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A unifying model for non-adiabatic coupling at metallic surfaces beyond the local harmonic approximation: From vibrational relaxation to scanning tunneling microscopy
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10.1063/1.4811150
/content/aip/journal/jcp/138/24/10.1063/1.4811150
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/24/10.1063/1.4811150

Figures

Image of FIG. 1.
FIG. 1.

Schematic representation of the non-adiabatic coupling of an adsorbate to a source (blue) and a sink (red) of density of states. The electrons are transferred either from a STM tip (orange) or a metallic substrate (grey) via a molecular bridge (green). The energy representation of the transfer is depicted in the bottom panel. An electron hops from the source to the bridge at a rate that depends on the position of the adsorbate. Energy (ℏω) is transferred from the electron to the anharmonic vibrations of the bridge, before the electron hops to the sink at lower energy.

Image of FIG. 2.
FIG. 2.

The central panel depicts schematically the inelastic electron transfer from a STM tip (orange) to a metallic substrate (grey) via an adsorbate bridge (green), as well as the reverse process. The left panel shows the electron (black dot) leaving the bridge for the metal after having lost some energy to the adsorbate vibrations, while the hole left behind (white dot) decays to inside the STM tip. The right panel shows the reverse situation.

Image of FIG. 3.
FIG. 3.

Behavior of the STM-induced transition rates as a function of the potential bias, computed according to Eq. (8) . The scaling factor is set to = 0.02. (Top panel) Inverse rate (ps) for the perpendicular () mode excitation from a given local minimum; fcc (dotted orange), hcp (dashed green), subsurface (solid blue), and bulk (long dashed black). (Bottom panel) Inverse rate (ps) for the parallel () mode excitation from a given local minimum; same colors as above.

Image of FIG. 4.
FIG. 4.

One-dimensional schematic representation of the above-threshold excitation mechanism using a scanning tunneling microscope along the coordinate perpendicular to the surface. The system is initially prepared in either the fcc ground state (orange), the subsurface octahedral site (blue), or the bulk octahedral site (black). Non-adiabatic effects induced by the STM tip couple the initial states to delocalized states (horizontal dashed black lines) above the diffusion barriers, represented by cyan arrows. Upon relaxation, the system decays to either one of the three local minima (dashed arrows). The vertical dashed grey line denotes the position of the first surface layer.

Image of FIG. 5.
FIG. 5.

Population evolution of the fcc (orange), hcp (dashed green), subsurface (blue), and bulk (black) ground states for different initial states at potential bias = 0.2 V (left panels) and = 1.0 V (right panels). (Top panels) Population decay from the fcc ground state. (Central panels) Population decay from the subsurface octahedral site. (Bottom panels) Population decay from the bulk octahedral site.

Image of FIG. 6.
FIG. 6.

STM-induced population decay for a fcc (orange), subsurface (blue), and bulk (black) initial states at potential bias = 1 V. The initial response of the system to the perturbation happens on a similar timescale in all three cases. A second decay mechanism depending on the initial state can be observed at longer times.

Image of FIG. 7.
FIG. 7.

Response (bottom panel) and transfer rates (top panel) obtained from Eq. (13) for the population decay from a fcc (orange), subsurface (blue), and bulk (black) initial state, as a function of the applied bias potential. The response and transfer rates were fitted to Eq. (14) .

Tables

Generic image for table
Table I.

Inverse downward transition rates computed using Eq. (4) for selected vibrational states of H/Pd(111). The states are labeled by their nodal structure perpendicular and along the surface, |ν, ν; ⟩, in different local centers = {, , , }. The transition energies in parentheses are expressed relative to the ground state in the local center.

Generic image for table
Table II.

Parameters for the population decay of various initial states induced by excitation using a scanning tunneling microscope, as a function of the applied potential bias. The response τ and transfer times τ obtained from fitting Eq. (13) are reported along with the amplitude of each mechanism. The last column reports the population of the state after a 1 ns excitation time followed by a 5 ps equilibration time. (Top part) Population decay from the fcc ground state. (Central part) Population decay from the subsurface octahedral site. (Bottom part) Population decay from the bulk octahedral site.

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/content/aip/journal/jcp/138/24/10.1063/1.4811150
2013-06-26
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A unifying model for non-adiabatic coupling at metallic surfaces beyond the local harmonic approximation: From vibrational relaxation to scanning tunneling microscopy
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/24/10.1063/1.4811150
10.1063/1.4811150
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