Topological Insulators - Center for Energy Efficient Electronics … · 2017. 9. 5. · Topological Insulators Three broad classes of insulators Band, Correlated and Topological Insulator

Topological Insulators

R. Ramesh

Annual Retreat

August 21, 2012

A Science & Technology Center

Topological Insulators

R. Ramesh

Annual Retreat

August 21, 2012

For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.

Correlated Oxides

Band Insulator

Mott Insulator LaTiO3 : d

1 state, BUT insulating

8/21/2012 For Internal E3S Use Only

These Slides May Contain Pre-publication Data and/or Confidential Information.

Topological Insulators Three broad classes of insulators

Band, Correlated and Topological

Insulator

Metallic Surface

• Bulk is an insulator, but the surface is conducting! • Driven by strong Spin-Orbit interaction. • It is a topological order, i .e. all the “good” properties are robust

against small perturbation.



Topological Insulators Three broad classes of insulators

Band, Correlated and Topological

8/21/2012 For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.

Topological surface state

Qi and Zhang, Rev. Mod. Phys. 83, 1057–1110 (2011)

• At surface states, electron spin and momentum are locked. • Potential platform for spintronics applications. • Spin chirality also prevents electrons from back scattering.

8/21/2012


Large MR in GeTe-Sb2Te3 Multilayers

Tominaga et al, APL 2012 8/21/2012


Research Directions

Pyrochlore Iridates Perfect epitaxial quality

Interfaces with band insulators Probe interface transport

XAS studies

Perovskite Iridates Strain control of transport

Doping effects : e- h-

Interfaces : electric field control

8/21/2012


1 meV 10 eV 1 eV 100 meV 10 meV 100 μeV

H=HKin+Ve-ion+Ue-e+HHund+Hs-s+He-ph+Hs-o

kinetic interaction

e-ion interaction

e-e interaction

Hund’s interaction spin-spin interaction

e-phonon interaction

crystal field

spin-orbital interaction

DM interaction

1 V/nm 0.1 V/nm 10 V/μm 1 V/μm Electric Field

100 T 10 T 1 T Magnetic Field

1000 K 100 K 10 K 1 K

Temperature

10 % 1 % 0.1 % 0.01 %

Epitaxial Strain

Interactions in complex oxide materials

Pyrochlore Iridates – Ln2Ir2O7

• Iridium 5d electrons has a strong spin-orbit coupling (0.2-1eV), comparable to correlation energy scale (1-2eV).

• Geometric frustration in the pyrochlore lattice leads to non-trivial topological effect.

• Pyrochlore iridates is the model system for oxides topological insulator


TBI : Topological Band Insulator TMI : Topological Mott Insulator GMI : Gapless Mott Insulator

Rich phase diagram of iridates

By tuning different energy scales, several exotic topological order emerge

Pesin and Balents, Nature Physics 6, 376 (2010) Wan, Vishwanath et. al. Phys. Rev. B 83, 205101 (2011) 8/21/2012


Pyrochlore iridates thin films

Substrate: YSZ

Y2Ti2O7 , Bi2Ti2O7, etc

Eu2Ir2O7

27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.02Theta-Omega (°)

0.1

3

1

3

10

3

100

3

1000

3

10000

3

100000

Inte

nsity (

counts

)

Our approach: thin film hetrostuctures grown by laser MBE, offering precise control of materials and interface. Create TI/ BI interfaces using epitaxy Explore transport at interfaces

Burkov and Balents, PRL 2011



Other examples of Strong Spin-Orbit Coupling :

Conducting domain walls in BiFeO3 Strong interface magnetism in LSMO/BFO

Strain effects on Sr2IrO4



Rhombohedral, R3c

apc = 3.96Å MFe2

[111]

MFe1

M

G-type AFM order

• TC ~ 830°C; Polarization along [111]

• G-type, TN ~ 370°C

• Strong correlations ; Bandgap ~ 2.6eV

• Small canted moment in bulk 8emu/cc

Magnetoelectric Multiferroic BiFeO3

71

°

180

°

109

°



Domain Walls : Natural Atomically Sharp Interfaces



Domain Walls : Natural Atomically Sharp Interfaces

FE Wall Width : 1-3nm 8/21/2012


Domain Walls : Natural Atomically Sharp Interfaces Magnetotransport through109° Domain Walls

0 50 100 150 200 250 300

0

50

100

150

200

250

300

350

R(

10

9

)

Temperature (K)

0 T

8 T

-50

-40

-30

-20

-10

0

R

/R0 (%

)

MR

-10 -5 0 5 10-100

-50

0

50

100

Cu

rre

nt

(pA

)

Voltage (V)

0 1 2 3 4 5 6 7-80

-60

-40

-20

0

20

R

/R0 (

%)

Magnetic Field (T)

H DW, in-plane

H out-of-plane

HDW, in-plane

Fitting

5

10

15

20

25

R (

10

9 )

3K

Metallicity at walls Spin Transport

How to enhance ?

