Laboratoire de Physique de l’Ecole normale supérieure
ENS, Université PSL, CNRS, Sorbonne Université, Université
Paris-Diderot, Sorbonne Paris Cité, Paris, France
www.phys.ens.fr
Alexandre Gourmelon
Dressed topological edge states
in HgTe-based 2D topological insulators
Erwann Bocquillon C2N - 02/04/20192
Acknowledgements
Uni. Würzburg (EP 3)
▻ Students : K. Bendias, S. Hartinger, L. Lunczer, R. Schlereth
▻ Staff : H. Buhmann, L.W. Molenkamp
LPENS (formerly LPA, Paris)
▻ Student : A. Gourmelon, H. Bartolomei
▻ Post-doc : M. C. Dartiailh (now at NYU)
▻ Permanents : G. Fève, B. Plaçais, J.-M. Berroir, E. Bocquillon
Alexandre Gourmelon Capri – 06/05/2019
Discussion: D. Bercioux, T. Van Der Berg, R. Calvo
Erwann Bocquillon C2N - 02/04/2019
Gate voltage Vg [V]
Re
sis
tan
ce
R
[kΩ
]
Many observations…
• Quantized transport
• SQUID imaging
• …
Erwann Bocquillon C2N - 02/04/20193
QSH edge states
H1
E1
edge states
The HgTe quantum well:
Experimental observations:
• 2D topological insulator
• Helical edges states
• Spin polarised
Alexandre Gourmelon Capri – 06/05/2019
… but not robust:
For L>few µm : Rxx is not
quantized anymore (h/(2e)2)
→ Scattering appears
M. König et al., Science, 318(5851):766, 2007
K. Bendias et al., Nanolett.4, 1839 (2018)
Erwann Bocquillon TMS 2018 - 08/2018Erwann Bocquillon TMS 2018 - 08/20184
J. I. Väyrynen et al., PRL 110, 216402 (2013)
Microwave as a diagnostic tool
Many possible mechanisms: Charge puddles, e-e interactions, inhomogeneous SOC,…
[1] A. Ström et al., PRL 104, 256804 (2010)
[2] F. Crépin et al., PRB 86, 121106 (2012)
[3] T. L. Schmidt et al., PRL 108, 156402 (2012)
[4] S. Essert et al., PRB 92, 205306 (2015)
[5] J. I. Väyrynen et al., PRB 90, 115309 (2014)
[6] J. Maciejko et al., PRL 102, 256803 (2009)
[7] F. Geissler et al., PRB 89, 235136 (2014)
Probing from DC to microwaves:
HgTe QW
Alexandre Gourmelon Capri – 06/05/2019
A powerful diagnosis tool :
• Resistive response : transport
• Capacitive coupling : probe of DOS
• Different dynamics for bulk and
edges
Erwann Bocquillon TMS 2018 - 08/2018
metal metal
Vg
oxide
∆𝐸 =𝑒2
𝐶𝑔𝑒𝑜
e-µ = 0
µ(𝑧)
Vg
∆𝐸 =𝑒2
𝐶𝑔𝑒𝑜+
𝑒2
𝐶𝑞
e-
Q
V
𝐶(𝑉) =𝑑𝑄
𝑑𝑉
µ ≠ 0
metal oxide HgTe QW
𝝆𝟐𝑫𝑬𝑮 ≠ ∞
ρ
µ
0
δµ =𝑒2
𝐶𝑞
Probe DOS by quantum capacitance
Alexandre Gourmelon Capri – 06/05/2019
Metal-Oxide-Metal : Metal-Oxide-Topological Insulator :
𝑪𝒒 𝜇 = 𝒆𝟐𝝏𝒏
𝝏𝝁= 𝒆𝟐𝝆(𝜇)
Probing Cq = probing the DOS
5
𝜇(𝑉𝑔) = න0
𝑉𝑔
1 −𝐶𝑡(𝑉)
𝐶𝑔𝑒𝑜𝑑𝑉
Erwann Bocquillon TMS 2018 - 08/2018
Experimental set-up
Hg0.32Cd0.68Te (15nm)
CdTe substrate
Hg0.32Cd0.68Te (70nm)
HgTe (5.8 - 10.6nm)
HfO2 (8 nm)
Gold electrode
(gate) Gold electrode
(source)
𝑪𝒈𝒆𝒐
𝑪𝒒𝑹𝒕
Sample: Cryogenic probe station:
Vector Network Analyzer measurement:
Port 1T ≈ 10K
Port 1 Port 2
R & C extraction (low frequency):
Alexandre Gourmelon Capri – 06/05/2019
𝑅𝑒(𝑌(ω)) ≈ 𝑹𝒕𝐶²ω²
𝐼𝑚(𝑌(ω)) ≈ i𝜔𝑪t
Adm
itta
nce (
mS
)
Frequency (GHz)0 0.2 0.4 0.6 0.8 1
0.4
0
0.5
0.2
0.3
0.1
6
