Sh

Topology in e-h Double Layers

Rui-Rui Du

Rice University

Shoucheng Zhang Memorial Workshop May 2-5,.2019

路漫漫其修远兮吾将上下而求索

I shall take a long Journeyto seek eternal truth

1989

1992

Composite Fermions

Du, Stormer, Tsui, Pfeiffer, West 1993

A Gift from Nature

Infrared Detectors

FQHELaser

Transistor

AlAsGaAs

Eg

Ge Si

InAs

GaSb

IQHE

QSHE

Exciton

Insulator

OUTLINES1. Introduction

2. Materials and Devices

3. Quantum Spin Hall Effect

4. Large Gap TI

Quantized Conductance of Edge States

Phys. Rev. Lett. 2011, Knez et al, Evidence for edge modes

Phys. Rev. Lett. 2012, Knez et al, Perfect Andreev reflection of edge-SC junction

Phys. Rev. Lett. 2015, Du et al, Quantized edge states for small samples

Phys. Rev. Lett. 2014, Stanton et al,

Phys. Rev. Lett. 2014, Knez et al.

Phys. Rev. Lett. 2015, Li et al

Phys. Rev. Lett. 2017, Du, et al , N.Comm. 2017, Du et al

Date: 01/09/2011 (04:54:27 PM CDT)

From: sczhang <sczhang@stanford.edu>

To: rrd@rice.edu

Cc: Ik5@rice.edu, Chaoxing Liu <lcxlight@gmail.com>

Dear Rui and Ivan,

I read your beautiful paper over and over

again, and simply can not withhold

my excitement about this important

breakthrough in the field!

Eg1

Large

Gap

Eg2

Small

Gap

Eg3

Negative

Gap

Mott, Philos Mag 1961

Keldysh, Yu.V., Fizika ,1964

Halperin & Rice, Rev Mod Phys

1968

+e

-e

Exciton Insulators

EF

EFTopological

Exciton Insulator

w/ edge states

OUTLINES

1. Introduction

2. Materials and Devices

3. Quantum Spin Hall Effect

4. Large Gap TI

10

Liu, et al, PRL 100, 236601(2008)

6.1 A Family

1. Band parameter

DE = E1 – H1

tuned by width, x, gates

2. DE < 0 inverted -0.15 eV to 0

Tunneling mix e-h and opens

a gap at finite k-vector

p

n SCSC

NTT, ETH

Wafer and Device

11

n-Inv

n-Metal

p-Metal

TI

NI

p-Inv

Two Limits of Coupling

Strong

Tunneling

1- D

Dirac Fermions

Majorana

Pair

Mini Gap

S-Superconductor+

Weak Tunneling

Strong Coulomb

2D

Excitons

Exciton

Insulator

Counter flow

Superfluid

-e

+e

E

Iin

Iout

Gerry Sullivan and Amal Ikhlassi

In front of GEN III MBEICQM PKU

OUTLINES

1. Introduction

2. Materials and Devices

3. Quantum Spin Hall Effect

4. Large Gap TI

Corbino Disk

rBulk >> 10 MW

Minigap ~ 66 K

Mobility gap

~ 26 K

Truly Insulating Bulk

15

Lingjie Du

Conductance Plateau up to 4 K

16

Non-Local Ede Transport: H-Bar

17Lingjie Du

18

SQUID Imaging of InAs/GaSb Edge Modes

Stanford: Spanton, Moler

Rice: Lingjie Du, RRDPRL 14

50 mm

Current(Horizontal)

Current(Vertical)

APS March Meeting 2018, LA, California, USA

QSHE vs. Exciton Condensation

A competition between even- and odd-parity exciton

condensate

the parity of order parameter

o For small A, topologically trivial s-

wave exciton condensate phase

o For large A, topologically nontrivial

QSH insulator phase with a p-wave

exciton order parameter

Phys. Rev. Lett.112,

176403(2014)

Coupling term between two layers

odd-parity even-parity

Editors' ChoicePhysics

Probing an excitonic insulator

1.Jelena Stajic

Science 22 Dec 2017:

Vol. 358, Issue 6370, pp. 1552-1553

DOI: 10.1126/science.358.6370.1552-g

Bohr Rad. ~ 45A

Intra. Dis. ~ 100-300A

Binding E. ~100K

THz Absorption Spectrum

Transport Measurements

Conductance Oscillations

in the Gap of Inverted InAs/GaSb

Frequency Jump from Metallic to Gap Regimes

QSH to QH Topological Phase Transition

OUTLINES

1. Introduction

2. Materials and Devices

3. Quantum Spin Hall Effect

4. Large Gap TI

Strained QWS

Strain Effects on the Band Structures

9.5 nm InAs/4 nm Ga0.75In0.25Sb

InAs/GaSb InAs/In0.25Ga0.75Sb

20% Indium

~ 1% strain in InxGa1-xSb

0 % 60 K

25% 130 K

32% 250 K

40% 480 K

Enhanced Bulk Hybridization Gaps

20% 25% 32%

B//

0

25

32%

B//

Quantized Edge Transport in 10 um Length

Quantized in a 10um Hall Bar

April 2018

All based on InAS/GaSb and InAs/InGaSb

Gap > 50 meV

Large Fermi velocity

Epitaxial Transfer Process

• (a,b,c) The epitaxially grown, single-crystal

InAs films are patterned with PMMA and

wet etched into nanoribbon (NR) arrays. (d)

A subsequent selective wet etch of the

underlying AlGaSb sacrificial layer. InAs

NRs are partially released. (e,f) transfer of

NRs by using an elastomeric PDMS slab

resulting the formation of InAs NR arrays on

Si/ SiO2 substrates.

Partially released InAs nanoribbons

(a) (b) (c)

(f) (e) (d)

姚思齐，韩中东

Marcus, Palmstrøm groups Hard Gap

SiO2GaInSbInAs

Al Al

Our Group

Double-Layer Excitonic Condensations

Strong

Tunneling

1- D

Dirac Fermions

Majorana

Pair

Mini Gap

S-Superconductor+

Weak Tunneling

Strong Coulomb

2D

Excitons

Exciton

Insulator

Counter flow

Superfluid

-e

+e

E

Iin

Iout

SUMMARY1) Quantum Spin Hall Effect inInAs/GaSb

2) Ground States becomes Excitoinc Insulator

3) Large gap TI is within reach

4) Next : Carry on

A clean laboratory for

electron/hole many-particle physics

1. Materials: Strained-Layer InAs/GaInSb

2. Large-Gap QSHI

3. Double-Layer Excitonic Condensation

40

6.1 A Family

1. Band parameter

DE = E1 – H1

tuned by width, x, gates

2. DE < 0 inverted -0.15 eV to 0

Tunneling mix e-h and opens

a gap at finite k-vector

Liu et al, PRL 100, 236601 (2008)

Infrared Detectors

p

n SCSC

NTT, ETH

Wafer and Device

41

n-Inv

n-Metal

p-Metal

TI

NI

p-Inv

C. Liu et al, PRL 100 236601

(2008)Phase Diagram

Three Regimes of InAs/GaSb System

Shallowly InvertedDeeply Inverted

(semimetal,

bulk still conducting)

Non-

inverted

(Normal

Insulator)

This is the regime

for QSHE !

Quantum Spin Hall Insulators (QSHIs)

L. Du et al, PRL 114 096802 (2015)

InAs/GaSb QWs in Shallowly

Inverted Regime

Larger samples:

Coherent length ~ 4 mm

Some backscattering

Small sample

44

* Quantized conductance for small samples

* Non-quantized conductance for large samples

* Conductance does not change under high B//

•Low velocity of edge modes

uF ~ 2 x104 m/s

kF ~ 1 x 106/cm

•Extreme. long scattering time

t=l/uF = 4mm/(2x104m/s)~200 ps

•Tunable mode dispersion

Properties of InAs/GaSb Edge States

HgTe

5 x105 m/sg = e2/ uF e

WHY Large-gap 2D Topological Insulators

• Recover single particle

properties

“Plain Vanilla QSHI”

• More insulating bulk gaps

• Long coherent length

Strained QWS

Strain Effects on the Band Structures

9.5 nm InAs/4 nm Ga0.75In0.25Sb

InAs/GaSb InAs/In0.25Ga0.75Sb

20% Indium

~ 1% strain in InxGa1-xSb

0 % 60 K

25% 130 K

32% 250 K

40% 480 K

Enhanced Bulk Hybridization Gaps

20% 25% 32%

B//

0

25

32%

B//

“Coherent Length” increase

with less inverted band:

Correlated with increased VF

- Less interacting 1D Electronic system

- Move away from Luttinger

Coherent length increases with increasing VF

Quantized Edge Transport in 10 um Length

Quantized in a 10um Hall Bar

TRS Protected Helical Edge States

9.5 nm InAs/4 nm Ga0.75In0.25Sb

SiO2

Compatible with III-V CMOS Technology

Marcus, Palmstrøm groups Hard Gap

SiO2GaInSbInAs

Al Al

Our Group

3. Double-Layer Excitonic Condensations

Strong

Tunneling

1- D

Dirac Fermions

Majorana

Pair

Mini Gap

S-Superconductor+

Weak Tunneling

Strong Coulomb

2D

Excitons

Exciton

Insulator

Counter flow

Superfluid

-e

+e

E

Iin

Iout

57

Mott, Philos Mag 1961

Knox, 1963

Keldysh, Yu.V., Fizika ,1964

Jerome, Rice, Kohn, 1967

Halperin & Rice, Rev Mod Phys, 1968

The Exciton Analog of BCS Superconductivity

Electron-Hole Pairing Cooper Pairing

58

BEC

BCSBCS

dDilute limit: 5 x 1010/cm2

Reasonably high mobility 105 cm2/Vs

Electron-hole symmetry

9.5nm

10nm

5nm

Observation

T > 4 K

Main Peak

Onset 40 K

Gap 90 K

Side Peak

Onset 15 K

Gap 25 K

Large Energy Scale

61

THz Absorption Shows e-h Pair-breaking Excitation

Summary for Large Gap QSHI in Strained Layer QWs

• The strained InAs/Ga1-xInxSb QWs offers

Larger bulk insulating gap up to 50 meV

Z2 2D topological insulator

Double-layer exciton condensation

• Future work:

• SC Proximity + Edge States + FM

Insulator

• Counter-flow experiments

QSH Edge

Majorana Platform