Discrete Electronic Subbands due to Bragg Scattering at Molecular Edges

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Discrete Electronic Subbands due to Bragg Scattering at Molecular Edges

A. Martín-Jiménez, J. M. Gallego, R. Miranda, and R. Otero

Phys. Rev. Lett. 122, 176801 – Published 30 April 2019

See Synopsis: Unconfined Electrons Exhibit Discrete Energy Levels

Abstract

The discretization of the electronic structure of nanometer-size solid systems due to quantum confinement and the concomitant modification of their physical properties is one of the cornerstones for the development of nanoscience and nanotechnology. In this Letter we demonstrate that the Bragg scattering of Cu(111) surface-state electrons by the periodic arrangement of tetracyanoquinodimethane molecules at the edges of self-assembled molecular islands, along with the dominant contribution of backscattering processes to the electronic density of states, discretizes the possible values of the electron momentum parallel to the island edge. The electronic structure consists thus of a discrete number of subbands which occur in a nonclosed space, and therefore without quantum confinement.

Received 8 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.176801

Physics Subject Headings (PhySH)

Quantum interference effects Surface states

Monolayer films

Scanning tunneling spectroscopy

Condensed Matter, Materials & Applied Physics

Synopsis

Unconfined Electrons Exhibit Discrete Energy Levels

Published 30 April 2019

A periodic structure deposited on copper produces an electron density pattern that could affect the chemical and physical properties of the surface.

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Authors & Affiliations

A. Martín-Jiménez¹, J. M. Gallego², R. Miranda^3,1, and R. Otero^3,1,*

¹Instituto Madrileño de Estudios Avanzados en Nanociencia (IMDEA-NANO), 28049 Madrid, Spain
²Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), 28049 Madrid, Spain
³Departamento de Física de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain

^*roberto.otero@uam.es

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Vol. 122, Iss. 17 — 3 May 2019

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Images

Figure 1
(a) STM image ( $30.2 \times 30.2 {nm}^{2}$ , $V_{bias} = 1.4 V$ , $I_{t} = 150 pA$ ) of the edge of a TCNQ island, showing the bulk and edge molecular arrangements. The rhomboidal unit cell is shown. (b) 1D Fourier transform (FT) of a scan line over the island edge. (c) 2D FT of the island bulk. Black tick marks correspond to the peaks in the 1D FT that correspond to the projection of the bulk reciprocal space over the edge direction, while red ticks mark the position of the new peaks due to the edge periodicity. (d) STM image ( $26.3 \times 8.6 {nm}^{2}$ , $I_{t} = 150 pA$ ) recorded at low voltage ( $V_{bias} = 100 meV$ ), where the standing wave pattern of the Cu(111) surface state is visible.
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Figure 2
(a) $d I / d V (x, E)$ measured along the perpendicular direction of a bare step edge ( $V_{bias} = 1.4 V$ , $I_{t} = 1.4 nA$ , $V_{mod} = 14 mV$ , length of the line 20 nm). (b) FFT of the data of (a), revealing the existence of only one band. (c) Cut of (a) for a bias voltage of $- 100 mV$ . (d) Cut of (b) for a bias voltage of $- 100 meV$ . (e) $d I / d V (x, E)$ measured on bare Cu(111) along the edge perpendicular to the TCNQ island ( $V_{bias} = 1.4 V$ , $I_{t} = 1.4 nA$ , $V_{mod} = 14 mV$ , length of the line 10 nm). (f) FFT of the data of (e), revealing the existence of three subbands. (g) Cut of (e) for a bias voltage of $- 100 mV$ . (h) Cut of (f) for a bias voltage of $- 100 meV$ .
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Figure 3
$d I / d V (x, y) |_{E}$ maps recorded with the lock-in amplifier at different bias voltages (a), (c), and (e) and their corresponding symmetrized 2D FT images (b), (d), and (f). All the maps have been recorded with the same modulation of 14m V, and current setpoints of 1.2 nA, 1.2 nA, and 0.3 nA, respectively. The 2D FTs have been performed in the molecule-free areas close to the molecular edges. At the constant-energy circles arising from scattering with different types of surface defects (white dotted circles), some points appear with a rather large intensity, being equally spaced in $Δ k_{∥}$ (white dotted lines). (g) The projection onto the $Δ k_{⊥}$ axis of the high-intensity points in the 2D FTs correspond to the momenta of the three parabolas found in Fig. 2.
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Figure 4
(a)–(c) Scattering geometry for three possible incidence angles of the incoming electron, calculated for an energy of $- 40 meV$ and $n = - 1$ in the Laue condition. Top panel: Real-space representation of the scattering process [orange area corresponds to the TCNQ edge, light cyan area to bare Cu(111)]. Blue (green) vectors represent the momentum of the incident (scattered) electron. Bottom panels: Ewald-sphere visualization of the scattering events (vertical dotted lines correspond to the reciprocal space of the TCNQ edge; solid circles represent the constant-energy surfaces). Momentum transfer vectors associated with these scattering processes are also drawn in red. (b) Extremal backscattering configuration. (c) Limiting grazing incidence case. (d) Momentum-transfer space derived from the previous analysis compared to the experimental $d I / d V (x, y) |_{E}$ maps at $- 40 meV$ , showing that the vectors contributing to the standing waves are those corresponding to backscattering processes. (e) Origin of the discrete subbands as intersections between the 2D surface-state paraboloid and the constant $k_{∥}$ planes originating from the Laue and backscattering conditions ( $k_{∥, n} = n G / 2$ ).
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