Quantum Matter in
High Magnetic Fields
Uli Zeitler
Semiconductors & Nanostructures
High Field Magnet Laboratory (HFML – EMFL)
Institute for Molecules and Materials (IMM)
Radboud University, Nijmegen, the Netherlands
北京大学 量子材 Seminar PKU-ICQM, 16-Nov-2017
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Contents
• Part I - Who are we
IMM@RU, HFML / FELIX
Research at HFML
• Part II – Low dimensional materials in high fields
Graphene et al. – 2D materials
Measuring Chirality
Ising superconductivity in MoS2 and WS2
Topological Matter
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Radboud University
www..ru.nl/
21 000 students
5 000 staff
300 professors
7000 publications
Broad Research University
The Netherlands
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Institute for Molecules and Materials
www..ru.nl/imm
Theme 1: Structure and Dynamics of Molecules
Theme 2: Chemistry and Spectroscopy of Complex Molecular Systems
Theme 3: Quantum Matter
• Interdisciplinary research institute: Chemistry & Physics
• Mission: Fundamental research to understand, design and control the functioning of molecules and materials
• Research Facilities
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Facilites @ IMM
www..ru.nl/imm
The IMM exhibits a multitude of advanced spectroscopic tools that allow for a detailed characterisation of matter in the nano-domain. Many facilities support each other and are used both by in-house and external users.
High Field Magnet Laboratory (HFML)
FELIX Laboratory (Free infrared lasers)
SPiN labs (Scanning probe)
NMR Laboratory
Life Science Trace Gas Facility
Clean rooms and laser facilities
HFML & FELIX @ Radboud University
http://www.ru.nl/felix/ http://www.ru.nl/hfml/
Cutting-edge technology Pioneering science
Mission of HFML/FELIX
• Develop infrared and THz sources
• Generate the highest possible DC-field
• Advanced instrumentation
• Research
- Molecular physics
- Condensed matter
• User facility
> 150 projects p/a
> 250 users p/a
• Public outreach
• Innovation
Smart Materials
Graphene / 2D materials
(topological) spintronics
High-Tc superconductors
Energy / Sustainability
catalysis: water H2
thermo-electricity
photosynthesis
Discover Control Manipulate
Health
targeted drug delivery
biomarkers for diagnosis
new structures for pharmaceuticals
Pioneering science Innovation
HFML/FELIX – a unique combination on a worldwide scale
IR/THz-FEL Facilities
DC HIGH-FIELD Facilities
>150 projects p.a.
>250 visitors p.a. from 25 countries
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
HFML @ RU
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
High Field Labs (HFML Nijmegen, Grenoble, Tallahassee, Tsukuba):
Superconductors 20 T
DC Bitter magnets & hybrid 30-45 T
Pulsed magnets (0.001s) 50-100T
Field strengths: typical magnetic fields
Highest man made fields (0.000001 s) Explosive, destructive 1000T
Neutron stars in the cosmos 100 000 000T
Magnetic fields at home: loudspeakers 1T
The earth magnetic field 0.000 05 T
The ‘smallest magnetic field: brain pulses 0.000 000 01 T
fridge magnet sticker 0.05 … 0.1 T
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
How to make high DC magnetic fields?
Cold water in
Magnetic Field
0 Bmax
20 MW DC supply
Cu
rre
nt
Heat-
exchanger
Warm water out
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
38 T resistive magnet
Bitter design
Cu/Ag disk
Isolation
Cooling Holes
Tie rod
37.53 T magnet:
• 40 kA, 21 MW
• 165 liter/sec water
2 Magnet halls, 6 magnets with
laboratoratories on top
Cooling installation, 7MW real
time, 165 l/s 25 Bar
22 MW, 40 000 A DC current,
550 V, 5 ppm ripple
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
European Magnetic Field Laboratory
Static fields
HFML Nijmegen
LNCMI Grenoble
Pulsed fields
HLD Dresden
LNCMI Toulouse
HFMLHLD
LNCMI-T
LNCMI-G
High field research facilities
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Global players in high magnetic fields
USA
Tallahassee (DC)
Los Alamos (pulsed)
Japan
Tsukuba (DC)
Tokyo (pulsed)
China
Hefei (DC)
Wuhan (pulsed)
Europe
Nijmegen (DC)
Grenoble (DC)
Toulouse (pulsed)
Dresden (pulsed)
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Everything is magnetic
Magnetic fields change the state of all matter through Lorentz force and spin splitting
in a reversible manner. Thermodynamic parameter
1.3185 1.3190 1.3195 1.3200
21 T
PL
In
ten
sity
(ar
b.
un
its)
Photon energy (eV)
19 T
Strongly correlated
electron systems
Soft condesed matter
& nanomaterials
Semiconductors &
nanostrucures
Research in high magnetic fields
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Correlated matter
• Phase diagrams
• Superconductivity
• Magnetism
• Strange metals
• …..
