Elastic contribution to the lifetime of excited surface states of alkali overlayers on Cu(111) Simona Achilli In collaboration with:
Mario Italo Trioni1, Sebastiano Caravati1, Gabriele Butti1
Prof. Eugene Chulkov2
1 University of Milan Bicocca, Italy 2 DIPC, San Sebastian, Spain
Elastic contribution to the lifetime of excited surface states of alkali overlayers on Cu(111) Simona Achilli In collaboration with:
Mario Italo Trioni1, Sebastiano Caravati1, Gabriele Butti1
Prof. Eugene Chulkov2
1 University of Milan Bicocca, Italy 2 DIPC, San Sebastian, Spain
Dynamics of electrons at surfaces plays a fundamental role in many processes They can rely if the involved excited electronic (hole) states have a long enough lifetime
Decay principally due to scattering :
electron - electron (inelastic) te-e +
electron - phonon (inelastic) te-p +
electron - defects (elastic) tel =
TOTAL LIFETIME ttot
probed by STM, STS, 2PPE
(t=1/G; G: linewidth of the peak)
Lifetime of bulk states femtosecond time scale
At surfaces and interfaces: longer living states their lifetime can vary on several order of magnitude depending on the coupling with bulk states
Elastic contribution deducible from the linewidth of the state theoretical method should be able to accede to this quantity Surf. Sci. Reports 52, 219 (2004)
Dynamics of electrons at surfaces plays a fundamental role in many processes They can rely if the involved excited electronic (hole) states have a long enough lifetime
Decay principally due to scattering :
electron - electron (inelastic) te-e +
electron - phonon (inelastic) te-p +
electron - defects (elastic) tel =
TOTAL LIFETIME ttot
probed by STM, STS, 2PPE
(t=1/G; G: linewidth of the peak)
Lifetime of bulk states femtosecond time scale
At surfaces and interfaces: longer living states their lifetime can vary on several order of magnitude depending on the coupling with bulk states
Elastic contribution deducible from the linewidth of the state theoretical method should be able to accede to this quantity Surf. Sci. Reports 52, 219 (2004)
IN A COMMON SLAB APPROACH
Periodic conditions restored taking repeated slab of few atomic layers surrounded by vacuum.
No qualitative difference between “bulk” states and surface specific features.
Surfaces states are splitted in two due to the interaction between the opposite sides of the slab.
No intrinsic linewidth of the surface states Clean Cu(111) dashed
and
Cs/Cu(111) continuous
WITHIN THE EMBEDDING METHOD We consider a really semi-infinite substrate which affects the solution in the embedding region by means of an additive potential (embedding potential) Embedding region LAPW basis set
DFT-GGA/LDA
Only 2-3 layers in the embedded region are enough in order to warrant convergence for metal surfaces
BULK SS Passing from one approach to another the k|| resolved DOS is more realistic LDOS at G
ALKALI OVERLAYERS on Cu(111)
At the saturation coverage (1 ML) these system show the following reconstructions:
Na (3/2 X 3/2) (0.44 nominal coverage) Hollow adsorption site
K (2 X 2) Atop adsorption site
Cs (2 X 2) Atop adsorption site
Na also has a stable (2x2) phase at 0.56 ML (0.25 nominal coverage). (Clean Cu 4.65 eV) Reduction of work function (2.84)
gap vacuum
Appearance of quantum well states
When an alkali thin film is grown over a metal substrate whose surface band structure has a projected gap for a selected range of k|| values, we observe the generation of one or more quantum well states, whose energy is tunable by controlling the thickness of the film.
k|| resolved DOS of Cs/Cu(111) OR, QWS, GS originate from s,p bands of Cs
Image states (IS) can be obtained thanks to the inclusion of the correct asymptotic behaviour of the potential Top view S. Caravati et al., PRB 75, 155403 (2007)
0.866 0.027
(0.04) Cs (2x2) 0.695 (0.81) -0.106 (-0.105) K (2x2) 0.638 (0.7) -0.173 (-0.127) Na (3/2x3/2) 0.809 (0.64) 0.239 (0.4) Na (2x2) 0.445
(0.43) -0.526
(-0.44) Clean Cu Surf. State m* BE (eV) Growing the size of the adsorbed atom the quantum well state shifts toward the centre of the gap and the effective mass becomes more and more similar to the free electron one G. Butti et al., PRB 72, 125402 (2005) Stable phases corresponding to the saturation coverage
DOS plotted with Im E =0.054 subtracting this contribution an additional width remains
The linewidth of the quantum well state is not artificial but it’s an intrinsic property Wave function localized on the overlayer K K LDOS at G
Due to the reconstruction the bulk bands of the (1x1) system are backfolded in the (2x2) Brillouin zone
The quantum well state lies in corrispondance of bulk states and hybridizes with them.
