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Evidence of 3D Dirac dispersion in PbSnSe by
the de Haas - van Alphen oscillations
Mario NovakDepartment of Physics
University of Zagreb
TOPOLOGICAL INSULATORSGRAPHENE vs
𝐻2𝐷 = ℏ𝑣𝐹𝝉 ∙ 𝒌 𝐻2𝐷 = ℏ𝑣𝐹𝝈 ∙ 𝒌
Latice pseudospin Pseudospin – momentum
locking - helicity
Real spin Spin – momentum
locking: 𝒌 ⊥ 𝝈 in plane
2D systemWeak S-O interactionLattice symmetry protection
By Google 107
𝒌𝝉𝒌 𝝉
𝒌
𝝈𝒌
𝝈
2D QSH3D Z2 invariantsStrong S-O interactionTRS protection
By Google 105
What are Topological insulators
Special materials with insulating balk and conducting surface
Origin of metallic surface lies special properties of bulk wave functionBulk surface correspondence
Bi2Se3
Rep. Prog. Phys. 75 096501 (2012)Binghai Yan and Shou-Cheng Zhang
Band inversion is curtail – NONTRIVIAL TOPOLOGYDirac cones at TRS pointsOdd number of Dirac cones in the band gap
InsulatororVacuum
Interesting field for testing Elemental Particle Physics concepts
- Dirac, Weyl and Majorana fermion, magnetic monopoles and axion dynamics
PbSnSe and Topological Crystalline Insulators
Topological crystalline insulator
Ordinary insulator
x
Topological Crystalline Insulators 𝑻𝑹𝑺 ⟷ 𝑪𝒓𝒚𝒔𝒕𝒂𝒍 𝑺𝒚𝒎𝒆𝒕𝒓𝒚
𝑃𝑏1−𝑥𝑆𝑛𝑥𝑆𝑒
For x=0.17 critical point- band inversion pintI. Zeljkovic et al.
Nature Materials 14, 318 (2015)
Topological SS@ x= 0.17 -Topological phase transition- 3D Dirac dispersion?
Band inversion
3D Dirac semimetals
3D equivalent of graphene
𝐻3𝐷 = ℏ𝑣𝐹𝝈 ∙ 𝒌
𝜎𝑥 , 𝜎𝑦, 𝜎𝑧 Spin Pauli matrix
𝑘𝑥 , 𝑘𝑦, 𝑘𝑧 kristal momentum
Robust to perturbation Dirac cone is spin degenerated Helicity
3D Dirac semimetals have nontrivial topology – due to band inversion- strong S-O interaction
Band gap is not open to crate Topological Insulator
𝜒 =𝝈 ∙ 𝒌
𝜎𝑘
𝒌𝝈
𝒌𝝈
Intrinsic 3D Dirac semimetal
- Crystal symmetry protection from gap opening
Cd3As2, Na3Bi, BaAgBi….
Q. D Gipson et al. arXiv:1411.0005
Accidental band touching
- Nontrivial topology- CB and VB touching by composition tuning- Always at Topological critical point
Cd3As2
Pb1-xSnxSe, Pb1-xSnxTe
Na3Bi
- High mobility 107 cm2/Vs- Very strong MR- Giant diamagnetism
TlBiSSe
Beyond 3D Dirac systems:
Weyl semimetals
New state of matter – Chiral Dirac particles
Left and right Dirac electrons
𝐻3𝐷 = ±ℏ𝑣𝐹𝝈 ∙ 𝒌 ′
Spin degenerate 3D Dirac
𝒌𝝈
𝒌𝝈
Dirac point
𝒌 ′𝝈 𝒌 ′𝝈
DP
Weyl point Weyl point arXiv: 1501.00755
Symmetry breaking
TaAs, TaP, NbAs, NbP
Family of recently predicted WSM
How to get information on type dispersion by magnetic and transport measurements?
∆𝑀~𝐴 𝑇, 𝐵 sin(2𝜋 𝐹
𝐵+ ∅(𝛾))
Lanadu quantization and de Haas von Alphon oscillations (dHvA)
Phase factor𝜙𝐵 = 2𝜋1
2− 𝛾
𝛾 =1/20
Berry phase
𝐴𝒌 𝜖𝒌 = 𝑛 + 𝛾 2𝜋𝑒𝐵/ℏ Osanger’s relation
Parabolic
Linear
∅ 𝛾 = 2𝜋(1
4±1
4− 𝛾 ±
1
8)
dHvA
Sample: Monocrystal of Pb0.83Sn0.17Se with reduced charge carriers ~1017 cm3
Sample information
20 40 60 800.0
0.2
0.4
0.6
0.8
1.0
(422)(420)(222)
(220)
(600)
(400)
Inte
nsity (
a.u
.)
2
(200)
Samples were grown by modified Bridgman method
Solid solution with cubic structure
0.2 0.4 0.6 0.8 1.0-0.2
-0.1
0.0
0.1
0.2 5K 7K
8K 10K
13K 15K
17K 20K
30K
M
(em
u/m
ol)
1/B (1/T)
5K
0 20 40 60 80
Am
pli
tud
e
F(T)
F=8.7 T
SQUID measurements of dHvA oscillations
dHvA oscillations FFT of the oscillations
Landau level indexing
Phase determination
Quadratic dispersion: Schrodinger electrons
Linear dispersion: Dirac electrons
0 1 2 3 4 5 6 7 80.0
0.2
0.4
0.6
0.8 MAX
MIN
QUADRATIC
LINEAR
1/B
n (
1/T
)
n
0.2 0.4 0.6 0.8 1.0-0.2
-0.1
0.0
0.1
0.2
M
(em
u/m
ol)
1/B (1/T)
∅ 𝛾 = 2𝜋(1
4±1
4− 𝛾 ±
1
8)
Spin splitting
0 5 10 15 20 25 300
1
Am
pli
tud
e
T(K)
m*=0.04m
e
Effective mass
0.0 0.2 0.4 0.6 0.8 1.0
-2.1
-1.8
-1.5
-1.2
-0.9
ln(
M B
1/2si
nh(
T/B
))
1/B (T-1)
dHvA
=5´-13
s
Scattering rate
Much stronger than form transport measurements
Thank you for your
attention