quantum heterostructures group: a research overvie · 2003. 9. 4. · 1.530 1.535 1.540 1.545 1.550...
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Quantum Quantum HeterostructuresHeterostructures Group: Group: A Research Overview
Emilio Mendez
NTT Basic Research LaboratoriesJuly 30, 2003
A Research Overview
Goal: Discover and Elucidate Quantum Phenomena forNovel Optical and Electronic Devices
GoalGoal: Discover and Elucidate : Discover and Elucidate Quantum Phenomena forQuantum Phenomena forNovel Optical and Electronic DevicesNovel Optical and Electronic Devices
Fernando CaminoJames Dickerson (Columbia U.)Elvira Gonzalez ( U. Madrid)Vladimir KuznetsovYiping Lin (NTT BRL)A. K. NewazBent NielsenJ. K. Son (Samsung)Woon Song
External CollaboratorsF. Agullo-Rueda, CSIC, SpainA. Allerman, Sandia National Lab.B. Bennett, Naval Research Lab.R. Magno, Naval Research Lab.S. Manotas. CSIC, Spain
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Recent ResearchRecent Research
•• Optical Properties of Semiconductor Microcavities(J. Dickerson and J. K. Son)
•• Electronic Vertical Transport in Type II Heterostructures(Y. Lin and E. M. Gonzalez)
•• Electronic Noise in Mesoscopic Systems(F. Camino, V. Kuznetsov, A.K. Newaz, J. K. Son, W. Song)
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Semiconductor MicrocavitesSemiconductor Microcavites
-
IntroductionIntroduction
Physics of semiconductor multilayers has been successful in mimicking atomic systems.Analog to the Fabry-Perot, two-level atom system is the microcavity.Interaction between the electromagnetic mode and the two-level atom yields Rabi splitting, Ω.
Two LevelAtom
Fabry-Perot Cavity
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Quantum Quantum --Well Well MicrocavityMicrocavity
G a A s
W e l l
λ/ 2 C a v i t y
S u b s t r a t e
p –t y p e A l A s / A l G a A sT o p M i r r o r
n –t y p e A l A s / A l G a A sB o t t o mM i r r o r
λ/ 4 L a y e r
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A Quantum A Quantum WellWell in a in a MicrocavityMicrocavity
DBR
DBR
K λ/2
E1
H1
E1 + H1 = EXCITON
+ =EXCITON CAVITY POLARITON
Rabi Splitting
λ λ
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Tuning Resonance ConditionTuning Resonance Condition
1 .4 8 1 .4 9 1 .5 0 1 .5 1 1 .5 2
R a b i S p lit t in g Ω
M ix e dP o la r ito n
M o d e s
R e s o n a n c e
A t R e so n a n c eE C a v ity = E E x c ito n
Q u a n tu mW e ll
M o d e
C a v ityM o d e
N o R e s o n a n c e
Ref
lect
ivity
(a.u
.)
E n e r g y (e V )
• Effective Cavity Length– Tapered cavity– Angle of incidence
• Exciton Energy– Temperature– Electric Field
0.800 0.804 0.808 0.812
Detu
ning
λ (µm)
3λ/2
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1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58
Ref
lect
ivity
(a.u
.)
Energy (eV)
Reflectivity of a QuantumReflectivity of a Quantum--WellWell--MicrocavityMicrocavity
80 100 120 140 160 180 200 220 240
1.520
1.525
1.530
1.535
1.540
1.545
1.550
1.555
1.560
Cavity
Heavy HoleLight Hole
Ω2 = 4.1meV
Ω1 = 6.7meV
Ener
gy (e
V)
Temperature (K)
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How to Enhance Rabi Splitting?How to Enhance Rabi Splitting?
Rabi Splitting proportional to• Exciton oscillator strength (∝binding energy)• Number of oscillators per unit length
??p-typ e AlAs / AlGaAs
M i r r o r
n-type AlAs / Al GaAs
M i r r o r
GaAs / AlGaAsS u p e r l a t t i c e
Recipe:• increase density
of quantum wells• make wells narrow
Contradictory?