Erwann Bocquillon C2N - 02/04/2019Erwann Bocquillon C2N - 02/04/2019
Rt & Cq vs µ
Alexandre Gourmelon Capri – 06/05/20197
k.p theory
H1
E1
H1
E1
H1
E1
Erwann Bocquillon C2N - 02/04/2019Erwann Bocquillon C2N - 02/04/2019
Rt & Cq vs µ
Alexandre Gourmelon Capri – 06/05/20197
• Rt peak aligned with the gap
k.p theory
Erwann Bocquillon C2N - 02/04/2019
• Cq good averall agreement at high µ…
• … but smear in the gap → inhomogeneities/disorder
Erwann Bocquillon C2N - 02/04/2019
Rt & Cq vs µ
Alexandre Gourmelon Capri – 06/05/20197
• Rt peak aligned with the gap
Can we distinguish our (1D) edges states ? → length study
k.p theory
Erwann Bocquillon C2N - 02/04/2019Erwann Bocquillon C2N - 02/04/2019
Length dependence
Topological A (10.6nm) Topological B (8nm)Trivial (5.8nm)
3 µm
5 µm
10 µm
20 µm
bulk{
edge
{
3 µm5 µm
10 µm
20 µm
Alexandre Gourmelon Capri – 06/05/20198
• L = 3, 5, 10, 20 µm
• No length dependance for trivial
• Clear length dependence for Topological A, B and other samples (not shown)
Normalized
by A = L²
Erwann Bocquillon C2N - 02/04/2019Erwann Bocquillon C2N - 02/04/2019
Length dependence
Alexandre Gourmelon Capri – 06/05/20199
• 2D contribution: cq2D follows k.p predictions (even better than cq) with smearing
• 1D contribution: cq1D
➢ only in Topological samples
➢ detected in gap and conduction band!
➢ cq1D ≃ 5-10 nF.m-1 very high! (in theory cq
1D = 4𝑒2
ℎ𝑣𝑓≃ 0.2 nF.m-1)
→ « Dressed » edge states
Topological A (10.6nm) Topological B (8nm)Trivial (5.8nm)
Erwann Bocquillon C2N - 02/04/2019Erwann Bocquillon C2N - 02/04/2019
Adm
itta
nce (
mS
)
Frequency (GHz)
0.05
0.15
0.1
0 1 2 3
0
0.2
1.5 meV
Alexandre Gourmelon Capri – 06/05/2019
High frequency mesurement : Overview
10
0.4
0
0.6
0.2Adm
itta
nce (
mS
)
-20 meV
Re(Y)
Im(Y)
Fit
Frequency (GHz)0 1 2 3
Far in the band: 1 mode transport (2D bulk) In the gap: 2 mode transport (2D bulk + 1D edges)
High frequency → evanescent waves
• Cross over at 𝒇𝒄 = ൗ𝟏𝟐π𝑹𝒕𝑪𝒕
• 1 characteristic 𝑹𝒕𝑪𝒕 time = 1 mode
• 2 characteristic times = 2 modes
➢ 𝑹𝒕𝟐𝑫𝑪𝒕
𝟐𝑫 = ൗ𝟏𝟐𝝅𝒇𝒄
𝟐𝑫 : slow bulk mode
➢ 𝑹𝒕𝟏𝑫𝑪𝒕
𝟏𝑫 = ൗ𝟏𝟐𝝅𝒇𝒄
𝟏𝑫 : fast edge mode
𝒇𝒄 𝒇𝒄𝟐𝑫 𝒇𝒄
𝟏𝑫
Erwann Bocquillon C2N - 02/04/2019
Vg = -0.3 V : empty bulk (pinned to VB)
‘dressed’ edge states
Erwann Bocquillon
The « dressed » edges states
edge
Vg = 0 V : homogeneously n-doped
Vg = -0.7 V : homogeneously p-doped
Vg = -0.5 V : p-doped bulk
‘clean’ edge states
Alexandre Gourmelon Capri – 06/05/201911
Band bending effect
edge
edge
edge
bulk
bulk
bulk
bulk
Erwann Bocquillon C2N - 02/04/2019Erwann Bocquillon
Conclusion
• Length dependence show indeed 1D contribution existing only for topological samples
• Validated by 2-mode dynamic
But this supposed edge states are very dense compared to expectation cq1D ≃ 10 nF m-1
→ New scenario : dressed edge states (electrostatic)
In agreement with results of M.R. Calvo et al.
Alexandre Gourmelon Capri – 06/05/201911
Erwann Bocquillon C2N - 02/04/2019
Thank you !