Transcript A IV B VI

Electronic Structure of
AIVBVI · m A2VB3VI
(AIV = Ge,Sn,Pb; AV = Bi,Sb;
BVI = Te,Se; m=1-3)
Topological Insulators
S.V. Eremeev, T.V. Menshchikova,
Yu.M. Koroteev, E.V. Chulkov
Outline
1- Introduction to topological insulators
2- Motivation
3- New family of ternary topological insulators
4- Summary and conclusions
Introduction
Topological insulators are one of the
materials of the moment. In these
unusual substances, the bulk
behaves like an insulator, whereas
the surface acts like a conductor. In
addition to a host of practical
applications, topological insulators
are particularly important because
they enable scientists to investigate a
plethora of exotic states.
Electrons in topological insulators
are able to flow only at the edges of
the material, not in the bulk.
NPG Asia Materials featured highlight
doi:10.1038/asiamat.2010.188
Introduction
 Classification of materials according to band theory,
Metalsl
Semi-metalsl
Insulatorsl
E(k)
EF
k
 But the quantum world can present more complex materials like,
* Superconductors
* Magnetic Materials
* Topological Insulators
Introduction
Introduction
Exotic properties
- Insulating bulk but metallic surface due to strong spin-orbit interaction.
- Unique surface state that make surface conducting, with linear
dispersion forming a Dirac Cone with a crossing point at the Fermi level.
- Helical spin structure with the
spin of the electron
perpendicular to its
momentum.
- Electrons in this surface state are protected against scattering.
- Very promising for spintronics or quantum computing applications.
Discovery of TI and motivation
1st Generation : HgTe Q. Wells (2D), BixSb1-x (3D)
Bernevig et al. Science 314(2006), Koenig et al. Science 318(2007), Fu and Kane PRB 76(2007), Hsieh et al. Nature
452(2008)
2nd Generation: Bi2Se3, Bi2Te3, Sb2Te3 3D crystals
Zhang et al. Nat. Phys. 5(2009), Xiao et al. Nat. Phys. 5(2009), Chen et al. Science 325(2009)
3rd Generation: Ternary Bi2Se3- and Bi2Te3-based
compounds (Bi2Te2Se, PbBi2Te4…), Heusler Compounds
(Li2AgSb, NdPtBi…), Tl-based Bi chalcogenides (TlBiSe2,
TlBiTe2), antiperovskite nitride (M)3BiN (M = Ca, Sr, Ba),
honeycomb-lattice chalcogenides LiAgSe and NaAgSe,
Pyrochlores…
Discovery of TI and motivation
2nd Generation: Bi2Se3, Bi2Te3, Sb2Te3 3D crystals
Zhang et al. Nat. Phys. 5(2009),
Chen et al. Science 325(2009)
Discovery of TI and motivation
Why look for more Topological Insulators???
- Bi2Se3 Dirac Point is close to the Bulk Valence Band
maximum scattering channels (S. Kim et al, PRL 107, 056803 (2011))
- hexagonal warping of the Dirac cone:
- more accurate
quasi-particle GW
approach reveals
several cases where
DFT identifications
of TI phases are
false
J. Vidal et al, PRB 84, 041109(R) (2011)
Intrapair scatterings in (a) and (b)
are forbidden by timereversal
symmetry. But interpair scatterings
in (b), for example, those between
k2 and k3, are allowed. (L.Fu, PRL
103, 266801 (2009))
AIVBVI · m A2VB3VI (AIV = Ge,Sn,Pb; AV = Bi,Sb; BVI = Te,Se; m=1-3)
ternary compounds
In this work the electronic structure of AIVBVI · m A2VB3VI (AIV = Ge,Sn,Pb; AV = Bi,Sb; BVI
= Te,Se; m=1-3) series of ternary compounds are analyzed.
The electronic structure was calculated in the density functional theory formalism as
implemented in VASP.
Like A2VB3VI these compounds have layered structure with ionic-covalent bonding within
layers and van der Waals gaps between them, but unlike the parent compounds with
simple quintuple layers structure, the structure of the ternary compounds contains
alternating in various sequences quintuple and septuple layers.
Peculiarities of bulk spectrum of these more complex materials give rise to more
complicated surface band structure that depends on surface termination, which can be
quintuple- or septuple-layer terminated.
We predict the existence of exotic buried topological surface states which are
characterized by a deep subsurface localization and Dirac states with the Dirac point in
the valence band gap.
Beside the Dirac cone states, which are peculiar to topological insulators, unoccupied
Rashba-type spin-split state and occupied surface states can reside in these systems.
We analyze dispersion and spatial charge density localization of the surface states. We
also performed a layer-by-layer analysis of the spin distribution in the surface states.