He et al, PRL, Feb 2012 8/21/2012 For Internal E3S Use Only


MnO2-BiO-FeO2 Interface

(BiO Interface)

MnO2-La0.7Sr0.3O-FeO2 Interface

(La0.7Sr0.3O interface)

Atomic Scale Design of Charge, Spin and Orbital Degrees of Freedom at Heterointerfaces

Yu et al, PRL, 2010 For Internal E3S Use Only These Slides May Contain Pre-publication Data and/or Confidential Information.



La0.7Sr0.3O Interface

SRO

2 μm

AFM:SrTiO3

Yu et al, PRL, 2010



60 80 100 120 140

55 Mn

88 Sr

139 La

MnO 2 term

La 0.7

Sr 0.3

O term = 5 o

MS

RI In

ten

sit

y (

a.u

.)

Atomic number

Time of Flight Surface Spectroscopy to probe average surface termination

Yu et al, PRL, 2010

8/21/2012

705 710 715 720 725 730 735-6

-4

-2

0

2

4

6

8

XM

CD

(%

)

Photon Energy (eV)

Interface BiFeO3

GaFeO3

-Fe2O

3

Bulk BiFeO3


Yu et al, PRL, 2010


Yu et al, PRL, 2010



-1200 -800 -400 0 400 800 1200

-3

-2

-1

0

1

2

3

Mag

neti

zati

on

(/M

n)

Magnetic Field (Oe)

5 nm LSMO + 30 nm BFO

0.2 T FC

-0.2 T FC

5 nm LSMO

1 T FC

(a)

Yu et al, PRL, 2010



Dynes, et al Nature Materials 2010

Controlling Exchange Coupling with E-Field

+60V

-60V



Dynes, et al Nature Materials 2010

660 690 720 750 780 810

Co L2

Co L3

Fe L2In

tens

ity

(a. u

.)

Energy Loss (eV)

Fe L3

EELS analysis at the interface BFO/CoFe

BFO

SRO / DSO

Co.90Fe.10

BFO

Pt

V

BFO

SRO

DSO

Sharp interface at the

atomic scale

Essential at the

magnetoelectic

interface

BFO- Ferromagnetic Metal Interfaces


Magnetization reversal @RT, non

volatile and reversible

PFM IP

PFM IP

Out of plane, reversible switching of M


Sr2IrO4 J. Phys.: Condens. Matter 20 (2008) 295201 Y Klein and I Terasaki

z = 3/4 z = 1/4

z = 0 z = 1/2

11oO

Sr

Ir

Figure 1. Structure of Sr2IrO4. Sr, Ir and O elements correspond tolarge green spheres, medium grey spheres and small red spheres,

respectively.

the gap at EF has not yet been clarified, but it is found to be

responsible for the insulating transport properties of Sr2IrO4,

which may discriminate 5d TMOs, from two 4d TMOs such

as Sr2RhO4 and Sr2RuO4. We expect that the difference in

experimental and theoretical results is due to some many-body

effect because that kind of phenomenon is not fully considered

in band calculations. Although an electronic specific heat was

measured to be γ ≈ 2 mJ K− 2 mol(Ir)− 1 [10], it does not

always mean weak correlation, because the carrier density is

reduced by the opening of the gap.

It was reported that Ca2+ and Ba2+ can be substituted

for Sr2+ by a small fraction, which does not change the

magnetic and transport properties [12]. This may be due to

the similar electronic configuration of these three alkaline-

earth elements. In the present work, two kinds of cationic

substitutions have been tried in order to tune the properties of

Sr2IrO4 and get some insight on its electronic state. Sr has been

substituted with La in order to see the response of the material

to electron doping. Rh has been inserted on the Ir lattice as a

perturbative element of the magnetic environment. Resistivity

(ρ), thermoelectric power (S) and magnetization (M) have

been measured and analysed. The electrical resistivity itself

is insufficient to understand the transport properties because

it depends on extrinsic phenomena such as grain-boundary

scattering and cannot distinguish n-type from p-type carriers.

We need another probe that is less affected by grain boundaries.

The thermoelectric power and the Hall coefficient are relevant

in the case of polycrystalline samples [13]. Here we show

results of thermoelectric power measured below 300 K.

