Transcript Doping Effects in Bi2Se3 and Bi2Te3 Topological Insulators

TAR College, Kuala Lumpur, Malaysia
13 July 2010
Topological Insulators
Yew San Hor
1Department of Chemistry
and
J. G. Checkelsky2, A. Richardella2,
J. Seo2, P. Roushan2, D. Hsieh2, Y. Xia2, M. Z. Hasan2, A.
Yazdani2, N. P. Ong2, and R. J. Cava1
2Department
of Physics
Princeton University
NSF-MRSEC DMR 0819860
Albert Einstein
E = mc2
Einstein’s
house at
Princeton
1935-55
Photo by Ch’ng Ping Choon
Princeton Campus
Princeton Chemistry Department
Spring 2009
Princeton Physics Department
Richard Feymann
Ch’ng Ping Choon
Princeton Science Library
Princeton Condensed Matter Group
Physics & Chemistry
NSF-MRSEC
Chemistry
Matthias Prize for New Superconducting
Materials 1996
Robert J. Cava
Physics
• Director of NSF MRSEC
DMR 081986
• 2006 Kamerlingh Onnes
Prize (For research
accomplishments in HTc
superconductor)
Nai Phuan Ong
Zahid Hasan
Yew San Hor
David Hsieh
Bob Cava
-32 sec
t=
10
~ 300,000 years
Relativistic energy
E2 = p2c2 + m2c4
Elementary particles
E
k
Dirac equation
(μ∂ μ + mc)ψ = 0
E~k
Non-relativistic energy
t ~ 300,000 years
Schroedinger Equation:
E
Condensed Matter
k
E~k2
t ~ 1.5 × 1010 years
t ~ 1.5 × 1010 years
source: spie.org
s
Bulk Insulator
L
E
BCB
k
BVB
Strong
Spin-Orbit
Coupling
2
E~k
E
Bulk InsulatorSCB
L
E k E~k
Surface
s Conductor
SVB
BCB
k
BVB
Strong
Spin-Orbit
Coupling
2
E~k
…is a band insulator which is
characterized by a topological
number and has Dirac-like
excitations at its boundaries.
Topology
…is the mathematical study of the
spatial properties that are preserved
under continuous deformations of
objects, for examples, twisting and
stretching, but no tearing or gluing.
Topology
=
sphere
ellipsoid
Topology
=
Topology
in condensed matter electronic phases…
Electron spin property
plays an important role.
Example:
A
B
Insulator
material does not conduct electric current
1. Band Insulator (valence band completely filled).
2. Peierls Insulator (lattice deformation).
3. Mott Insulator (Coulomb repulsion).
4. Anderson Insulator (impurity scattering).
A new class of insulator
Topological Insulator
Topological Insulators
• Bulk band insulators.
E
Gapped bulk insulator
E ~ k2

Bulk
Conduction
Band
k
Bulk
Valence
Band
• Gapless Dirac excitations at its boundaries.
Gapless surface state
E~k
Ingredients:
Strong spin-orbit coupling.
Time reversal symmetry.
E
Surface
Conduction
Band
k
Surface
Valence
Band
Consider a simpler system
2D electron gas as an analogy
2D electron gas
No boundary
Applied B-field out of plane
When boundary is created,
interface with vacuum state
→ Edge state.
Electron charge → Quantum Hall effect
Insulator
Vacuum
…but this breaks Time Reversal Symmetry.
Electron charge → Quantum Hall effect
Broken Time Reversal Symmetry
Electron charge → Quantum Hall effect
Electron charge → Quantum Hall effect “charge”
Classical Hall Effect
Quantum Hall Effect
(Klaus von Klitzing, 1980)
Lorentz Force
F = -e x B
Quantization of
Hall conductance
xy = ie2/h
h/e2 = 25812.807 
Hall conductance
xy = -ne/B
1985 Nobel Prize in Physics
Fractional Quantum Hall Effect
(discovered in 1982)
Daniel Tsui
1998 Nobel
Prize in
Physics
Quantization of
Hall conductance
xy = ie2/h
i = 1/3, 1/5, 5/2, 12/5 ..
Horst Stormer
Robert Laughlin
Devices utilize electron charge
property: Semiconductor
Transistor, AT&T Bell Labs (1947).
Single Crystal Germanium (1952).
Single Crystal Silicon (1954).
IC device, Texas Instrument (1958).
IC Product, Fairchild Camera (1961).
