SLIDE 1
Georgia State University, Atlanta, GA USA
Microwave-induced transport Transport characteristics of the microwave driven 2D negative magneto-conductivity state
QT2DS-Luchon – 5/28/2015
SLIDE 2 I I
B = [4/(4j+1)] Bf 1. A 2DES device 2. Low temperature, ~ 1.5 K 3. Weak magnetic field 4. Low energy photons, f
Radiation-induced zero-resistance-states in the 2DES
f Bf = 2π f m*/e
j = 1, 2, 3…
- R. G. Mani et al., Nature 420, 646, (2002)
- M. A. Zudov, R. R. Du, L. N. Pfeiffer, and K. West, Phys. Rev. Lett. 90, 046807 (2003).
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60 120 4 8 12 B (mT) 0.5 K R
xx (Ω)
Low B transport: GaAs/AlGaAs heterostructure
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60 120 4 8 12 B (mT) 0.5 K f = 50 GHz R
xx (Ω)
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60 120 4 8 12 B (mT) 0.5 K f = 50 GHz R
xx (Ω)
60 120
0.00 0.15 0.30 w/ radiation R
xy (kΩ)
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60 120 4 8 12 Bf = 2πf m*/e B (mT) 0.5 K f = 50 GHz R
xx (Ω)
60 120
0.00 0.15 0.30 w/ radiation R
xy (kΩ)
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60 120 4 8 12 Bf = 2πf m*/e
4/9 Bf
B (mT) 0.5 K f = 50 GHz R
xx (Ω)
60 120
0.00 0.15 0.30 4/5 Bf w/ radiation R
xy (kΩ)
Bf
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Other interesting experimental features
SLIDE 9 dark w/ microwaves Plateaus disappear
ZRS
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Re-entrant IQHE under microwave excitation
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Questions: What is the mechanism that produces the radiation-induced magnetoresistance oscillations ?
SLIDE 12 Theories for the radiation-induced magnetoresistance oscillations
- displacement theory: microwaves modify impurity scattering: σph
(1)
T-independent
Ryzhii … ’03, Durst et al., PRL ’03
- inelastic theory: microwaves change the distribution function: σph
(2)
⇒ ∝ τin , strongly T-dependent
Dmitriev et al., Dorozhkin
claim: σph
(2)/σph (1) ~ τin /τq >> 1 for relevant T
- radiation-driven electron orbit model: σp
(3)
exact treatment of harmonic oscillator under microwave photo-excitation + perturbative treatment of elastic scattering:
Inarrea and Platero, PRL ‘05
- non-parabolicity model: σp
(4)
photo-conductivity arises for linearly polarized radiation in a non-parabolic system
Koulakov and Raikh, PRB ’03
- Others: Shepelyansky, Chepelianskii, Rivera & Schulz, Mikhailov etc.
SLIDE 13 Common characteristic of some theories:
- Prediction of negative magnetoresistivity/magnetoconductivity
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Negative resistivity Inelastic model Negative resistivity Displacement model
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Non parabolicity model for obtaining magneto-resistance oscillations
Negative magnetoconductivity
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Experiment shows zero resistance… Theory says negative resistivity… Question: How do the negative resistivity/conductivity states transform into experimentally observed zero-resistance states?
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- Negative resistivity is unstable!
- Assume: the resistivity is a function of current
- Currents are set-up such that the resistance
vanishes
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0.0 0.5 1.0 1.5 2.0 2.5 ρ
xx (Ω)
0.000 0.050 0.100 0.150 0.200
0.0 0.5 1.0 1.5 2.0 2.5 ZRS Rxx (Ω) B (Tesla) ZRS
Negative resistivity → zero-resistance Current domain theory:
Unstable
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Why is negative resistivity/conductivity unstable? Answer: negative resistivity/conductivity is like negative differential resistivity/conductivity. Gunn diode device unstable towards oscillations
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However, negative resisitivity/conductivity in the presence of a magnetic field is not the same as negative resistivity / conductivity at B=0 Due to huge Hall effect in high mobility GaAs/AlGaAs
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Negative magnetoresistivity/conductivity has not been encountered before by experiment →signature of the negative magnetoresistivity / conductivity state is unknown What are the magneto-transport characteristics of a 2DES driven to negative magnetoresistivity/conductivity? Here: simulations to address this question
SLIDE 22 V I
+
y
xx
V
xy
Measurement configuration
SLIDE 23 V I
+
x y
xx
V
xy
Measurement configuration
Simulate potential distribution within a Hall bar device
SLIDE 24 Simulation ∇.J = 0 J = σ E σ = 2D conductivity tensor
- Solution of laplace equation in finite difference form
- Boundary condition: current injected at the current contacts
restricted to flow within conductor Influential parameter in simulations is the Hall angle tan θH = σxy/σxx
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0.0 0.5 1.0 5 10 15 20 0.0 0.5 1.0
0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10
5 10 15 20 20 40 60 80 100
θH = 00 B = 0
V = 1 V = 0
Bar length to width ratio = 5
Results
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0.0 0.5 1.0 5 10 15 20 0.0 0.5 1.0
0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10
5 10 15 20 20 40 60 80 100
θH = 600
V = 1 V = 0 Results
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0.0 0.5 1.0 5 10 15 20 0.0 0.5 1.0
0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10
5 10 15 20 20 40 60 80 100
θH = 88.50
V = 1 V = 0 Results
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How to simulate the negative conductivity state? Influential parameter in simulations is the Hall angle tan θH = σxy/σxx Positive conductivity: 00 ≤ θH < 900 Negative conductivity: 900 ≤ θH < 1800 → Compare potential profile for θH < 900 with potential profile for θH > 900
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0.0 0.5 1.0 5 10 15 20 0.0 0.5 1.0
0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10
5 10 15 20 20 40 60 80 100
θH = 88.50
V = 1 V = 0
σxx = +0.025σxy
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0.0 0.5 1.0 5 10 15 20 0.0 0.5 1.0
0.40 0.50 0.60 0.70 0.30 0.80 0.20 0.90 0.10
5 10 15 20 20 40 60 80 100
θH = 91.50
V = 1 V = 0
σxx = -0.025σxy
SLIDE 31 0.0 0.5 1.0 5 10 15 20 0.0 0.5 1.0
0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10
5 10 15 20 20 40 60 80 100 0.0 0.5 1.0 5 10 15 20 0.0 0.5 1.0
0.40 0.50 0.60 0.70 0.30 0.80 0.20 0.90 0.10
5 10 15 20 20 40 60 80 100
θH = 88.50 θH = 91.50 x y σxx = -0.025σxy σxx = 0.025σxy RXX always positive! Sign reversal in Hall effect
SLIDE 32 0.000 0.050 0.100 0.150 0.200
0.0 250.0 500.0 Rxy (Ω) B (Tesla) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Rxx (Ω) negative conductivity regime
Transport Expectations for neg. conductivity / resistivity regime:
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Summary: Negative magneto conductivity / resistivity should lead to positive resistance along with sign reversal in the Hall effect. No instability in a positive resistance???
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Acknowledgements: MBE material by Prof. W. Wegscheider Part 1 with Dr. Annika Kriisa Part 2 with Dr. Tianyu Mark Ye Funding by the DOE, BES and the Army Research Office
