Research fueled by: Universität zu Köln November 12 th, 2010 JAIRO SINOVA Texas A&M University...
-
date post
21-Dec-2015 -
Category
Documents
-
view
215 -
download
3
Transcript of Research fueled by: Universität zu Köln November 12 th, 2010 JAIRO SINOVA Texas A&M University...
Research fueled by:
Universität zu KölnNovember 12th, 2010
JAIRO SINOVATexas A&M University
Institute of Physics ASCR
Echoes of special relativity in condensed matter physics: anomalous Hall effect, spin-helix transistors, and topological thermoelectrics
Hitachi CambridgeJoerg Wünderlich, A. Irvine, et al
Institute of Physics ASCRTomas Jungwirth, Vít Novák, et al
University of Würzburg Laurens Molenkamp, E. Hankiewiecz, et al
University of Nottingham Bryan Gallagher, Richard Campion, et al.
2Nanoelectronics, spintronics, and materials control by spin-orbit coupling
I. Introduction: using the dual personality of the electron•Internal coupling of charge and spin: origin and present use•Control of material and transport properties through spin-orbit coupling•Overview of program
II. Anomalous Hall effect: from the metallic to the insulating regime•Anomalous Hall effect basics, history, progress in the metallic regime•Anomalous Hall effect in the hopping regime
III.Spin injection Hall effect: a new paradigm in exploiting SO coupling•Spin based FET: old and new paradigm in charge-spin transport•Theory expectations and modeling•Experimental results
•Topological thermoelectrics:Thermoelectric figure of meritI.Increase of ZT in topological insulators.
Echoes of special relativity in condensed matter physics:
anomalous Hall effect, spin-helix transistors, and topological thermoelectrics
Echoes of special relativity in condensed matter physics:
anomalous Hall effect, spin-helix transistors, and topological thermoelectrics
3Nanoelectronics, spintronics, and materials control by spin-orbit coupling
The electron: the key character with dual personalities
CHARGECHARGEEasy to manipulate: Coulomb interaction
SPIN 1/2SPIN 1/2Makes the electron antisocial: a fermion
quantum mechanics
E=p2/2mE→ iħ d/dtp→ -iħ d/dr
““Classical” external manipulation of charge & spinClassical” external manipulation of charge & spin
special relativity
E2/c2=p2+m2c2
(E=mc2 for p=0)
+ particles/antiparticles & spin
Dirac equation=
4
ee--
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Internal communication between spin and charge:spin-orbit coupling interaction
(one of the few echoes of relativistic physics in the solid state)
This gives an effective interaction with the electron’s magnetic moment
Classical explanation (in reality it arises from a second order expansion of Dirac equation around the non-relativistic limit)
• “Impurity” potential V(r)Produces
an electric field
In the rest frame of an electronthe electric field generates an effective magnetic field
• Motion of an electron
5
ee--
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
(one of the few echoes of relativistic physics in the solid state)
This gives an effective interaction with the electron’s magnetic moment
Classical explanation (in reality it arises from a second order expansion of Dirac equation around the non-relativistic limit)
• “Impurity” potential V(r)Produces
an electric field
∇V
BBeffeff
pss
In the rest frame of an electronthe electric field generates an effective magnetic field
• Motion of an electron
Consequence #1:Spin or the band-structure Bloch states are linked to the momentum.
Internal communication between spin and charge:spin-orbit coupling interaction
6
ee--
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
(one of the few echoes of relativistic physics in the solid state)
This gives an effective interaction with the electron’s magnetic moment
Classical explanation (in reality it arises from a second order expansion of Dirac equation around the non-relativistic limit)
• “Impurity” potential V(r)Produces
an electric field
∇V
BBeffeff
pss
In the rest frame of an electronthe electric field generates an effective magnetic field
• Motion of an electron
Consequence #2Mott scattering
Internal communication between spin and charge:spin-orbit coupling interaction
7Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Control of materials and transport properties via spin-orbit coupling
AsAsGaGa
MnMn
New magnetic materials
Nano-transport
Spintronic Hall effects
Magneto-transport
Topological transport effects
Effects of spin-orbit coupling in
multiband systemsCaloritronics
8
Caloritronics
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Effects of spin-orbit coupling in
multiband systems
AsAsGaGa
MnMn
New magnetic materials
Nano-transport
Spintronic Hall effects
Magneto-transport
Topological transport effects
Control of materials and transport properties via spin-orbit coupling
Anomalous Hall effects
I
FSO
FSO
majority
minority
V
Nagaosa, Sinova, Onoda, MacDonald, Ong, RMP 10
9Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Simple electrical measurement of out of plane magnetization (or
spin polarization ~ n↑-n↓)InMnAs
Spin dependent “force” deflects like-spin particles
ρH=R0B ┴ +4π RsM┴
Anomalous Hall Effect: the basics
I
_ FSO
FSO
_ __
majority
minority
V
M⊥
AHE is does NOT originate from any internal magnetic field created by M⊥; the field would have to be of the order of 100T!!!
