Metallic surface states on semimetals: a model for quasi two-dimensional metals
Two-dimensional metals
• testing ground for fundamental theory
Metallic surface states
• interesting phenomena: quantum Hall effect,
charge density waves, (high TC superconductivity)
• Surface-localized electronic states with a Fermi
surface
• difficult to make
• On semimetals / insulators: almost perfect two
dimensional metal
• directly accessible by photoemission and STM
SGM-3 beamline on ASTRID's undulator (angle-resolved photoemission)
• spherical grating monochromator on ASTRID's undulator
three gratings
energy range: 12-130 eV
resolving power ~15.000
G
1000 400
1500
3800
1750
9.5 0
HFM VFM
400
4800
155 0
2200
TPM
2500
1782
60
1259
60
1520
• experimental chamber
75mm hemispherical analyzer on motorized two-axis goniometer
energy resolution: better than 25 meV
variable angular resolution: better than 0.7º
multi channel detection
cryo-cooling of the sample
preparation chamber
ISA
Institute for Storage Ring Facilities
University of Aarhus
Applications of the SGM-3 beamline
• Dispersion of electronic states along selected k-lines
-0.1
binding energy (eV)
0.0
Bi(100) at 27 K,
Gayone, Hofmann et al.
0.1
0.2
0.3
0.4
0.5
0.6
Γ1
M2
K3
M'2
K2
M'1
Γ1
K2
M3
• Fermi surface mapping
Borisenko, Fink et al.
Bi2Sr2CaCu2O2+δ (Bi-2212)
Pb-doped Bi-2212
Bi-2201
• Temperature dependence of the electronic structure
ISA
Institute for Storage Ring Facilities
University of Aarhus
Outline
• α-Ga and the (010) surface: general properties
• The thermal stability of α-Ga(010)
• The surface phase transition on α-Ga(010)
α-Gallium: bulk properties
Structure: face-centred orthorombic with 8 atoms per unit cell
and only one nearest neighbour (Ga2-molecules, Ga-dimers).
The ends of the molecules form the so-called buckled planes.
b
a = 4.5107 Å
b = 4.5167 Å
c = 7.6448 Å
a
c
• a "molecular (semi) metal"
• very anisotropic transport properties
• low melting temperature (29.78°C)
• strong electron-phonon coupling (λ=0.97)
• phonon bandwidth 40 meV
α-Ga bulk electronic structure
-2
-4
-6
-8
-10
Γ
• good conductor perpendicular to dimers (in the buckled planes)
• bad conductor parallel to dimers
• pseudogap at the Fermi level
• molecular bonding-antibonding optical transitions
• flat bands in the Γ-Z direction confirmed by photoemission
M. Bernasconi, G. Chiarotti and E. Tosatti, Phys. Rev. B 52, 9988 (1995).
Z
Γ
Z
Γ
α-Ga(010): structure
two possible terminations for the truncated bulk crystal
A
B
top view
dimers not cut
large corrugation
dimer termination
LEED at -2°C
4.51 Å
4.52 Å
dimers cut
small corrugation
buckled plane termination
glide plane
STM at room temperature
missing spots
E = 90 eV
5Å
1000 Å
Züger and Dürig, Phys. Rev. B 46, 7319 (1992).
Thermal Stability of the α-Ga(010) surface
Züger and Dürig, Ultramicroscopy 42-44, 520 (1992)
• After heating the crystal briefly over the bulk melting temperature
and cooling to 23°C solidified droplets of molten bulk Ga are
visible on the surface.
• The rest of the surface is still crystalline.
• There is no surface melting observed. The surface is more
stable than the bulk.
Phase transition on α-Ga(010)
above ~ 235 K (-38ºC)
(1x1)
glide plane
below ~ 235 K (-38ºC)
E=90eV
"(√2x√2)R45º"
"(2√2x√2)R45º"
Ph. Hofmann, Y. Cai, Ch. Grütter and J.H. Bilgram, Phys. Rev. Lett. 81, 1670 (1998).
Two questions
• Why is there no surface melting?
• What drives the surface phase transition?
α-Ga(010): electronic structure
surface Brillouin zone
C
X
EF
C
W
Γ
W
C
X
C
Experiment
Ph. Hofmann et al.
Phys. Rev. Lett. 81, 1670 (1998).