λ/2 C a v i t y
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Semiconductor Quantum Wells and Semiconductor Quantum Wells and SuperlatticesSuperlattices
E1
H1
EgW
CB
EgB
VB
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Superlattice Regime
Coupled QW regime
Isolated QW regime
ElectricElectric--field Induced Localizationfield Induced Localization
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Reflectivity of Reflectivity of SuperlatticeSuperlattice--MicrocavityMicrocavity
1.46 1.48 1.50 1.52 1.54
5KStep
313K
188K
Ref
lect
ivity
(a.u
.)
Energy (eV)180 200 220 240 260 280 300 320
1.47
1.48
1.49
1.50
1.51
1.52
1.53
1.54
Ω1 = 9.5meV
Ω1
X0
C
Ene
rgy
(eV
)
Temperature (K)
E ≠ 0
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Reflectivity of Reflectivity of SuperlatticeSuperlattice--MicrocavityMicrocavity
1.46 1.48 1.50 1.52 1.54
5KStep
313K
188K
Ref
lect
ivity
(a.u
.)
Energy (eV)180 200 220 240 260 280 300 320
1.47
1.48
1.49
1.50
1.51
1.52
1.53
1.54
Ω1 = 9.5meV
Ω1
X0
C
Ene
rgy
(eV
)
Temperature (K)
E ≠ 0
Ω2 = 6.9meV
Ω2
X+1
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Reflectivity of Reflectivity of SuperlatticeSuperlattice--MicrocavityMicrocavity
1.46 1.48 1.50 1.52 1.54
5KStep
313K
188K
Ref
lect
ivity
(a.u
.)
Energy (eV)180 200 220 240 260 280 300 320
1.47
1.48
1.49
1.50
1.51
1.52
1.53
1.54
Ω1 = 9.5meV
Ω1
X0
C
Ene
rgy
(eV
)
Temperature (K)
E ≠ 0
Ω2 = 6.9meV
Ω2
X+1
E ≈ 15 kV/cm
X-1X+1 X0 X-1X+1 X0
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Photocurrent from Photocurrent from SuperlatticeSuperlattice MicrocavityMicrocavity
0 10 20 30 40 501.53
1.54
1.55
1.56
1.57
1.58
1.59
1.60
1.61
1.52 1.54 1.56 1.58 1.60 1.62
1 µA
0º
5º
10º15º
20º
25º
30º
35º40º
V = +0.25 Volts E ≈ 29 kV/cm T = 80 K
Phot
ocur
rent
(a.u
.)
Energy (eV)
50º
Heavy Hole
Light Hole
Cavity
∆ hh = 11.5 meV∆ lh = 7.2 meV
Dip
Ene
rgy
(eV
)
Angle (º)
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Summary of Rabi SplittingsSummary of Rabi Splittings
2
3
4
5
6
7
8
9
10
11
12
13
0 20 40 60 80 100
2
3
4
5
6
7
8
9
10
11
12
13
T = 80 K Heavy Hole Light Hole
Rab
i Spl
ittin
g (m
eV)
Electric Field (kV/cm)
1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0
Large Angle Small Angle
Flatband
StarkLadder QCSE
Applied Voltage (V)
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ConclusionConclusion
• When a superlattice is immersed in a microcavity,• there is polariton coupling with individual superlattice
states;• exciton-cavity coupling can be drastically enhanced;• coupling can be tuned by an electric field.
References:Enhancement of Rabi Splitting in a Microcavity with an Embedded Superlattice,J. H. Dickerson, E. E. Mendez, A. A. Allerman, S. Manotas, F. Agulló-Rueda,
and C. Pecharromán, Phys. Rev. B 64, 155302 (2001).Electric Field Tuning of the Rabi Splitting in a Superlattice-Embedded Microcavity, J. H. Dickerson, J. K. Son, E. E. Mendez, and A. A. Allerman, Appl. Phys. Lett. 81, 803 (2002).