Microprocessor, Intel (1971).
Personal Computer (1975).
Semiconductor crisis
Gorden Moore (co-founder of Intel 1964):
Number of transistors doubled every 12 months
while price unchanged.
In 1980s, number of transistors doubled every
18 months.
*Size limit
*Heat dissipation
So, we need to find a new material
New materials utilize electron spin
property:
Topological Insulators
Topological Insulators
Spintronic devices
- apply electron spin property.
Quantum computer
- apply quantum mechanical phenomena.
- use qubit (quantum bit) instead of bit.
Topological Insulator
is also important for…
1. Quantum Spin Hall Effect.
2. The search of Majorana fermion.
3. Axion electrodynamic study.
4. Magnetic monopole.
3D Topological Insulator
Strong spin-orbit coupling
L
L
s
s
L
s
L
s
L
s
L
s
No boundary
Bulk insulator
Large atomic number → Large orbital moment, L
3D Topological Insulator
L
L
s
s
L
s
Bulk insulator
Strong spin-orbit coupling
3D Topological Insulator
Etrap
Etrap
k x Etrap ~ B
s
k1
k2
s
L
s
Bulk insulator
Strong spin-orbit coupling
3D Topological Insulator
Etrap
Etrap
s
-k2
-k1
s
When T-operator is Time
applied…
Reversal Symmetry
Invariant!
Bulk insulator
s
L
Strong spin-orbit coupling
3D Topological Insulator
Electron spin
Quantum spin Hall effect
Surface Dirac-like spin current.
Zero net current, but spin-polarization,
protected by Time Reversal Symmetry
L
L
s
s
L
s
Bulk insulator
Strong spin-orbit coupling
Topological insulators
•
•
•
•
•
•
•
Bi
Bi1-xSbx
Sb
Bi2Se3
Bi2Te3
Sb2Te3
will look for more…
Bi
Bi1-xSbx
Science 321, 547 (2008)
Bi2Se3
Bi0.9Sb0.1
Nature Physics 5, 398 (2009)
Nature 452, 970 (2008)
Basics of ARPES
(Angle-resolved photoemission spectroscopy)
ARPES is surface sensitive
Can measure E vs k of bulk and
surface states separately
h
Damascelli et al. RMP 2003
Surface Dirac-like spin current.
Zero net current, but spin-polarization,
protected by Time Reversal Symmetry
Dirac surface state
ARPES
E
SCB
E k E~k
SVB
Challenging problem
for
Dirac surface state
transport measurements
E
EF
Gapless
surface
state
BCB
k
Bulk electron is measured
Why not bulk insulator?
Imperfect World
Defect chemistry in Bi2Se3
Se
Bi
e-e-
SeSe → VSe●● + Se (gas) + 2 e-
Se
Bi
Se
Se
Bi
Se
Bi
Se
Se
Bi
Se
10 nm
defect
STM
n-type Bi2Se3
Ca-doped in Bi2Se3
Se
Bi
e-e-
2Ca → 2CaBi’ + 2h•
Se
Bi
Se
Se
Bi
Se
Bi
Se
Se
Bi
Se
10 nm
defect
STM
p-type
n-type Bi2Se3
Bi2-xCaxSe3 Crystal growth
1st step: (i) stoichiometric mixture of Bi and Se in vacuum quartz tube.
(ii) melting at 800 oC for 16 hours.
(iii) air-quenching to room temperature.
2nd step: (i) add Ca to Bi2-xSe3 and sealed in vacuum quartz tube.
(ii) 400 oC for 16 hours.
(iii) 800 oC for 1 day.
(iv) 1 day slow cooling
to 550 oC.
(v) stay at 550 oC for
3 days.
PRB 79 195208 (2009)
n- to p-type Bi2-xCaxSe3 topological insulator
E
E
X=0
X=0
X=0.02
k
X=0.02
x=0
k
x = 0.005,
0.02, 0.05
PRB 79 195208 (2009)
Fine tuning in Bi2-xCaxSe3
Bi2Se3
Bi1.9975Ca0.0025Se3 Bi1.99Ca0.01Se3
Nature 460, 1101 (2009)
x=0
x > 0.005
x = 0.0025
Bi2-xCaxSe3 transport properties
Non-metallic.
Onset at T~130 K.
Metallic behavior.
PRL 103, 246601 (2009)
Bi1.9975Ca0.0025Se3
Quasi-periodic fluctuations
Surface state?