The potential component with the periodicity of the substrate has non zero value in the overlayer
16 0.8 Na (2x2) 20 0.4 Na (3/2x3/2) 21 2 K (2x2) 18 2.4 Cs (2x2) Gtot (meV) Gel (meV) PRL 95, 176802(2005)
Moving from G the linewidth of the state grows different number of bulk states available for hybridization
Cs/Cu(111)
What about the other contributions?
INELASTIC e-e scattering
1D model potential (reproduces QWS and the n=1 image state)
Lifetime given by:
Where translational invariance in x,y is assumed.
GW approximation for self energy
RPA approximation is used for c.
0.4* 8.5 13 0.4* Ge-e (meV) Cs(2x2) K(2x2) Na(3/2x3/2) Na(2x2) E. V. Chulkov et al., PRB 68, 195422 (2003) *A. Arnau et al., PRL 95, 176802 (2005)
Summary The embedding method applied to realistic surfaces allows to accede to elastic contribution to lifetime
The ab initio calculation for alkali overlayers on Cu(111) shows that, due to the surface reconstruction, the quantum well state acquires an intrinsic linewidth.
We have deduced the elastic contribution by the linewidth of the QWS in the k|| resolved DOS.
The elastic term doesn’t explain the whole lifetime experimentally observed.
The inelastic electron-electron term was estimated using GW-RPA approximation and 1D potential.
Thank you for your attention!
We start investigating Na adsorption by considering saturation coverage and a
submonolayer one. At saturation (0.44 ML nominal coverage) a good consensus exists that
the overlayer displays a (3/2×3/2) structure with the Na atoms occupying four nonequivalent
hollow sites per p(3×3) unit cell. In the submonolayer regime the existence of an ordered phase
is still debated [9, 10], but in the experiment by Dudde et al [24] a clear 2×2 pattern is reported,
which should indicate the existence of a second phase corresponding to a nominal coverage of
0.25 ML. Subsequently, theoretical studies suggested the hollow site as the preferred adsorption
one also for this p(2 × 2) structure [29]. Therefore we will discuss these two structures.
Currently the most used geometry for adsorption phenomena is the slab one. One recovers a
fictitious periodic system by repeating slabs in the orthogonal direction, separated by a portion
of vacuum, and can use standard methods for 3D periodic systems, i.e. the usual supercell
Geometry
Slabs are finite systems in the direction normal to the surface, so their states are discrete
ones at fixed parallel momentum. There are, however, surface properties in which the truly
semi-infinite solid and hence the continuum of states should be included in the theory. In
particular, to study the dispersion of the surface electronic states we wish to use a method
capable of distinguishing between discrete or resonant structures.
Second, we discuss electronic states. As an example we compare the DOSs calculated
with the two approaches for a free Cu(111) surface. While the DOSs integrated in the surface
Brillouin zone (SBZ) are fairly similar, the DOSs at (or at any fixed k)may display important
differences. Figure 4 reports the DOSs obtained in the supercell and embedding approaches in
the upper and lower panel, respectively (note that no dispersion in the direction normal to the
surface is considered in the supercell geometry). In the DOS in the upper panel we observe
a series of peaks; they represent discrete states and should be delta of Dirac, to which we
have assigned a 0.025 eV width in order to be able to plot them. On the other hand, the DOS
calculated by the embedding approach is...
Image states of Cu(111)
In a common slab approach
No qualitative difference between “bulk” states and surface specific features.
No intrinsic linewidth of the surface states
To obtain the result of hybridization semi-infinite calcuations are needed EMBEDDING METHOD
Comments