2. Experimental details

Sr2− xLax IrO4 (x = 0 and 0.05) and Sr2Ir1− yRhyO4 (y = 0.05,

0.1 and 0.2) polycrystalline samples were synthesized from the

solid state reaction of SrCO3, IrO2, La2O3 and Rh2O3 powders.

Mixtures were heated in air at 900 ◦ C for 24 h, 1000 ◦ C for

Figure 2. X-ray diffraction patterns of the polycrystalline samplesSr2− xLax IrO4 (x = 0 and 0.05) and Sr2Ir1− yRhyO4 (y = 0.05, 0.1and 0.2). The Cu Kα is used as an x-ray source.

24 h and 1100 ◦ C for 60 h with intermediate grindings. Note

that this conventional technique is completely different than

the rapid heating and quenching technique used recently to

synthesize Sr2− xLax IrO4 [14].

The x-ray diffraction was measured using a standard

diffractometer with Cu Kα radiation as an x-ray source in

the θ–2θ scan mode. The resistivity was measured though

a four-terminal method, and the thermoelectric power was

measured using a steady-state technique with a typical gradient

of 0.5 K cm− 1. The magnetic properties were studied with

a dc SQUID magnetometer (2–400 K, 0–7 T) by recording

magnetization as a function of temperature.

2.1. Structural analysis

Figure 2 shows the x-ray diffraction patterns of the sintered

samples. All the peaks are indexed according to the I41/ acd

space group. This shows that La and Rh are substituted for

Sr and Ir, respectively. For La content exceeding x = 0.05,

we observed a tiny peak corresponding to some unknown

impurity. As a consequence, the solubility limit of La to

Sr is determined to be x = 0.05. In figure 3, we plot the

evolution of the cell parameters as a function of the La and

Rh contents. For the mother compound, the a and c axes

have been reported many times with different values, ranging

from 5.4921 to 5.4994 Å for a and 25.766 to 25.798 Å for

c [6, 9, 11, 12, 14, 15]. We calculated the lattice constants to

be 5.4955 Å and 25.783 Å for a and c, respectively, which are

in the range of the reported values. Concerning the effect of

2

Klein & Terasaki, J. Phys.: Cond. Mater. (2008) 8/21/2012


0 90 180 270 360 (deg)

Inte

nsity (

arb

. units)

(b) (a)

(c) SrTiO3(101)

Sr2IrO4(116)

10 20 30 40 50 6010

0

105

2 (deg)

Inte

nsity (

arb

. u

nits)

STO(002) STO(004) SIO(00 12)

SIO(00 8)

SIO(00 4)

SIO(00 16)

4.63 nm

0.04 nm

1.0µm

Ir

Sr

[100]SrTiO3



40 42 44 46 48

1010

1015

1020

2 (deg)

Inte

nsity (

arb

. units)

Qx (Å

-1)

Qy (

Å-1

)

0.93

0.935

0.94

Qx (Å

-1)

Qy (

Å-1

)

0.93

0.935

0.94

Qx (Å

-1)

Qy (

Å-1

)

-0.366 -0.365 -0.364 -0.363 -0.362

0.93

0.935

0.94

Fig. 2 Selectable unit cell distortion via thin film thickness

(b) 5 nm

10 nm

60 nm

(a) SrTiO3( 0 0 2)

(c)

(d)

5 nm

10 nm

60 nm



Fig. 3 Strain induced transition from 2-D towards 3-D system

Room temperature X-ray linear dichroism decreases with increasing strain. Data shows a strain-induced transition from a layered 2-D system (60 nm) {strong difference between horizontal and vertical absorption} into a 3-D scenario {less difference between horizontal and vertical absorption}. This is in excellent agreement with the collapse of c-parameter observed in X-ray diffraction and anticipates a transport mechanism scenario more similar to Sr3Ir2O7 or SrIrO3 compounds.


These Slides May Contain Prepublication Data and/or Confidential Information.

Fig. 4 Strain-tuned electrical transport mechanism. 100% reduction of activation energy at 300 K

ε[100] = 0.17%

ε[100] = 0.23%

ε[100] = 0.31%


These Slides May Contain Prepublication Data and/or Confidential Information.

SIO

BFO

STO

BFO/SIO/STO

8/21/2012 For Internal E3S Use Only These Slides May Contain Prpublication Data and/or Confidential Information.

Going Forward

Pyrochlore Iridates Perfect epitaxial quality

Interfaces with band insulators Probe interface transport

XAS studies

Perovskite Iridates Strain control of transport

Doping effects : e- h-

Interfaces : electric field control

8/21/2012


Documents

Topological Insulators - Center for Energy Efficient Electronics … · 2017. 9. 5. · Topological Insulators Three broad classes of insulators Band, Correlated and Topological Insulator