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Anomalous Hall effect (scaling with ρ for metals)
Material with dominant skew scattering mechanismMaterial with dominant scattering-independent mechanism
σxx>106 (Ωcm)-1σxx ~104-106 (Ωcm) -1
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Anomalous Hall effect (scaling for insulators)
Diagonal hopping conductivity for most systems showing approximate scaling
σxy~σxx1.4-1.7 over a few decades for σxx <104 (Ωcm) -1
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Nagaosa et al RMP 10
Tentative phase diagram of AHE
2
13
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Valenzuela et al Nature 06
Inverse SHE
Anomalous Hall effect: more than meets the eye
Wunderlich, Kaestner, Sinova, Jungwirth PRL 04
Kato et al Science 03
IntrinsicExtrinsic
V
Mesoscopic Spin Hall Effect
Intrinsic
Brune,Roth, Hankiewicz, Sinova, Molenkamp, et al
Nature Physics 2010
Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09
Spin-injection Hall Effect
Anomalous Hall Effect
I
_ FS
OFS
O
_ _majority
minority
V
Spin Hall Effect
I
_ FS
OFS
O
_ _
V
Topological Insulators
Kane and Mele PRL 05
14
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Cartoon of the mechanisms contributing to AHE
independent of impurity density
Electrons have an “anomalous” velocity perpendicular to the electric field related to their Berry’s phase curvature which is nonzero when they have spin-orbit coupling.
Electrons deflect to the right or to the left as they are accelerated by an electric field ONLY because of the spin-orbit coupling in the periodic potential (electronics structure)
E
SO coupled quasiparticles
Intrinsic deflection B
Electrons deflect first to one side due to the field created by the impurity and deflect back when they leave the impurity since the field is opposite resulting in a side step. They however come out in a different band so this gives rise to an anomalous velocity through scattering rates times side jump.
independent of impurity density
Side jump scatteringVimp(r) (Δso>ħ/τ) ∝ λ*∇Vimp(r) (Δso<ħ/τ)
B
Skew scattering
Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. Known as Mott scattering.
~σ~1/niVimp(r) (Δso>ħ/τ) ∝ λ*∇Vimp(r) (Δso<ħ/τ) A
15
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
•1880-81: Hall discovers the Hall and the anomalous Hall effect
The tumultuous history of AHE
•1970: Berger reintroduces (and renames) the side-jump: claims that it does not vanish and that it is the dominant contribution, ignores intrinsic contribution. (problem: his side-jump is gauge dependent)
Berger
Luttinger
•1954: Karplus and Luttinger attempt first microscopic theory: they develop (and later Kohn and Luttinger) a microscopic theory of linear response transport based on the equation of motion of the density matrix for non-interacting electrons, ; run into problems interpreting results since some terms are gauge dependent. Lack of easy physical connection.
Hall
•1970’s: Berger, Smit, and others argue about the existence of side-jump: the field is left in a confused state. Who is right? How can we tell? Three contributions to AHE are floating in the literature of the AHE: anomalous velocity (intrinsic), side-jump, and skew contributions.
•1955-58: Smit attempts to create a semi-classical theory using wave-packets formed from Bloch band states: identifies the skew scattering and notices a side-step of the wave-packet upon scattering and accelerating. .Speculates, wrongly, that the side-step cancels to zero.
The physical interpretation of the cancellation is based on a gauge dependent object!!
16
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
The tumultuous history of AHE: last three decades
•2004’s: Spin-Hall effect is revived by the proposal of intrinsic SHE (from two works working on intrinsic AHE): AHE comes to the masses, many debates are inherited in the discussions of SHE.
•1980’s: Ideas of geometric phases introduced by Berry; QHE discoveries
•2000’s: Materials with strong spin-orbit coupling show agreement with the anomalous velocity contribution: intrinsic contribution linked to Berry’s curvature of Bloch states. Ignores disorder contributions.
•2005-10’s: Linear theories treating SO coupling and disorder finally merge: full semi-classical theory developed and microscopic approaches are in agreement among each other in simple models.
17
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Contributions understood in simple metallic 2D models
Semi-classical approach:Gauge invariant formulation
Sinitsyn, Sinvoa, et al PRB 05, PRL 06, PRB 07
Kubo microscopic approach:in agreement with semiclassical
Borunda, Sinova, et al PRL 07, Nunner, Sinova, et al PRB 08
Non-Equilibrium Green’s Function (NEGF) microscopic approach
Kovalev, Sinova et al PRB 08, Onoda PRL 06, PRB 08
Restriction to homogeneous magnetization. Magnetic textures lead to the so called topological AHE.
18
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Generalization to 3D: scattering in dependent AHE
Step 1. Use linearized version of Keldysh formalism to obtain
where
Kovalev, Sinova, Tserkovnyak PRL 2010
19
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Scattering-independent contribution to the AHE
Well known intrinsic contributionSide jump contribution related to Berry curvature
Remaining side jump contributionKovalev, Sinova, Tserkovnyak PRL 2010
expressed through band structure only !!
20
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Results for Luttinger model: simplest model of GaMnAs
Kovalev, Sinova, Tserkovnyak PRL 2010
It gives a formalism that allows for a systematic study of AHE through ab-initio calculations (ongoing collaboration with S. Blügel and Y. Mokrousov)
21
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Nagaosa et al RMP 10
Tentative phase diagram of AHE
Terra incognita
Previous Theories: S. H. Chun etal., PRL 2000; Lyanda-Geller et al PRB 2001 (Theory for Manganites; no scaling)
A. A. Burkov and L. Balents, Phys. Rev. Lett. 91, 057202 (2003),
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Phonon-assisted hopping between localized states
The Hamiltonian describing localized states and e-ph interaction (Holstein 1961)
with
Localization:phonon-assisted
hopping
Electric current between two sites:
Ri
RjRk
: direct conductance due to two-site hopping. Responsible for longitudinal conductance.
: off-diagonal conductance due to three-site hopping.
i j k
phonon
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Transverse charge transport: Three-site hopping (Holstein, 1961)
Interference term
Hall transition rate
Typical two real phonon process:
Typical one real (two virtual) phonon process:
Direct hoppingIndirect hopping
Geometric phase: break chirality
m: the number of real phonons included in the whole transition.
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Macroscopic anomalous Hall conductivity/resistivity via percolation theory
In the thermodynamic limit, we get the AHC:
Unfortunately, too complicated to get an analytical calculation!!!
Critical path/cluster appears when:
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
The lower and upper limits are given by (note the differences in the constrain)
For the Mott hopping, we find
Physically, the upper limit (γ=1.38) corresponds to the situation that most triads in the system are equilateral triangles (this is actually a regular distribution), while for the lower limit (γ=1.76) the geometry of triads is randomly distributed. Since the impurity sites are randomly distributed, we expect the realistic result is usually close to the lower limit in most systems.
Xiong-Jun Liu, Sinova, unpub. 2010
Anomalous Hall conductivity via percolation theory
26Nanoelectronics, spintronics, and materials control by spin-orbit coupling
I. Introduction: using the dual personality of the electron•Electronics, ferromagnetism, and spintronics•Internal coupling of charge and spin: origin and present use•Control of material and transport properties through spin-orbit coupling•Overview of program
II. Anomalous Hall effect: from the metallic to the insulating regime•Anomalous Hall effect basics, history, progress in the metallic regime•Anomalous Hall effect in the hopping regime
III.Spin injection Hall effect: a new paradigm in exploiting SO coupling•Spin based FET: old and new paradigm in charge-spin transport•Theory expectations and modeling•Experimental results
•Topological thermoelectrics:Thermoelectric figure of meritI.Increase of ZT in topological insulators.
Echoes of special relativity in condensed matter physics:
anomalous Hall effect, spin-helix transistors, and topological thermoelectrics
Echoes of special relativity in condensed matter physics:
anomalous Hall effect, spin-helix transistors, and topological thermoelectrics
27
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Towards a realistic spin-based non-magnetic FET device
[001][100]
[010]
Can we achieve direct spin polarization injection, detection, and manipulation by electrical means in an all paramagnetic semiconductor system?
Long standing paradigm: Datta-Das FET (1990)Exploiting the large Rashba spin-orbit coupling in InAs
Electrons are confined in the z-direction in the first quantum state of the asymmetric trap and free to move in the x-y plane.
gate
ky [010]
kx [100]
Rashba effective magnetic field
⊗⊗⊗
28
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Can we achieve direct spin polarization injection, detection, and manipulation by electrical means in an all paramagnetic semiconductor system?
