Catching the bound states in the continuum of a phantom atom in graphene

L. H. Guessi, R. S. Machado, Y. Marques, L. S. Ricco, K. Kristinsson, M. Yoshida, I. A. Shelykh, M. de Souza, and A. C. Seridonio

Phys. Rev. B 92, 045409 – Published 9 July 2015

Abstract

We explore theoretically the formation of bound states in the continuum (BICs) in graphene hosting two collinear adatoms situated at different sides of the sheet and at the center of the hexagonal cell, where a phantom atom of a fictitious lattice emulates the six carbons of the cell. We verify that in this configuration the local density of states near the Dirac points exhibits two characteristic features: (i) a cubic dependence on energy instead of a linear one for graphene as found in New J. Phys. 16, 013045 (2014), and (ii) the formation of BICs as an aftermath of a Fano destructive interference assisted by the Coulomb correlations in the adatoms. For the geometry where adatoms are collinear to carbon atoms, we report an absence of BICs.

Received 4 March 2015
Revised 13 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.045409

Authors & Affiliations

L. H. Guessi¹, R. S. Machado², Y. Marques², L. S. Ricco², K. Kristinsson³, M. Yoshida¹, I. A. Shelykh^3,4,5, M. de Souza^1,*, and A. C. Seridonio^1,2

¹IGCE, Unesp–Universidade Estadual Paulista, Departamento de Física, 13506-900, Rio Claro, SP, Brazil
²Departamento de Física e Química, Unesp–Universidade Estadual Paulista, 15385-000, Ilha Solteira, SP, Brazil
³Division of Physics and Applied Physics, Nanyang Technological University 637371, Singapore
⁴Science Institute, University of Iceland, Dunhagi-3, IS-107 Reykjavik, Iceland
⁵ITMO University, St. Petersburg 197101, Russia

^*Present address: Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Austria.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 92, Iss. 4 — 15 July 2015

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The geometry of the system we consider. (a) The dotted-red circles represent a fictitious lattice composed by phantom atoms in graphene. (b) At the position $R = 0$ , the STM tip couples to the adatom 1 and the six atoms of carbon (only shown for an arbitrary $R$ ). (c) Phantom atoms (shaded-red spheres) emulating the cells of (b).
Reuse & Permissions
Figure 2
(a) LDOS of graphene coupled to the STM tip for two configurations: the tip above the carbon atom of graphene (labeled as carbon) and the tip in the center of the hexagonal lattice (labeled as phantom). (b) Density of states for the pair of adatoms ${DOS}_{j j} = {DOS}_{11} = {DOS}_{22}$ within the valence band. The parameters are $E_{d} = - 0.07 D, U = 0.14 D, V = 0.14 D, v_{F} \approx c / 300$ , and $▵ E = 0 .$ Two additional peaks in the conduction band are symmetrically placed if the condition $2 E_{d} + U = 0$ is satisfied; those peaks are not shown. (c) Contributions to the LDOS of graphene from the adatom pair. The diagonal contribution shows two pronounced peaks, while the mixing term shows a single pronounced antiresonance. (d) Total LDOS revealing the BIC (marked by vertical line) at the position where the resonance of the diagonal term in the LDOS is compensated by the antiresonance in the mixing term. (e) Sketch of the energy diagram of the system. Left: energy levels without the dressing of the adatoms by conducting electrons. Right: the energy diagram accounting for the Coulomb dressing. The pair of BICs is indicated by red arrows. In both the right and left panels, the coupling of the graphene sheet to the STM tip turns the linear $| E |$ dependence within the density of states of the host into a cubic one $({| E |}^{3})$ .
Reuse & Permissions
Figure 3
(a) $E_{d} = - 0.07 D, U = 0.14 D, V = 0.14 D, v_{F} \approx c / 300$ , and $▵ E = 0$ : LDOS in the region around the position of the BIC. The latter lies at $E \approx - 6.3 \times 10^{- 2} D$ and is invisible in the LDOS; its position is shown by a vertical line. (b) The LDOS in the region around the position of the BIC for nonzero detuning between the energies of the upper and lower adatoms $▵ E = 10^{- 4} D$ ; all other parameters are the same as in panel (a). One clearly sees that the BIC is reflected in the LDOS in the form of a tiny peak at $E \approx - 6.3 \times 10^{- 2} D$ and thus should become detectable in transport measurements. (c) Same as panel (a), but for different values of the parameters: $E_{d} = - 0.02 D, U = 0.04 D$ , and $v_{F} \approx c / 150 .$ (d) The LDOS in the region around the position of the BIC for nonzero detuning between the energies of the upper and lower adatoms $▵ E = 10^{- 5} D$ ; all other parameters are the same as in panel (c).
Reuse & Permissions
Figure 4
(a) Density of states for the pair of adatoms ${DOS}_{j j} = {DOS}_{11} = {DOS}_{22}$ within the valence band. The parameters are $E_{d} = - 0.07 D, U = 0.035 D, V = 0.14 D, v_{F} \approx c / 300$ , and $▵ E = 0$ . Four peaks are present within the valence band, as $2 E_{d} + U \neq 0$ particle-hole symmetry is broken. (b) Contributions to the LDOS of graphene from the adatom pair. The diagonal contribution shows four pronounced peaks, while the mixing term shows a couple of pronounced antiresonances. (c) Total LDOS revealing the BICs (marked by vertical lines) at positions where resonances of the diagonal term in the LDOS are compensated by the antiresonances in the mixing term. (d) Sketch of the energy diagram of the system.
Reuse & Permissions
Figure 5
(a) Adatoms aligned with one of the carbon atoms. (b) $E_{d} = - 0.07 D, U = 0.14 D, V = 0.14 D, v_{F} \approx c / 300$ , and $▵ E = 0$ : ${DOS}_{j j} = {DOS}_{11} = {DOS}_{22}$ of the adatoms in which unresolved peaks emerge, thus attesting that BICs cannot be formed in such a geometry. (c) Dirac cones persist exhibiting unresolved resonances simultaneously within the valence and conduction bands.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics