1. Topological Transport in Sb Quantum WellsTopological Transport in Sb Quantum Wells
Shayne CairnsShayne Cairns
University of Oklahoma, NormanUniversity of Oklahoma, Norman
Homer L. Dodge Department of PhysicsHomer L. Dodge Department of Physics

2. Outline

Topological Insulators
– Theory Discussion
– Previous Experiments
– Sb as a Topological Insulator

Growth of Sb thin films

Device Processing of Sb thin films
– Hall Bar devices

Sb thin film magneto-transport experiments
– Zero Field, Low Field, High Field
• Conclusion

3. Types of Solids in Condensed
Matter
Conductors and Insulators
Consider the topology of the bands → New type of insulator?
Topology is related to Genus

4. Topology and Genus
Genus- Counts the number of holes
Doughnut and Coffee cup
– Topological Invariance
Analog to Genus → Chern Number
Hasan and Kane RMP 82, 3045
g=0
g=1

5. Quantum Hall State
2DEG with applied magnetic field
Insulating interior with conducting edge states
Chern number corresponds to number of edge
states along one edge
Can we get a similar system
without a magnetic field?
E
Position

6. Time Reversal Symmetry
No Spin-Orbit Coupling With Spin-Orbit Coupling
-π/a π/a -π/a π/a

7. Z2
Topological Insulator
Hasan and Kane RMP 82, 3045
Even number of crossings → n=0; Trivial topology
Odd number of crossing → n=1; Non-trivial topology

8. Parity Method for Determining Z2
invariant
Liu and Allen PRB 52, 1566 (1995)
Fu and Kane PRB 76,
045302 (2007)

9. Why so important?
Impervious to weak disorder
No Anderson Localization
Back-scattering Suppressed
Spin Polarized Edge/Surface States
Spintronics
Potential for Majorana Fermions
Applications in Quantum Computing
Linear Dispersion
Graphene like

10. First Proposed 2D TI
HgTe/CdTe QWs
CdTe – Typical
Ordered Bandstructure
HgTe – Inverted
Bandstructure
Bandstructure of HgTe
evolves depending on
well thickness →
Critical Thickness dc
Bernevig et al., Science,
314, 1757 (2006)-cited
1,533

11. First Observed 2D TI
HgTe Quantum Wells
Konig et al. Science, 318,
766 (2007)-cited 1,425
Device I- Insulator
Device II-IV -TI
Device III and IV show
expected quantized
conductance
Device II – Phase
breaking length
Device Length Well Width
I 20 um 5.5 nm
II 20 um 7.3 nm
III 1 um 7.3 nm
IV 1 um 7.3 nm
Critical thickness = 6.3 nm

12. First Proposed 3D TI
Kane, Princeton Summer School (2010)

13. Experimental Realization
Angled-Resolved PhotoEmission Spectroscopy
Iowa State Spectroscopy Group

14. Experimental Realization Cont.
Hsieh et al., Science 323, 919 (2009)
Bi-Sb alloy- ARPES spectrum
Γ K
M
Number of Fermi level
crossings → Odd; Non-
trivial topology
White lines are a guide to
the eye
The arrows indicate spin
polarization, green line is a
constant energy cut for S-
ARPES

15. Outline

Topological Insulators
– Theory Discussion
– Previous Experiments
– Sb as a Topological Insulator

Growth of Sb thin films

Device Processing of Sb thin films
– Hall Bar devices

Sb thin film magneto-transport experiments
– Zero Field, Low Field, High Field
• Conclusion

16. Topological Nature of Sb
Semi-metal with
Trivial Topology
Narrow gap
insulator with Non-
Trivial Topology
Semi-metal with
Non-Trivial
Topology
Kane, Princeton Summer School (2010)
Sb is a topological semi-metal

17. Previous Experiments on Bulk Sb
Hsieh et al. Science 323 919 (2009)
Seo et al. Nature 466 343 (2010)
ARPES
STM
Semi-metallic bulk shorts out
topological surface states.
Our experiments reduce the
bulk conduction by quantum
confinement

18. Band Structure of Sb Films
Zhang et al. PRB 85 201410(R) (2012)

19. Motivation for Ultra Thin Film Sb

Potentially rich phase diagram

Elemental TI → simple stoichiometry

Compatibility with III-V MBE

Potential integration with semi-
conductors

20. MBE Growth Stack
Thin film Sb structures
Δt ranges from 2 to 16 BL
Sb films grown on GaAs
and GaSb substrates
Sb (111) and GaSb(111)
surface have only a 0.1%
lattice mismatch
GaSb cap (optional)
N-GaSb (111)A Substrate
GaSb buffer
Δt Sb(111)
GaSb cap (optional)
SI-GaAs (111) Substrate
GaSb buffer
Δt Sb(111)
Growth History I Growth History II

21. Growth History I
GaAs(111) Substrates (Summer 2011 – July 2012)
~40 samples grown by Chomani Gaspe
Initial growth procedure → Lack of thickness
control
Modified procedure 1
– Fixed substrate temperature at 300 C
Modified procedure 2
– Fixed substrate temperature at 280 C

22. Thickness Calibration on GaAs
1nm
4.1 nm
GaSb buffer
GaSb cap
4.5 nm
Sb layer
Hole
Image taken by Tetsuya Mishima
T461-40 sT445-60 min

23. Van der Pauw Method
Allows for quick measurement of samples without
processing
Works on arbitrary geometry
Square samples → Simplifies resistance
calculation
Hall Measurement → Carrier Density
Calculation of mobility

24. Temperature Dependence on GaAs
Films show metallic or
insulating behavior
depending on
thickness
Films below 2.0 nm →
Appears to be a
percolation
transition

25. T530: GaSb/GaAs
Growth Quality Evaluation
T528: GaSb/Sb/GaSb/GaAs
Voids in buffer layer
propagate through
subsequent top layers
T537b: Sb/GaSb/GaAs
Images taken by Joel Keay
1um

26. Growth History II
GaSb(111) Substrates (Fall 2012 – present)
Samples grown by Chomani Gaspe and Kaushini
Wickramasinghe
Series 1- Wafer Tech substrates (August 2012 – Nov 2012)
Substrate temperature ~185 C
Limited supply
Series 2-Chinese substrates (Nov 2012 – Oct 2013)
Poor quality
Series 3-Wafer Tech (Nov 2013 - Feb 2014)
Exhausted supply → Need replacements
Series 4-Galaxy Wafer (Feb 2014 - present)

27. Growth on GaSb vs GaAs
substrates
Buffer Layer Growth
GaAs substrate GaSb substrate
Surface- Bi-layer stepping for
capped 3.6 nm Sb film

28. Device Processing Fabrication of Hall Bars
Photolithography-Use UV light to
expose a photosensitive
resist through an optical
mask to define mesa
Wet Etching-Use an aqueous
solution of HF, H2
O2
, and
Lactic Acid to etch mesa into
sample
2nd
layer of photolithography-
Define contact areas
Contact Deposition-Thermally
evaporate In on sample and
lift-off photoresist
Bonding and Packaging-Hall bars
are cleaved into smaller
pieces using Tempress
scriber and pasted into
headers to be wire bonded
using K&S wedge bonder

29. Initial Testing of Devices
Problems with device at 77K
– Resistance larger on processed devices compared
to unprocessed devices
– Step by Step failure analysis → Developer source
of problem; Etching sample
Solutions
Kapton Mask
Thicker Cap

30. Experiment Overview
Zero Field Conductance
Low Field Magneto-transport
High Field Magneto-transport
Nano-wire Devices

31. Conductance vs Film Thickness
Reduced conduction
when compared to a
bulk like film
Residual
conductance at zero
film thickness points
toward surface
conduction
Conductance shows
discontinuity below ~
2 nm
20 K

32. Important Points
1. Conductance vs Thickness plot shows residual
surface conductivity
2. Transition in conductance of films as a function of film
thickness in good agreement with theory

33. Quantum Interference
Wave Nature of Electrons
Classical Probability vs. Quantum Probability
Quantum Phase → Interference Effects
Relevant for paths less than phase
breaking length

34. Localization
Electrons travel in closed
path trajectory
WL
WAL
Increased probability to return to origin
Weak Localization
Include Spin Orbit Interaction
Weak Anti-Localization

35. Theoretical Model for WL/WAL
HLN Model – Hikami, Larkin, Nagaoka
Application to Topological Insulators
– Reduction of Backscattering
– α = -0.5 per conducting channel
• Two channels → αTI
= -1
Hikami, Larkin, Nagaoka, Prog Theo Phys (1980) 63 (2)

36. Low Field Magneto-resistance:
Weak Anti-localization
Strong WAL around zero
field
WAL signal decreases with
increasing temperature →
Change in phase breaking
length
1.8 nm film

37. WAL Fitting Procedure
Background subtraction- Linear or Parabolic
Plot conductivity correction for fitting to HLN
model
HLN model for WAL is a good fit
for film thicknesses between
2 – 6 nm and temperatures below
15 K
2.3 nm film

38. Phase breaking length is close to T-1/2
dependence at high
temperatures but saturates below 1K
Temperature dependence indicates main dephasing
mechanism is electron-electron scattering
2.3 nm film
Phase Breaking Length
Temperature Dependence
Symbols
larger than
error bars

39. HLN Parameters vs. Film Thickness
Pre-factor α is ~ 1/2 regardless of film thickness → Surface
coupling through bulk
Measurements on other 3D TIs show varying values of α
Phase breaking length at 300mK shows little dependence on
thickness

40. Important Points
1. Conductance vs Thickness plot shows residual
surface conductivity
2. Transition in conductance of films as a function of film
thickness in good agreement with theory
3. WAL parameters independent of film thickness

41. Magneto-transport Theory
Drude Model
Classical Effect → Steady State; Drift Velocity &
Scattering Time
Parabolic Field Dependence
• B2
Field dependence compared to Drude model
• Classical Magneto-resistance