Nigel Hussey & Alix McCollam
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Soft Matter
Courtesy of Prof. J. Valles, Brown University, USA
e.g: Paramecium Caudatum
Peter Christianen & Hans Engelkamp
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Paramecium Caudatum
Courtesy of Prof. J. Valles, Brown University, USA
Field: 0 T Field: 25 T
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Semiconductors & Nanostructures
Hermann J. Suderow,
Opening the gate on superconductivity, Science 350, 1316 (1215)
MoS2
graphene
e.g.: 2D materials and devices
Uli Zeitler & Steffen Wiedmann
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
STM @ 35 T
W. Tao et al., Rev. Sci. Instr. 88, 093706 (2017).
Landau levels on graphite
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Quantum Matter in
High Magnetic Fields
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
E ˆ H
ˆ 2
1
1
2
N
i
i em
Ap ˆ H
ßB g Bσ ˆ 2
1 *
,
)( j
ji
ieeV rr
)( i
ipV r
kinetic
potential
Zeeman
Coulomb
quantum Hall effect
magnetism
superconductivity
........
everything
Laplace´s Demon of quantum mechanics
semiconductor:
most versatile system
to tune properties
The theory of everything
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
1e
ˆ 2
1
*
1
2
Nm
B
em i
i
Ap
totßB Bg Bσ ˆ 2
1 *
,
Bl
eV
Br
j
ji
iee0
2
4)( rr
)( i
ipV r
Landau quantization
integer QHE
• quantization of momentum
• Landau-level degeneracy
(no BS!)
• LL separation determined by band structure
disorder potential (tend to ignore)
Landau-level broadening
localization
(single-particle) spin
interaction
QH ferromagnetism
FQHE
2DES is high magnetic fields
heB / L n
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Quantum Hall effect
I
2DES
B
Uxx
Uxy
I
2DES
B
I
2DES
B
Uxx
Uxy
sweep magnetic field
successively depopulate Landau levels
1/B-periodic oscillations in Rxx
quantized plateaus in Rxy = (h/ne2)
Rxx 0 in quantum Hall plateaus
Rxx (kW
)
0 2 4 6 8 10
0
10
20
30
B (T)
0
1
2
3
4
n=2
1
34
6R
xy
(kW
)
D(E)
EEF
• Landau-quantized 2DES
• Localization between LL
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Graphene
• mono-atomic layer of carbon
• first truly 2D system
(that should not exist !!)
• unique electronique properties
(zero-gap semiconductor with
massless chiral Dirac fermions)
Monolayers and bilayers
of graphite on SIMOX are visible
under an optical microscope
Other truly 2D systems
Novoselov et al., PNAS 2005
Blake et al., APL 2007
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Other 2D materials: Borophene – Phosphorene
Silicence – Germanene – Stanene
Mannix et al.,
Science 350, 1513 (2015)
2D boron on Ag (111)
2D Ge on Pt (111)
Li et al.,
Adv. Mater. 26, 4820 (2016)
2D Si on Ag (110)
Aufrey et al.,
APL 96, 183102 (2010)Zhou et al.,
Nat. Mater. 14, 1020 (2015)
2D Sn on Bi2Te3
2D Black phosphorous
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Hexagonal boron nitirde
• Insulator
• (nearly) latticed-matched
to graphene
• Substrate for graphene
heterostructures
(Hofstadter’s butterfly) Now: Stacking by exfoliation
Future (?): Layer-by-layer growth
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Transition metal dichalcogenides
• Van-der-Waals stacking
• Bi-atomic graphene
• Direct-gap semiconductors
• Optical applications
• Valleytronics
• Photovoltaics
MoS2, WS2, MoSe2, WSe2, MoTe2
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
VG (V)
SiO2
gate insulator
Si backgate
Au contactsgraphite
Novoselov et al.,
Science 2004, PNAS 2005-80 -40 0 40 80
0
2
4
6
holes electrons
260 K
4 K
conducting “without” any charge carriers !!!
r(kW
)
Field effect doping in a MOSFET
ed
AV
e
CV
e
Qn r0
W k 6.5 4 2e
h
Ambipolar field-effect transistor
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Novoselov et al; Zhang et al, Nature 2005
n (1012 cm-2)
xy
(4e
2/h
)
rxx (kW
)
-2-4 40 2
5
10
0
1.5
-1.5
-2.5
-3.5
-0.5
2.5
3.5
0.5
12T )( 4
21
2
Nh
exy
of four-fold degenerate Landau levels
Half-integer quantum Hall effect
)(221
212
, NeBcEN
chirality
pseudospin locked
to momentum
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Vg (V)
rxx(kW
)
-6
2
4
-60 -30 0 6030
xy (e
2/h)
0
10
20
30
-4
-2
0
29 T
300 KB
E
EF
previously only below 30 K !