PRL 103 246601 (2009)
Te annealing of Bi2Te3
Te powder
As-grown Bi2Te3 crystal
Annealing temperature: 400 – 440 C (1 week)
Transport property of Bi2Te3
EB (eV)
S4
S3
S2
EF

S1
As-grown
kx (Å-1)
Fine tuning of Bi2Te3+
EB
EB
Dirac States in topological insulator Bi2Te3
kx
kx
H
H
H
dxx/dH
H
Non-metallic
2D Fermi Surface
Metallic
3D Bulk State
Science (in press)
On the other hand…
Bi2Se3 can be doped to become more
conducting…
Superconductor
Cu-intercalated Bi2Se3
superconductor
By C.Kane (U Penn.)
Cux
Cux
Cux
CuxBi2Se3
Cu-doped Bi2Se3 crystal growth
• Mixtures of high purity elements Bi, Cu, Se in sealed vacuum quartz tubes.
• Melt at 850 oC overnight.
• Slow cooling: 850 → 620 oC for 24 hours.
• Quench in cold water at 620 oC.
STM topography of Cu0.15Bi2Se3
T = 4.2 K
Cu clusters on surface.
Cu atoms intercalated between layers
Superconductivity of CuxBi2Se3
Superconductivity only found in 0.1 < x < 0.3
Tc~3.8 K
~20 %
SC phase
Superconductivity of CuxBi2Se3
SC phase is not fully connected.
PRL 104 057001 (2010)
Strongly type II superconductor
Upper critical field Hc2 is anisotropic
Bi2Se3 topological insulator
+
CuxBi2Se3 superconductor

Majorana Fermionic Physics.
(?)
Topological magnetic insulators
• Motivated by:
• Axion electrodynamics theory → E x B.
• Magnetic monopole → symmetries of Maxwell’s
equations.
• by Zhang group (Stanford), arXiv:0908.1537v1
Ferromagnetism in Bi2-xMnxTe3
For axion electrodynamics
Point charge
Surface current
induced
Vacuum
Topological
insulator
S. C. Zhang,
Science 323 1184 (2009)
Magnetic monopole induced
1. Quantum Spin Hall Effect: (b) Transport measurements
Axion electrodynamics
Sharp tip acts as a point charge
E field
Gold-copper
alloy contacts
Induced
surface current
TI crystal
I+ V+
V-
I-
Schematic diagram for the studies of axion electrodynamics
1. Quantum Spin Hall Effect: (b) Transport measurements
Mn-doped Bi2Te3
Te
Bi/Mn
Te
Bi/Mn
Te
Te
Bi/Mn
Te
Bi/Mn
Te
Te
Bi/Mn
Te
Mn-substituted Bi2Te3 (Bi2-xMnxTe3)
STM topography of Bi1.91Mn0.09Te3
Black triangles: substitutional Mn on Bi sites.
No Mn-clustering is found.
DC Magnetization of Bi2-xMnxTe3
TC ~ 9 – 12 K for x = 0.04 and 0.09
ARPES
T=15 K
Topological surface state is still present.
Dispersion relation of the state is changed in a subtle fashion.
PRB 81,195203 (2010)
Summary
● Ca-doped Bi2Se3 → Topological “Insulator”.
suppress bulk conductance to show up Dirac electron
surface state.
● Cu-added Bi2Se3 → Superconductor.
interface with Bi2Se3 to have proximity effect, Majorana
fermionic physics (?).
● Mn-doped Bi2Te3 → Magnetic topological
insulator.
in search for magnetic monopole (?) and
axion electrodynamics studies (?).
Acknowledgements
Cava group:
Funding agencies:
•
•
•
•
•
•
•
•
•
•
•
•
•
Air Force Office of
Scientific Research (AFOSR).
Professor Robert Cava
Tyrel McQueen (JHU)
Don Vincent West (U Penn)
Anthony Williams
David Grauer (UC Berkeley)
Jared Allred
Shuang Jia
Siân Dutton
Esteban Climent-Pascual
Martin Bremholm
Ni Ni
Ulyana Sorokopoud
Linda Peoples
Materials Research Science &
Engineering Centers (MRSEC).
References:
Bernevig, Hughes, Zhang, Science 2006.
Fu, Kane, Mele, PRL 2007.
Moore, Nature 2010.
Bjorken, Relativistic Quantum Mechanics.
Thank you