42. Tilted Field Measurements
Plots collapse onto each other →
2D conduction
3.6 nm
5.8 nm

43. Important Points
1. Conductance vs Thickness plot shows residual
surface conductivity
2. Transition in conductance of films as a function of film
thickness in good agreement with theory
3. WAL parameters independent of film thickness
4. Tilted field magneto-transport data shows 2D
conduction

44. Monotonic evolution
from parabolic to
sub-linear field
dependence as a
function of
decreasing film
thickness
High Field Magneto-resistance
Shifted for clarity

45. Linear Magnetoresistance Theories
Abrikosov
Silver Chalcogenides
Linear Dispersion
Extreme quantum limit
– All states in lowest Landau level
Carrier density too large to reach this limit
Wang & Lei
Linear dispersing material with overlapping Landau
levels
Sign of linear magnetoresistance depends on sign of
g-factor
Antimony is expected to have a negative g-factor
Abrikosov PRB 58, 2788 (1998)
Wang and Lei PRB 86, 035442 (2012)

46. High Field MR Model
Model resistance as two parallel channels
Bulk channel with classical MR ~RB(1+μ2
B2
)
Surface channel with WAL (Rs, Lφ)
Four parameters (RB
, RS
, μ, Lφ)
Rs, Lφ are experimentally determined and held constant
RB
and μ varied with thickness
Resulting model quantitatively mimics observed high field MR

47. Important Points
1. Conductance vs Thickness plot shows residual
surface conductivity
2. Transition in conductance of films as a function of film
thickness in good agreement with theory
3. Tilted field magneto-transport data shows 2D
conduction
4. WAL parameters independent of film thickness
Point towards a 2D surface state with bulk background
→ Confirmed by simple model using surface and bulk
channels in concert

48. Conclusions

Santos group has successfully grown epitaxial Sb films on
GaSb(111) for thicknesses 1.5 – 6 nm
– Bulk conduction suppressed
– dR/dT<0 (Insulating behavior)
– Extrapolated residual surface state conductivity
– Abrupt transition to trivial insulator ~ 2.0 nm

Low field magneto-resistance shows well behaved WAL with α =
1/2 and thickness independent phase breaking length

High field magneto-resistance evolution with decreasing film
thickness can be explained by simple model

Future experiments: UCF, Aharonov-Bohm, and gate
development

49. Acknowledgments
Transport: Murphy Group
Nolan Teasdale
Zhong-He Liu
Jeremy Massengale
National Science
Foundation
National High
Magnetic Field
Laboratory
Tallahassee, FL
Growth: Santos Group
Chomani Gaspe
Kaushini Wickramasinghe
Tetsuya Mishima
Device Fabrication
Matt Johnson
Joel Keay
Lu Li
Rassel Shazzad

50. Nano-Wire Devices
Fabricated using Electron Beam Lithography (EBL) and Reactive
Ion Etching (RIE)
EBL-SEM used to write patterns in e-beam resist; pattern is
designed using CAD software
To determine optimal dosing parameters a dose test is
performed
Dose Test- Take a repeated pattern with dimensions of the
desired feature size with varying doses (nC/cm)

51. Nano-Wire Devices
RIE
- Plasma chemically reacts with surface to cause
etching (e.g. Ar + BCl3
)
-RIE is a anisotropic etch process (etches faster in
one direction) vs. wet etching which is an isotropic
etch (etch rate equal in all directions)

52. Transport in Lithographic Nano Wires
Fabricated using EBL
and RIE
Nominal width 400nm
Goal is to study
quantum interference
effects

53. Universal Conductance Fluctuations
Why universal?
– Fluctuations on the order of e2
/h
– Independent of sample
Samples larger than phase breaking length
– Samples with multiple conduction channels
reduces the magnitude of the fluctuations

54. Universal Conductance Fluctuations
Features track with B perpendicular →
Implies 2D Behavior
1
cos(θ)
Nominal device size L = 2 um, W = 450 nm

55. ARPES Studies of Sb Layers
•
ARPES by Takahashi
Group (Tohoku Univ.)
•
Sb grown on Bi/Si(111)
•
FS1 due only to surface
states
•
FS2 is a coupling of surface
and bulk hole states
•
This coupling causes
suppression of the spin
polarization
•
Coupling of surface and
bulk hole states even for
thickness of 18 BL (6.3 nm)
A. Takayama et al., New J. Phys.
16 , 055044 (2014).

56. Hall Results
0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0
0 . 0 0 0 0 0 0
0 . 0 0 0 0 0 5
0 . 0 0 0 0 1 0
0 . 0 0 0 0 1 5
0 . 0 0 0 0 2 0
HallVoltage(V)
F ie ld ( T )
Hall data across multiple samples shows linear slope up to high field
Sign of Hall slope indicates p-type carriers
Using single carrier fit, calculated density is 2-5x1014
cm-2
Calculated density is an over estimate since band structure shows
multiple carriers present
Multi-carrier fits did not produce well constrained parameters
From band structure density is expected to be 2-5x1012
cm-2

57. Tilted Field Measurements
Rotator Stage Calibration
A - Maximum value of Hall
Slope
x – Linear position of tilter
in inches
B – Tilter position in inches
corresponding to 0 degree
C – Conversion factor in
rads/turn