K.S. Novoselov et al., Science 315, 1379 (2007)
Room Temperature QHE at 30 T
T 30at K 2300 2 2
01 eBcE
more than just gaps !!
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
1.02
1.00
0.983.02.5
n or p (1013 cm-2 )
Rxy
(h/2
e2)
300 K
45 T
Rxy quantized
within 0.1 %
With:
Z. Jiang,* Y. Zhang, H. L. Stormer,
G. Boebinger,* and P. Kim,
Columbia University, New York, USA
*National High Magnetic Field Laboratory,
45 T
Room Temperature QHE at 45 T
K.S. Novoselov et al., Science 315, 1379 (2007)
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Other 2D systems: QHE in InSe
D.A. Bandurin et al.; Nature Nanotechnology 12, 223 (2017).
• 6L InSe on BN
• High mobility (104 cm2 V−1 s−1)
• Conventional QHE with
spin-split Landau levels
• New playground for
quantum-Hall physics
( m* = 0.14, g ≈ 2 )
• High-speed electronics !?
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Measuring Chirality
In Graphene
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Chiral electrons in graphene
Gr – BN – Gr tunneling diode
K and K’-valleys displaced
“no” tunneling
Slight angular mismatch (~1o)
J. R. Wallbank et al.; Science 355, 575 (2016)
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Resonant tunneling
emittercollector
Resonant tunneling at finite bias
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Lorentz boost in a magnetic field
B
d
B
Δp (a) (b)
B field provides extra parallel momentum
can bring two slightly displaced valleys into resonance
Δp = -e d×B
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Angular dependent tunneling
J. R. Wallbank et al.; Science 355, 575 (2016)
Bp = 28 T T = 4.2 K
• 60o-preiodic pattern
resonances with six K-valleys
• Asymmetric pattern
chiral section
• ideally: only one chirality can tunnel
(real life: 30%)
need smaller misalignment
and/or higher fields
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
TMDC field effect
transistors
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Motivation
Carrier density dependent material properties
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Monolayer WS2 transistor
Two types of gating
• Ion gating
set n 1014 cm-2
• Solid gate (Si/SiO2)
fine tune
n 1012 .. 1013 cm-2
MoS2: J.M. Lu et al.; Science 355, 575 (2016)
WS2: J.M. Lu et al.; arXiv:1703.06369 [cond-mat.supr-con].
Jianting Ye
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Sweeping through the dome
effective voltage defined by
- Ion gate (kV, colours)
- Solid gate ( 80 V)
Insulator – (quasi) metal –
superconductor –
(quasi) metal – insulator
transition driven by gating
{ Phase defined by R(T) }
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
R (T)
- dR/dT < 0: insulator
- dR/dT > 0: (quasi) metal
- R = 0: superconductor
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Phase diagram
Insulator – (quasi) metal –
superconductor –
(quasi) metal – insulator
transition driven by gating
Also seen in
- Hall mobility
- Hall concentration
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Re-entrant insulator
Low n
Single exponential
Thermal excitation
from impurty band
High n
Two exponentials
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Re-entrant insulator
High n
- Electrons trapped in
Coulomb traps of poorly
screened cations
- Coulomb interaction splits
impurity band into two
branches
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Where is the Field?
Superconductor in a high field – a bad idea !
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Superconductor in a high magnetic field
B
(nearly) no measurable suppression
of TC in parallel magnetic field
Pauli limit: Bpauli = 1.86 Tc = 3 .. 5 T
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Pauli limit
Cooper pair
BCS = 1.76 kB T
Zeeman z = g B B
Pauli limit: BCSZ 2
paramagnetic breaking
of Cooper pairs
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Ising protection
Pauli limit violator
External B
Orthogonality between spin and B
protects superconductivity
from paramagnetism
See also: Xing et al., Nano Lett..17, 6802 (2017).
Bp 250 T
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Topological
matter @ HFML
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Topological Insulators
“Definition”:
A topological insulator, like an ordinary insulator, has a bulk energy gap
separating the highest occupied electronic band from the lowest empty band.