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Vertical Transport in Type II (InAs/GaSb) Heterostructures
Vertical Transport in Type II (InAs/GaSb) Heterostructures
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InAs/AlSb/GaSb SystemInAs/AlSb/GaSb System• Nearly-matched lattice constant ~ 6.1 Å• Versatile band lineups
– Straddling (AlSb/GaSb)– Staggered (InAs/AlSb)– Broken-gap (InAs/GaSb)
GaSbAlSb
InAs
0.812.300.41Eg (eV)What’s Special About this System?
• Coexistence of electron and hole gases• Advantages of InAs
– small me* (0.023 m0), larger g* (-15)– no Schottky barrier with metals
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InAs/AlSb/GaSb Type II InAs/AlSb/GaSb Type II QWsQWsEn
ergy
(meV
)
InAsInAs
AlSb
GaSb
AlSb
60Å
H0
E0E0
EF
Ideally,2Ne = NhIdeally,2Ne = Nh
T = 300K
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3-4
-2
0
2
4
Cur
rent
(mA
)
Voltage (V)
Is it Possible toObserve
Rashba Splitting?
??
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Evidence for Two Kinds of 2D GasesEvidence for Two Kinds of 2D Gases
0 1 2
T = 4.2K
0o
15o
θ = 20o
Cond
ucta
nce
(arb
. uni
ts)
Perpendicular Magnetic Field (T)
2D Electrons2D ElectronsNe = 5 – 7 ×1011 cm-2
. . ... .
0 2 4 6 8 10 12
θ = 90o
50 %
∆σ
/σ0
Magnetic Field (T)
θH
2D Holes2D Holes
electronsholes
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Vertical Vertical ShubnikovShubnikov -- de Haas Oscillationsde Haas Oscillations
0 2 4 6 8 10
20
40
60
80
ν = 4ν = 6
Cond
ucta
nce
(mS)
Magnetic Field (T)
0 2 4 6 8 10 12 14
34
36
38
40
ν = 6 ν = 4
0 2 4 6 8 10 12 140
40
80
120
160
ν = 6 ν = 4
75 Å GaSb
80 Å GaSb
GaSb
H⊥
0.25 0.50 0.75 1.00 1.25 1.50
System B60 Å GaSb
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MagnetotunnelingMagnetotunneling between 2D Gasesbetween 2D Gases
E0
L4
E0’
L3 0.0 0.5 1.0 1.5 2.0
0.08
0.12
0.16
0.0 0.5 1.0 1.5 2.0
0.02
0.04
0.06Con
duct
ance
(S)
Magnetic Field (T)
0∆ ≠
0∆ =Δ
-
• For gases with slightly different Ns, at low fields,
tunneling between states with ∆L ≠ 0 is favored
InIn--plane Momentum Conservation?plane Momentum Conservation?
0 2 4 6 8 10
∆L=0 ∆L=1 ∆L=2 ∆L=3
Cond
. (ar
b. u
nit)
Magnetic Field (T)
-
Comparison Between Theory and ExperimentComparison Between Theory and Experiment
0 2 4 6 8 10
Cond
. (ar
b. u
nit)
Magnetic Field (T)
ΔL=2ΔL=1
ΔL=0
-
0.0 0.5 1.0 1.5 2.0
0.08
0.12
0.16
0.0 0.5 1.0 1.5 2.00.09
0.12
0.15
0.0 0.5 1.0 1.5 2.0
0.02
0.04
0.06
Cond
ucta
nce
(S)
Magnetic Field (T)
8 7 6 5 4 3 20.0
0.1
0.2
8 7 6 5 4 3 20.00
0.05
0.10
0.15
8 7 6 5 4 3 20.00
0.05
0.10
Cond
ucta
nce
(S)
Filling Factor (ν)
Effect of 2DEG Asymmetry
7.1×1011 cm-2
7.6×1011 cm-2
6.6×1011 cm-2
((ΔΔN ~ 1% NN ~ 1% Naveave))
Naverage
-
0.00
0.04
0.08
0 2 4 6 8 10 12 140.00
0.04
0.08
T = 4.2 K
5/28 6 3
ν = 4
T = 1.7 K
Con
duct
ance
(S)
Magnetic Field (T)
High-field Magnetotunneling
N = 2 N = 13
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MagnetotunnelingMagnetotunneling at Very High Magnetic Fieldsat Very High Magnetic Fields
0 5 10 15 20 25 3020
40
60
80
100
120
140
160
180
2002 3/2 15/23468
Filling FactorT
unne
ling
Con
duct
ance
(arb
. uni
ts)
Magnetic Field (T)
V = 0
V = 12 mV
T = 0.5K
0 5 10 15 20 25 3020
40
60
80
100
120
140
160
180
2002 3/2 15/23468
Filling FactorT
unne
ling
Con
duct
ance
(arb
. uni
ts)
Magnetic Field (T)
-
What is the Origin of the What is the Origin of the νν = 5/2 Minimum?= 5/2 Minimum?