-5
-10
Γ
theory: termination A
W
C
X
C
Γ
theory: termination B
theory: termination C
(epitaxial GaIII)
γ = 59 mRy/atom (unrelaxed)
γ = 57 mRy/atom (relaxed)
γ = 70 mRy/atom (unrelaxed)
γ = 57 mRy/atom (relaxed)
γ = 47 mRy/atom
EF
EF
EF
-5
-5
-5
-10
-10
-10
Γ
W
C
X
Γ
C
Γ
W
C
X
Γ
C
Γ
W
M Bernasconi,G.L. Chiarotti and E. Tosatti,Phys.Rev. B 52, 9999 (1995)
C
X
Γ
C
Geometric structure of α-Ga(010) close to the melting temperature by LEED
B
dimers cut
small corrugation
• very good agreement between experiment and simulation
• qualitative agreement with surface x-ray scattering
• a very low surface Debye temperature of 175 K has to be assumed (bulk 320 K)
Thermal stability
• The thermal stability of the surface is not caused by
a Ga-III type termination as suggested based on
LDA calculations.
• It may be related to a re-hybridization caused by the
truncation of the dimers in the B termination.
• The surface Debye temperature is anomalously low.
Phase transition
• What is the structure of the low T phase?
Low temperature structure of α-Ga(010)
top view
side view
-
-
• The LT structure is not very different from the HT structure (no major mass transport involved).
• There is a certain degree of dimerization within the first layer and between first and second layer.
• The (√2x√2)R45º and (2√2x√2)R45º structures are similar and give both reasonable R-factors.
• Also for the LT structure, a very low surface Debye temperature of 160 K has to be assumed (bulk 320 K).
Phase transition on α-Ga(010) studied with SPA-LEED
no saturation
glide plane
different colour scaling,
some spots saturated
T<230 K,
E=85 eV
• The (1/2,1/2) spots are split along the glide plane direction. The other fractional order spots
appear to be elongated. The (1x1) spots are not split.
• The size of the splitting correspods to a length ca. 18 times longer than the unit cell. No higher
order diffraction fringes are observed.
• All the spots are very narrow. The average dimension of the islands can be estimated
to be around 300 Å.
Phase transition on α-Ga(010) studied with SPA-LEED
Spot (0,1)
0.38
intensity (a.u.)
Lorentzian width (V)
0.36
0.34
0.32
0.30
0.28
0.26
0.24
0.22
180
190
200
210
220
230
240
250
260
270
180
190
Temperature (K)
• The transition happens in narrow temperature window.
• Disorder is present at the transition temperature.
200
210
220
230
Temperature (K)
240
250
260
270
Phase transition
• What are possible mechanisms for the
phase transition?
Phase transition from a local point of view
C surface state (dangling bonds)
Züger and Dürig:
glide plane
explain transition by dimerization
5Å
Züger and Dürig, Phys.Rev. B 46, 7319 (1992)
M Bernasconi, G.L. Chiarotti and E. Tosatti,Phys.Rev. B 52, 9999 (1995)
• problem 1: LDA shows that the dimers repell each other.
• problem 2: Züger and Dürig observed the dimerization at high temperature where it should
not be present according to LEED (it breaks the glide plane symmetry).
Surface Charge Demsity Wave (CDW)?
• For simplicity, let us assume that the reconstruction is (√2x√2)R45º .
• A CDW is favoured by nesting.
• It is also supported by strong electron-phonon coupling.
Bulk Fermi surface projection (educated guess)
X
low T SBZ
Γ
Γ
C
Γ
W
high T SBZ
Γ
Fermi surface nesting
Phase transition
• Use angle-resolved photoemission to learn about
electron-phonon coupling, the dispersion of the
surface states and the Fermi surface.
Surface state dispersion close to C
T = 253 K
0.0
0.5
Binding energy (eV)
1.0
1.5
2.0
• The phase transition does not change
the overall dispersion.
T = 78 K
0.0
0.5
1.0
1.5
2.0
C
XC
WC
Γ
The low-temperature peak at C
hν = 15.5 eV
SL
hν = 15.5 eV
X
C
X
EF
2.0
1.5
1.0
0.5
-0.4
Binding energy (eV)
hν = 24.5 eV
Intensity (arb. units)
Photoemission Intensity (arb. units)
SH
-0.2
EF
0.2
0.4
0.80
0.0
Binding Energy (eV)
• In the low temperature phase a second surface state can be found at C.
• It is strongly localized in k.
• Caused by an umklapp process?