Classification of topological phases
Three-dimensional materials with inversion symmetry are classified with
four Z2 topological invariants 0; (1, 2, 3), which can be determined by
the parity m(i)=±1 of occupied bands at eight time-reversal invariant
momenta (TRIM) i =(n1,n 2,n3) = (n1 b2 + n2 b2 + n3 b3)/2, where b1, b2,
b3 are primitive reciprocal lattice vectors, and nj = 0 or 1 [1, 2]. The Z2
invariants are determined by the equations
8
1   i
0
i
k
and  1 

i  ( n1, n 2 , n 3)
nk 1; nj  k  0 ,1
N
where  i    2 m (i )
m 1
For rhombohedral lattice the TRIMs are ,Z, and
three equivalent L and F points.
0=1 characterize a strong topological insulators.
[1] L. Fu, C.L. Kane, and E.J. Mele, Phys. Rev. Lett. 98, 106803 (2007).
[2] L. Fu, and C.L. Kane, Phys. Rev. B 76, 045302 (2007).
The topological number 0 for n AIVBVI · m A2VB3VI (n=1; m=1–3)
compounds based on Bi2Te3, Sb2Te3 and Bi2Se3 parent phases
m Bi2Te3
0
Sb2Te3
1
GeBi2Te4
1
GeSb2Te4
SnBi2Te4
1
SnSb2Te4
PbBi2Te4
1
PbSb2Te4
1
GeBi4Te7
1
GeSb4Te7
1
SnBi4Te7
1
SnSb4Te7
1
PbBi4Te7
1
PbSb4Te7
1
GeSb6Te10
0
2
3
GeBi6Te10 1
SnBi6Te10
1
PbBi6Te10
1
0
Bi2Se3
1
Planar
1
SnBi2Se4
Perp.
0
0
PbBi2Se4
1
PbBi4Se7
1
Crystal Structure of PBT compounds
parent compound Bi2Te3
SOC-induced band inversion marked by green ellipse
parent compound Bi2Te3
surface band structure of
Bi2Te3 and spatial charge
density distribution of the
Dirac state
NATURE 460, 1101 (2009).
layer-resolved spin structure
Bulk band structure of PBT compounds
SOC-induced band-gap
inversion in PbBi2Te4
More complicated band
structure in PbBi4Te7
Surface band structure of PbBi2Te4
counter-clockwise spin rotation in the topmost Te atom
Layer-resolved spin structure of the Dirac
state in the topmost 7L block of PbBi2Te4,
given by spin projections Sx, Sy, and Sz at
30 and 90 meV above DP.
Surface band structure of
n AIVBVI · m A2VB3VI (n=1; m=1)
counter-clockwise spin
rotation in the topmost
Te atom
Surface band structure of 7L-terminated
PbBi4Te7(0001)
The character of p states changes from
dominating py and pz in all subsurface layers to
px in the topmost Te layer which can change the
spin-orbit interaction and reverse the spin
orientation.
Surface band structure of 5L-terminated
PbBi4Te7(0001)
Charge density
distribution of the
occupied and unoccupied
surface states integrated
over xy planes
Surface band structure of 5L-terminated
PbBi4Te7(0001)
Layer-resolved spin structure of the Dirac state
at 5L-term PbBi4Te7(0001) at 100 meV.
Spin projections for occupied SS
Surface band structure of
n AIVBVI · m A2VB3VI (n=1; m=2)
Surface band structure of 7L-terminated
and 5L-terminated PbBi6Te10(0001)
PbBi6Te10(0001) with two 5L blocks on the top
Summary and conclusions
— We have shown that, in the homologous series of ternary compounds
based on Bi2Te3, Bi2Se3 and Sb2Te3, most of the compounds AIVBVI · m
A2VB3VI (AIV = Ge,Sn,Pb; AV = Bi,Sb; BVI = Te,Se; m=1-3) are 3D topological
insulators.
— Part of these systems (m = 2,3) represent naturally grown superlattices
composed of 5L and 7L blocks, which demonstrate much richer physics than
the parent TIs.
— More complex surface electronic and spin structures, originating from
peculiarities of the bulk spectrum of these materials, provides an efficient way
to manipulate both the spin structure and the spatial localization of the
conducting state. This subsequently may allow for a variation of the depth of
the spin transport channel below the surface.
References: С.В. Еремеев и др., Письма в ЖЭТФ, т. 92, с. 183 (2010),
S.V. Eremeev et al., Nature Comm. 3:635, DOI: 10.1038/ncomms1638 (2012),
Kuroda et al. PRL (under reviewing)
Thank you for your attention
Prospective devices
Structure of proposed memory cell, based on a
TI block with a magnetically doped surface. A bit
is stored by the perpendicular magnetization of
the surface.
Gate-tuned normal and
superconducting transport at the
surface of a topological insulator
T. Fujita et al., Applied Physics Express 4 (2011) 094201
B. Sacepe et al., Nat. Comm (2011)