Facts:• Observable only when two 2D electron gases have same density• Observable at high T ( ≤5K), weakly dependent on T• Slightly enhanced by an in-plane magnetic field
Possible (“trivial”) Explanation:• Due to 2D holes with a ν = 5 filling factor, if Nh = 2Ne (ideal)• Unlikely, because:
• in practice, Nh is much less than ideal• holes not present in Shubnikov-de Haas oscillations• large m*h favors strong T dependence of H-induced features
-
ConclusionConclusion
• Beating effects in magneto-conductance oscillations are due to extrinsic asymmetries between 2D electron gases, not to Rashba splitting.
• In symmetric 2D-2D systems, new features are found for non-integer Landau-level occupation, whose origin is still unclear.
References:Magnetotunneling of a Two Dimensional Electron-Hole System Near Equilibrium, E. Gonzalez, Y. Lin, and E. E. Mendez, Phys. Rev. B 63, 033308 (2000).Tunneling Characteristics of an Electron-Hole Trilayer in a Parallel Magnetic
Field, Y. Lin, E.E. Mendez, and A.G. Abanov, Phys. Rev. B. 66, 195311 (2002).Magnetotunneling between Two-dimensional Electron Gases in InAs-AlSb-GaSb Heterostructures, Y. Lin, E. M. Gonzalez, E. E. Mendez, R. Magno, B. R. Bennett, and A. S. Bracker, Phys. Rev. B 68, 035311 (2003).
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Shot Noise in Negative Differential Conductance Devices
Shot Noise in Negative Differential Conductance Devices
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A OneA One--minute Introduction to Shot Noiseminute Introduction to Shot Noise
• Noise: temporal fluctuations of the average current through (or voltage across) a device.
• The magnitude of noise is frequently expressed in terms of thespectral density, that is, the mean of the squared currentfluctuations, δ I(f), per unit bandwidth.
• Thermal Noise: due to thermal agitation, present even if device is in equilibrium.
• Shot Noise: results from the discretenessof the electrical charge; present only when system is out of equilibrium.
ffI
fS∆
=2)(
)(δ
Shot noise measurements can unveil the nature of charge transport, beyond information provided by the electrical conductance.
-
Coexistence of Thermal and Shot NoiseCoexistence of Thermal and Shot Noise
H. Birk et al., Phys. Rev. Lett. 75 1610 (1995).
-
Shot Noise and Fano FactorShot Noise and Fano Factor
If charge transport is a random and independent process (i.e. PoissonianPoissonian), spectral density of current fluctuation is
IqS 2=
TheThe FanoFano factorfactor is defined as
IeSF
2≡
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Two Examples of Shot NoiseTwo Examples of Shot Noise
Normal Metal-Superconductor Tunnel JunctionBecause current flows in terms of Cooper Pairs (Q=2e) and the process is Poissonian,
Single Barrier DiodeBecause charge flow is random and independent, S=2eI and F=1.
22
==Ie
SF
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QuestionQuestion
Can we use noise to differentiate among differenttransport mechanisms in devices that have the same negative differential conductance characteristics ?
