼20 kOe, σ(0, -1.0 1.5
indicating that the conducting phase has been entirely -
3 T) h)
1222 qfitlahueyeleednrac.nshugeTpldeph.reoefWstasoeeptsaphlltiahmcvaeeatgicsoonhnneotdwwoucinctothnfiundrrgeutschpptehaercnatsc[4eet]oiitnsthdhtaehetpe2eaDnsudmpeealneegrtcnpltyeortosoiinc-f σ(H,|| -1.5 3579 kkkkOOOOeeee 2∆σ|| (e/ 01..50 T=0.25 K
7
tion of this term and orbital effects associated with the 10 kOe
9
11 kOe 0.0
at/ pHearlpleonsdciilcluatlaiorncsom[5p].onentofthefieldwhichgivequantum 1123 kkOOee 0 H5|| (kOe1)0 15
m Theunexpectedconductingphaseintwodimensionsin 14 kOe
15 kOe
- theabsenceofamagneticfieldhasbeenobservedrecently
d -2.0
for holes in SiGe quantum wells [7] and GaAs/AlGaAs 0.2 0.4 0.6 0.8
n
o heterostructures[8,9,10]. Althoughconsiderablysmaller, T (K)
c a negative magnetoconductance (positive magnetoresis-
: tance) [10,11] found in these systems has also been at-
v tributed to the suppression of the conducting phase. FIG. 1. Magnetoconductivity ∆σ(H||,T) ≡ σ(H||,T) −
Xi Anin-planemagneticfieldaffectsthespinsoftheelec- σ(0,T)versustemperature T forseveral magnetic fields H|| ap-
pliedparalleltotheplaneoftheelectrons. Thesampleisinthecon-
r tronsonly,andhasnoeffectontheirorbitalmotion. The
a ductingphasewithanelectrondensityδ =(ns−nc)/nc =0.10.
quenching of the conducting phase by a magnetic field
Thedotted lines areguides to the eye. Theinset shows the abso-
applied parallel to the plane of the electrons thus pro-
vides strong indication that the electrons’ spins play a lute value of the magnetoconductivity |∆σ(H||,T)| versus H||
at the lowest measured temperature, T =0.25 K. Note the rapid
central role in the anomalous conducting phase in these
two-dimensionalsystems. Wenowdemonstratethatnear increaseof|∆σ(H||,T)|followedbysaturationabove≈13kOe.
the metal-insulator transition, the magnetoconductivity
The maximum mobility of the sample used in these
of the H = 0 conducting phase in high-mobility dilute
experiments was µmax ≈ 25,000 cm2/Vs. The
silicon MOSFETs scales with H/T, obeying the form T=4.2K
conductivity was measured in magnetic fields up to
∆σ(H ,T)≡σ(H ,T)−σ(0,T)=f(H /T). (1) 15 kOe applied parallel to the plane of the electrons.
|| || ||
1
0.0
H=5 kOe
||
7 kOe
9 kOe
100 10 kOe
11 kOe
h) 12 kOe
-0.5 2e/
T)| (
) H,||
2/h 3.0 ∆σ(
(e | 10-1
) 2.5
T
0, -1.0
σ( 2.0
-
T) K)
σ(H,|| T (011..05 100 (gµBH||/kBT)2 101 102
-1.5 0.5 FIG. 3. Magnetoconductance ∆σ(H||,T)versus gµBH||/kBT
on a logarithmic scale for H|| = 5 to 12 kOe (see text).
0.0 The dashed line is a fit to Eq. 7 in Ref. [21], ∆σ(H,T) =
0 gµ H1/k (K) 2 −0.084e2/(πh)γ2(γ2+1)(gµBH/kBT)2. γ2 =1.3.
B || B
∆σ can be collapsed onto a single curve by applying a
-2.0 different multiplicative factor to the abscissa for each
0.2 0.4 0.6 0.81.0 curve, as illustrated in Fig. 2. The scaling parameter T0
T/T
0 isplottedintheinsetasafunctionoftheZeemanenergy,
gµBH||/kB (in Kelvin). Here g is the g-factor (equal to
FIG. 2. The magnetoconductance ∆σ as a function of T/T0. 2 in Si MOSFETs), µB is the Bohr magneton, and kB
TheinsetshowsthescalingparameterT0 plottedasafunctionof is the Boltzmann constant. A power-law fit (shown by
α
gµBH||/kB. (Symbolsfordifferentfields,H||,arethesameasin the solid curve) yields T0 ∝ H||, with α = 0.88±0.03.