The surface (or edge in 2D) of a topological insulator, however, necessarily has
gapless states that are protected by time-reversal symmetry.
strong spin-orbit interaction leads to topological insulating
electronic phases (applications ranging from spintronics to
quantum computation)
Topological insulators can be understood within the framework
of the band theory of solids
What is necessary for a topological insulator ?
How can we understand a topological insulator ?
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
2D Tis – HgTe quantum wells
inverted bandstructurenormal bandstructure
4 6 8 10 12-75
-50
-25
0
25
50
H3
H2
H1
E1
E (
me
V)
dQW (nm)
normal inverted band structure
dc
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Temperature driven transition
→ task: perform magneto-transport experiments at different
temperatures
TEMPERATURE ?
S. Wiedmann et al., PRB, 91, 205311 (2015)
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Low-temperature magnetotransport
→ ‘quantum Spin Hall regime’ for
a quantum well with d=12 nm
Vg
S. Wiedmann et al., PRB, 91, 205311 (2015)
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Magnetotransport at 300 K
→ two-carrier charge transport at T=300 K
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Temperature-driven transition
S. Wiedmann et al., PRB, 91, 205311 (2015)
Eight-band k·p band structure calculations
dispersion
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
3D Ti – strained HgTe
Ambipolar surface QHE
top surface
bottom surface
0 5 10 15 20 25 300
5
10
15
20
Rxx (
kW
)
electrons
0
5
10
15
-4V
-6V
i=2
i=4i=3
Rxy (
kW
)
i=7+3V
0 5 10 15 20 25 300
10
20
30
i=6i=4
i=2i=7
i=5i=3
B (T)
holes
Rxx (
kW
)
-15
-10
-5
0
Rxy (
kW
)
0 5 10 15 20 25 300
10
20
30
40
i=1i=7
i=5i=3
holes
Rxx (
kW
)
-30
-20
-10
0
Rxy (
kW
)
4 2 0 -2 -4 -6-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
nbottom surface
ntop surface
nHall
nbottom surface
+ntop surface
n, p (
10
12 c
m-2)
Vg (V)
0 50 100 150 2000.3
0.4
0.5
0.6
0.7
Rxx (
kW
)
T (K)
Vg=0
• 3D bulk states
• Topological 2D surface states
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Thermoelectric power in strained HgTe
Heater: ~500 Ω
Thermometers: RuOx - matched
heater thermometers
sample contacts
5 cm
cold sink
in vacuum
𝑆𝑥𝑥 =−𝐸𝑥𝛻𝑥𝑇
𝑆𝑥𝑦 =−𝐸𝑦
𝛻𝑥𝑇
Seebeck effect:
Nernst-Ettingshausen effect:
diffusion TEP / phonon drag
A. Jost et al., PNAS 114 , 3381 (2017)
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Low-field data
63
Transition from electrons to holes
Dirac point of surface states
at Vg=-1.85 V
Vg> 0: electrons; Vg<0: holes
TEP constant for electrons
|Sxx,holes |~ 30·|Sxx,electrons|
Maximum in Sxy at Dirac point
Small maximum in Sxx at Dirac point
Diffusion TEP:
0
1
2
3
4
B = 0T
Rxx (
kW
)
T = 1.2K
B = 0.2T
T = 1.5K
B = 0T
-10
0
10
20
30
Sxx (
V/K
)
-4 -2 0 2
0
20
40
60
Sxx (
V/K
)
Vg (V)
T = 1.5K
B = 0.2T*
0.0
0.4
0.8
Rxy (
kW
)
15
20
25
30
35
S xy (
V/K
)
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
High-field quantum oscillations
0 4 8 120
100
200
i=-5
i=-3
B (T)
Sxx (
V/K
)
0
40
80
120
holes
i=4
-Sxx (
V/K
)
i=3electrons
0.0
0.2
0.4
0.6
0.8r
xx (
kW)
0.0
0.4
0.8
1.2
rxx
(kW
)
-> as in transport: odd sequence of plateaus is observed
0 4 8 12 160
200
400
600
7 56
4
7 5
4
7 53
7 5
-6.0V
-5.5V
-5.0V
S xx (
V/K
)B (T)
-4.5V3
nt
sn
b
s
DOS
E
top
bottom
top
bottom
nt
s=n
b
s
E
DOS
Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler
Conclusions
• High magnetic field as a probe to condensed matter
Semiconductors – metals – superconductors
and the new fundamental phenomena therein
Soft matter can also be fun
• 2D Materials - a rising star of condensed matter science
New physics in graphene et al.: QHE and more
Chirality can be controlled Chiralotronics
Extremely protected Ising superconductor WS2
High fields can reveal topological states in 2D and 3D
Apply for magnet time: http://www.emfl.eu/user.html
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