We consider three different cases:
Double Barrier Diode
Superlattice Tunnel Diode
Multiple-Quantum-Well Photodiode
-
Quantum-mechanical Effects on Shot Noise• Pauli exclusion principle can make shot noise sub-Poissonian• Fano factor measures deviations from Poissonian process
eISF2
)(ω≡
• In a double-barrier potential,
RΓ
eV
LΓ
2
22
ΓΓ+Γ
= RLF
21
=Γ=Γ FRLIf
1≅Γ>>Γ FRL
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Fano Factor in Resonant Tunneling Diodes
100 200 300 400
0.0
0.2
0.4
0.6Actual Noise
2eI
Resonant-tunneling Diode
T = 4.2K
S I(p
A2 /H
z)
Voltage (mV)
200 250 300 350 4000.5
1.0
1.5
2.0
2.5
Fano
Fac
tor
(S/2
eI)
Voltage (mV)
0 100 200 300 4000.0
0.2
0.4
0.6
0.8
1.0
1.2
100A-40A-100A
T = 4.2K
GaAlAs-GaAs-GaAlAsC
urre
nt (µ
A)
Voltage (mV)
eV1
eV2
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Explanation of Shot Noise Enhancement
Qualitatively
(Iannaccone et al., PRL 80, 1054 (1998)
Enhancement is due to “anticorrelation” effects,when the tail of the density of states isin resonance with the emitter´s band edge.
Quantitatively
Blanter and Buttiker, PRB 59, 10217 (1999)
( )
( )UQJ
Ce
eJ
F
R
∂Γ∂
≡≡Λ
Γ∆Γ−Λ
+=
hh 2
2
2
2
21
Self-consistent calculation of charging effects reveals multi-stability of current and leads to enhancement of shot noise.
Jh response of current to change in potential of the well
-
Superlattice Tunnel DiodeSuperlattice Tunnel Diode
Current starts to flows when small bias is applied.
Superlattices form minibands of bandwidth ∆.
When applied voltage is large enough, the minibands’energygap at the collector blocks tunneling and current drops.
Charge does not accumulate in STD.
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Shot Noise in Superlattice Tunnel DiodeShot Noise in Superlattice Tunnel Diode
0 50 100 150 200 250 3000
5
10
Cur
rent
(µA
)
0 50 100 150 200 250 300
1
2
Voltage (mV)
Superlattice Tunnel Diode
Fano
fact
or
Sample: Central barrier: 102ÅGaAlAs Electrodes: 50 GaAs/GaAlAs periods, each 42 Å / 23ÅFano factor is constant (=1) throughout the applied voltage range.
Throughout positive and negative differential conductance regions, shot noise does not show either enhancement or reductionfrom Poissonian noise.
Song et al., Appl. Phys. Lett. 82, 1568 (2003)
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ConclusionConclusion
Shot-noise measurements can tell whether there is significant quantum-state occupation and net charge accumulation during transport process, in which case the noise power spectrum is non-Poissonian, that is, different from S = 2eI.
References:Shot Noise Enhancement in Resonant Tunneling Structures in a Magnetic Field,
V. V. Kuznetsov, E. E. Mendez, J. D. Bruno, and J. T. Pham, Phys. Rev. B 58, R10159 (1998).Shot Noise in Negative-Differential-Conductance Devices, W. Song, E. Mendez, V. V. Kuznetsov, and B. Nielsen, Appl. Phys. Lett. 82, 1568 (2003).
Quantum Heterostructures Group: A Research OverviewIntroductionQuantum -Well MicrocavityTuning Resonance ConditionReflectivity of a Quantum-Well-MicrocavityHow to Enhance Rabi Splitting?Reflectivity of Superlattice-MicrocavityReflectivity of Superlattice-MicrocavityReflectivity of Superlattice-MicrocavityPhotocurrent from Superlattice MicrocavitySummary of Rabi SplittingsConclusionInAs/AlSb/GaSb SystemInAs/AlSb/GaSb Type II QWsVertical Shubnikov - de Haas OscillationsMagnetotunneling between 2D GasesIn-plane Momentum Conservation?Comparison Between Theory and ExperimentHigh-field Magnetotunneling
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