Long standing paradigm: Datta-Das FET (1990)Exploiting the large Rashba spin-orbit coupling in InAs
Towards a realistic spin-based non-magnetic FET device
High resistance “0”Low resistance “1”
BUT lMF << LS-D at room temperature
29
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Dephasing of the spin through the Dyakonov-Perel mechanism
LSD ~ μm
lMF ~ 10 nm
30
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Problem: Rashba SO coupling in the Datta-Das SFET is used for manipulation of spin (precession) BUT it dephases the spin too quickly (DP mechanism).
New paradigm using SO coupling: SO not so bad for dephasing
1) Can we use SO coupling to manipulate spin AND increase spin-coherence?
• Can we detect the spin in a non-destructive way electrically?
31
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Spin-dynamics in 2D electron gas with Rashba and Dresselhauss spin-orbit coupling
a 2DEG is well described by the effective Hamiltonian:
α > 0, β = 0[110]
[110]_
ky [010]
kx [100]
Rashba: from the asymmetry of the confinement in the z-direction
α = 0, β < 0 [110]
[110]_
ky [010]
kx [100]
Dresselhauss: from the broken inversion symmetry of the material, a bulk property
1) Can we use SO coupling to manipulate spin AND increase spin-coherence?
32
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Spin-dynamics in 2D electron gas with Rashba and Dresselhauss spin-orbit coupling
Something interesting occurs when
• spin along the [110] direction is conserved• long lived precessing spin wave for spin perpendicular to [110]
The nesting property of the Fermi surface:
Bernevig et al PRL 06, Weber et al. PRL 07
Schliemann et al PRL 04
33
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Effects of Rashba and Dresselhaus SO coupling
α= -β
[110]
[110]_
ky [010]
kx [100]
α > 0, β = 0[110]
[110]_
ky [010]
kx [100]
α = 0, β < 0[110]
[110]_
ky [010]
kx [100]
34
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Spin-dynamics in 2D systems with Rashba and Dresselhauss SO coupling
For the same distance traveled along [1-10], the spin precesses by exactly the same angle.
[110]
[110]_
[110]_
35
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Persistent state spin helix verified by pump-probe experiments
Similar wafer parameters to ours
36
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Spin-helix state when α ≠ β
Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09
For Rashba or Dresselhaus by themselves NO oscillations are present; only and over damped solution exists; i.e. the spin-orbit
coupling destroys the phase coherence.
There must be TWO competing spin-orbit interactions for the spin
to survive!!!
37
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Problem: Rashba SO coupling in the Datta-Das SFET is used for manipulation of spin (precession) BUT it dephases the spin too quickly (DP mechanism).
New paradigm using SO coupling: SO not so bad for dephasing
1) Can we use SO coupling to manipulate spin AND increase spin-coherence?
• Can we detect the spin in a non-destructive way electrically?
Use the persistent spin-Helix state and control of SO coupling strength(Bernevig et al 06, Weber et al 07, Wünderlich et al 09)
✓
38
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Type (i) contribution much smaller in the weak SO coupled regime where the SO-coupled bands are not resolved, dominant contribution from type (ii)
Crepieux et al PRB 01Nozier et al J. Phys. 79
Two types of contributions: i)S.O. from band structure interacting with the field (external and internal)ii)Bloch electrons interacting with S.O. part of the disorder
Lower bound estimate of skew scatt. contribution
AHE contribution to Spin-injection Hall effect in a 2D gas
Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09
39
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Local spin-polarization → calculation of AHE signal
Weak SO coupling regime → extrinsic skew-scattering term is dominant
Lower bound estimate
Spin-injection Hall effect: theoretical expectations
1) Can we use SO coupling to manipulate spin AND increase spin-coherence?
• Can we detect the spin in a non-destructive way electrically?