α
Fig.1). Apower-lawfit,shownbythesolidcurve,yieldsT0 ∝H We note that H/T scaling of the form Eq. (1) requires
||
with α = 0.88±0.03. The dotted straight line corresponds to thatα=1,correspondingtoT0 =gµBH||/kB (indicated
T0 =gµBH||/kB; deviations fromstraight-linebehavior areat- in the inset by the dotted line). We suggest that the
tributedtosaturationathighfields. deviation of α from unity is associated with the satura-
tion of the magnetoconductance at H|| >∼ 13 kOe shown
Measurements were taken between 0.25 and 0.9 K with
in the inset to Fig. 1, where one might well expect the
the sample immersed in the 3He-4He mixing chamber of
scaling to break down. We therefore exclude the data
a dilution refrigerator. The electron density was set by
setsatthethreelargestfields(forwhichtheproximityof
the gate voltage at ns = 9.43×1010cm−2, placing the the scaling parameter T0 to saturation is apparent). For
sample on the conducting side and near the conductor-
in-plane fields in the range H =5...12 kOe, the absolute
to-insulator transition (nc = 8.57×1010cm−2). In the value of magnetoconductance|,| |∆σ(H )|, is shown as a
||
absenceofamagneticfield,theresistancewas13.9kOhm function of (gµBH||/kBT)2 in Fig. 3. For this range of
at the lowest measured temperature, T =0.25 K.
magnetic fields and for anelectrondensity fairly closeto
The magnetoconductivity, ∆σ(H ,T) = σ(H ,T) − the critical density, the magnetoconductance scales well
|| ||
σ(0,T),isshowninFig.1asafunctionoftemperaturefor with H /T.
||
various fixed values of parallel magnetic field. The mag- Basedonquitegeneralarguments,Sachdev[12]showed
netoconductanceisnegative,itsabsolutevalueincreasing thattheconductivitynearasecond-orderquantumphase
withappliedfieldandwith decreasingtemperature. The transition is a universal function of H/T for a system
noise for small H derives from the subtraction of two with conservedtotal spin. If the magnetoconductanceof
||
large(andcomparable)quantities,σ(H ,T)andσ(0,T). our silicon MOSFET does indeed scale with H/T (the
||
The inset to Fig. 1 shows the absolute value of the mag- dotted straight line in the inset to Fig. 2) rather than
α
netoconductivity as a function of H at a temperature H/T with α 6= 1 (the solid curve), this would imply
||
of 0.25K. The absolute value of magnetoconductance thatspin-orbiteffectsarerelativelyunimportantnearthe
rises rapidly and begins to saturate above ∼ 13 kOe, transition. For a weakly interacting 2D system, Lee and
consistent with earlier measurements [1,2]. The data for Ramakrishnan[13,14]obtainedscalingoftheformEq.(1)
2
associatedwiththenegative|Sz|=1tripletchannelcon- supported by RFBR(97-02-17387)and by INTAS.
tribution to the conductance. We note that the scaling
reported here for the 2D system in silicon MOSFETs is
remarkably similar [15] to the H/T scaling of the mag-
netoconductance observed by Bogdanovich et al. [16] in
three-dimensional Si:B near the metal-insulator transi-
tion, where it was attributed to the mechanism of Ref.
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[14]. H/T scaling is also expected within theories that
Pudalov, Phys.Rev. Lett. 79, 2304 (1997).
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[5] Theresponsetoaperpendicularfieldisconsiderably more
scaling for a relative density δn ≪1 implies that γ2 is at
complicated and has been studied by the authors of Refs.
most a weaklytemperature-dependent quantity near the
[2], [4], and [6].
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|| ||
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This work was supported by the US Department of En- mat/9801006.
ergy under Grant No. DE-FG02-84ER45153. V. P. was [22] P. A.Lee, private communication.
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