• A band pulled below the Fermi energy?
C
0.6
0.90
1.00
k|| (Å-1)
1.10
Temperature-dependence of the surface state at C
low T
hν=24.5 eV
T25.5#5
450
linewidth (meV)
photoemission intensity (a.u.)
400
350
300
250
T15.5#1
T15.5#4
T15.5#5
T15.5#2
T15.5#3
T24.5#1
T24.5#2
T24.5#3
T24.5#4
T24.5#5
T24.5#6
T24.5#7
T24.5#8
T24.5#9
T24.5#10
T24.5#11
phase
transition
200
-250
high T
22.0 22.5 23.0 23.5 24.0 24.5
kinetic energy (eV)
-200
-150
-100
T(ºC)
-50
0
• There is an anomalous amount of spectral intensity in the projected
bulk band gap.
• In the low temperature phase, a second feature is visible at EF.
• There is a drastic change at the phase transition temperature.
Temperature-dependence of the surface state at C
400
Tc
Tm
• The linewidth of the surface state can be interpreted
as an inverse hole lifetime:
Γ = Γe − e + Γe − i + Γe − ph
• The only significant temperature-dependence is in
300
Linewidth Γ (meV)
ω max
Γe − ph = 2πh
2
∫ dω ′α F(ω ′)[1 − f (ε − ω ′ ) + 2n(ω ′) + f (ε + ω ′)]
0
• The experimental data can be fitted according to
200
Γ(T,ω D ,ε, λ) = Γ0 + Γe − ph (T,ω D , ε, λ)
100
λ = 1.28
Γ0 = 58 meV ωD = 37 meV
λ = 1.06
Γ0 = 92 meV ωD = 28 meV
λ = 0.98
Γ0 = 103 meV ωD = 24 meV
in order to extact the electron-phonon mass
enhancement parameter λ (Debye model).
• The electron-phonon coupling here is strong.
0
0
50
100
150
200
Temperature (K)
250
300
13.0
0°C
-10°C
-20°C
-30°C
-40°C
-50°C
-60°C
-70°C
13.5
C
hν=15.5 eV
14.0 14.5 15.0
kinetic energy (eV)
15.5
photoemission intensity (a.u.)
photoemission intensity (a.u.)
Phase transition: photoemission intensity close to the Fermi level
13.5
0°C
-10°C
-20°C
-30°C
-40°C
-50°C
-60°C
-70°C
off C
hν=15.5 eV
14.0
14.5
15.0
kinetic energy (eV)
• quasi "discontinuous" decrease of spectral intensity between ss and EF
• new peak at C
15.5
Photoemission intensity at the Fermi level
T = 273 K
T = 83 K
X
X
C
Ky (Å-1)
0.5
hν = 15.5 eV
difference in %
0.5
200
0
ΓΓ
W
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
150
100
-0.5
-0.5
50
0
-0.5
0
0.5
-0.5
0
0.5
-0.5
Ky (Å-1)
0.5
0.5
0.5
hν = 17 eV
0
60
50
40
30
20
10
0
0
-0.5
-0.5
0
0.5
-0.5
0
0.5
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
-0.5
-0.5
0
0.5
-1
Kx (Å )
• overall loss of intensity at the Fermi level in the band gap, except exactly at C.
• no clear signs of Fermi surface nesting
The phase transition: main findings
• The electron-phonon coupling is strong.
• The surface state linewidth increases quasi discontinuously at the phase transition.
• The transition is accompanied by a loss of spectral intensity at EF (and below).
• There is no clear nested Fermi surface found for the high temperature phase
Possible Scenario
• We interpret the transition as a so-called strong coupling CDW. Only long range order is lost at the
transition temperature. The high temperature structure is still mostly ordered on a short scale.
Open questions
• What is the nature of the low temperature "kink"?
• Is the phase transition accompanied by a phonon anomaly?
• How does it look in real space? Is the STM result of Züger and Dürig caused by fluctuations?
People involved in this work
Århus
Zürich
Ch. Grütter
J.H. Bilgram
Ch. Søndergaard
Ch. Schultz
S. Agergaard
H. Li*
Z. Li
S.V. Hoffmann
Ph. Hofmann
*also: Department of Physics,
Zhejiang University, Hangzhou, China
Berkeley
Berlin
E. Soares
M.A. Van Hove
S. More
Y. Cai
Trieste
S. Lizzit
A. Baraldi