Use the persistent spin-Helix state and control of SO coupling strength
Use AHE to measure injected current polarization electrically
✓
✓
40
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Spin-injection Hall device measurements
VL
SIHE ↔ Anomalous Hall
Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09
41
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
T = 250K
Further experimental tests of the observed SIHE
42
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
VH2
I
VbVH1
x
VH2
VbVH1
x
(a)
(b)
SiHE: new results
Spin Hall effect transitor:Wunderlich, Irvine, Sinova, Jungwirth,
et al, arXiv:1008.2844
SiHE
inverse SHE
43
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
VH
Vg
I
Vb
VH
VgVb
x
Δx=1μm
σ+
SiHE transistor
Spin Hall effect transitor:Wunderlich, Irvine, Sinova, Jungwirth,
et al, arXiv:1008.2844
44
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
σ-
σ-σ-
σ-
H1 H2
0+0.1
-0.1
Vg2 [V]
RH1
[Ω]
0 12 RH2
[Ω]0 66 3
SHE transistor AND gate
45Nanoelectronics, spintronics, and materials control by spin-orbit coupling
I. Introduction: using the dual personality of the electron•Electronics, ferromagnetism, and spintronics•Internal coupling of charge and spin: origin and present use•Control of material and transport properties through spin-orbit coupling•Overview of program
II. Anomalous Hall effect: from the metallic to the insulating regime•Anomalous Hall effect basics, history, progress in the metallic regime•Anomalous Hall effect in the hopping regime
III.Spin injection Hall effect: a new paradigm in exploiting SO coupling•Spin based FET: old and new paradigm in charge-spin transport•Theory expectations and modeling•Experimental results
•Topological thermoelectrics:Thermoelectric figure of meritI.Increase of ZT in topological insulators.
Echoes of special relativity in condensed matter physics:
anomalous Hall effect, spin-helix transistors, and topological thermoelectrics
Echoes of special relativity in condensed matter physics:
anomalous Hall effect, spin-helix transistors, and topological thermoelectrics
46
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Control of materials and transport properties via spin-orbit coupling
AsAsGaGa
MnMn
New magnetic materials
Nano-transport
Spintronic Hall effects
Magneto-transport
Topological transport effects
Effects of spin-orbit coupling in
multiband systemsCaloritronics
Topological thermoelectrics
47
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
From AHE to topological insulators to thermoelectrics
Vishwanath et al Nature Physics 09
Dislocations have 1D channels which also protected
Topological Insulators: edge (2D) or surface states (3D) survive disorder effects when the bulk gap is produced by spin-orbit coupling
Kane, Zhang, Molenkamp, Moore, et al
Zhang, Physics 1, 6 (2008)
X
X
QSHE in HgTe
48
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
From AHE to topological insulators to thermoelectrics
Best thermoelectrics
Can we obtain high ZT through the topological protected states; are they related to the high ZT
of these materials?
Vishwanath et al 09
Dislocations have 1D channels which also protected
??
Seebeck coefficient
electrical conductivity
electric thermal conductivity phonon thermal conductivity
49
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Bi1−xSbx (0.07 < x < 0.22)where the L’s are the linear Onsager dynamic coefficients
Localized bulk states
Possible large ZT through dislocation engineering
Tretiakov, Abanov, Murakami, Sinova APL 2010
50
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Possible large ZT through dislocation engineering
Remains very speculative but simple theory gives large ZT for reasonable parameters
Tretiakov, Abanov, Murakami, Sinova APL 2010
51Nanoelectronics, spintronics, and materials control by spin-orbit coupling
• Anomalous Hall effect: from the metallic to the insulating regimeI.Established a consistent theory of Anomalous Hall effect for metallic regime with homogeneous magnetizationII.Theory of observed scaling in Anomalous Hall effect in the hopping regime
•Spin injection Hall effect: a new paradigm in exploiting SO couplingI.Modeled and constructed a spin FET in the diffusive regimeII.First spin AND gate with pure spin currents
I.Topological thermoelectrics:Speculative theory of how to increase of ZT in topological insulators via line dislocations.
SUMMARY: anomalous Hall effect, spin-helix transistors, and
topological thermoelectrics
SUMMARY: anomalous Hall effect, spin-helix transistors, and
topological thermoelectrics
Control of materials and transport properties via spin-orbit coupling
A long list of challenges: DMSs, Antiferromagnetic semiconductors, current driven magnetization dynamics, pseudo-spintronics in double layer systems, spin-caloritronics (Spin Seebeck effect)
52
Nanoelectronics, spintronics, and materials control by spin-orbit coupling
Allan MacDonald U of Texas
Tomas JungwirthTexas A&M U.
Inst. of Phys. ASCRU. of Nottingham
Joerg WunderlichCambridge-Hitachi
Laurens MolenkampWürzburg
Xiong-Jun LiuTexas A&M U.
Mario BorundaTexas A&M Univ.
Harvard Univ.
Nikolai SinitsynTexas A&M U.
U. of TexasLANL
Alexey KovalevTexas A&M U.
UCLA
Liviu ZarboTexas A&M Univ.
Xin LiuTexas A&M U.
Ewelina Hankiewicz(Texas A&M Univ.)
Würzburg University
Sinova’s group
Principal Collaborators
Gerrit BauerTU Delft
Bryan GallagherU. of Nottingham
and many others
Oleg TretiakovTexas A&M U.