dressed topological edge states in hgte-based 2d

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

http://www.phys.ens.fr

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


Gate voltage Vg [V]

Re

sis

tan

ce

R

[kΩ

]

Many observations…

• Quantized transport

• SQUID imaging

• …


QSH edge states

H1

E1

edge states

The HgTe quantum well:

Experimental observations:

• 2D topological insulator

• Helical edges states

• Spin polarised


… 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


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


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):


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


k.p theory

H1

E1

H1

E1

H1

E1


Rt & Cq vs µ


• Rt peak aligned with the gap

k.p theory


• Cq good averall agreement at high µ…

• … but smear in the gap → inhomogeneities/disorder


Rt & Cq vs µ


• Rt peak aligned with the gap

Can we distinguish our (1D) edges states ? → length study

k.p theory


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


• 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


Length dependence


• 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)


Adm

itta

nce (

mS

)

Frequency (GHz)

0.05

0.15

0.1

0 1 2 3

0

0.2

1.5 meV


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


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


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.



Thank you !

dressed topological edge states in hgte-based 2d

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