$p$-Band Engineering in Artificial Electronic Lattices

Open Access

$p$ -Band Engineering in Artificial Electronic Lattices

M. R. Slot, S. N. Kempkes, E. J. Knol, W. M. J. van Weerdenburg, J. J. van den Broeke, D. Wegner, D. Vanmaekelbergh, A. A. Khajetoorians, C. Morais Smith, and I. Swart

Phys. Rev. X 9, 011009 – Published 16 January 2019

Abstract

Artificial electronic lattices, created atom by atom in a scanning tunneling microscope, have emerged as a highly tunable platform to realize and characterize the lowest-energy bands of novel lattice geometries. Here, we show that artificial electronic lattices can be tailored to exhibit higher-energy bands. We study $p$ -like bands in fourfold and threefold rotationally symmetric lattices. In addition, we show how an anisotropic design can be used to lift the degeneracy between $p_{x}$ - and $p_{y}$ -like bands. The experimental measurements are corroborated by muffin-tin and tight-binding calculations. The approach to engineer higher-energy electronic bands in artificial quantum systems introduced here enables the realization of complex band structures from the bottom up.

Received 19 September 2018
Revised 21 November 2018

DOI:https://doi.org/10.1103/PhysRevX.9.011009

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Two-dimensional electron gas Two-dimensional electron system

Free-electron model Scanning tunneling microscopy Scanning tunneling spectroscopy Tight-binding model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. R. Slot^1,‡, S. N. Kempkes^2,‡, E. J. Knol³, W. M. J. van Weerdenburg³, J. J. van den Broeke², D. Wegner³, D. Vanmaekelbergh¹, A. A. Khajetoorians³, C. Morais Smith^2,*, and I. Swart^1,†

¹Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, Utrecht 3584 CC, Netherlands
²Institute for Theoretical Physics, Utrecht University, Princetonplein 5, Utrecht 3584 CC, Netherlands
³Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, Nijmegen 6525 AJ, Netherlands

^*Corresponding author. C.deMoraisSmith@uu.nl
^†Corresponding author. I.Swart@uu.nl
^‡These authors contributed equally to this work.

Popular Summary

Manipulating the charge and spin of an electron is the basis of creating functional electronic devices, ranging from transistors to magnetic data storage units. However, electrons also have an orbital degree of freedom, which offers more flexibility with respect to its magnitude and internal structure than spin or charge. To realize the potential of this new branch of electronics, it is essential to have full control over the orbitals and how they couple. Artificial lattices provide such control, but thus far researchers have only studied $s$ -type orbitals. Here, we extend this control to $p$ -type orbitals.

By arranging carbon monoxide molecules with atomic-scale precision on a copper surface using the tip of a scanning tunneling microscope, we confine the surface-state electrons to create a lattice of coupled artificial atoms. By tailoring the geometry, we access bands derived from $p$ -type orbitals. Furthermore, by modifying the design we show how to selectively lift the energy degeneracy of $p_{x}$ and $p_{y}$ orbitals, thereby creating the artificial lattice analog of a crystal field. We find that the $p$ -orbital description holds for lattices with different symmetries.

Our approach applies also to other systems that harbor a 2D electron gas. In particular, lithographically patterned semiconductors provide an attractive platform to realize devices that exploit the orbital degree of freedom.

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Issue

Vol. 9, Iss. 1 — January - March 2019

Subject Areas

Condensed Matter Physics

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Images

Figure 1
(a) Differential-conductance map acquired at $V = 550 mV$ above a Lieb lattice, shown for part of the lattice. Images of the entire lattice can be found in the SM [40]. The unit cell (blue dashed box) contains three artificial-atom sites (green): one corner site (1) and two edge sites (2 and 3). The sites are generated by the configuration of CO molecules on a Cu(111) surface indicated by the red contours. The $p$ -like orbitals in the unit cell are outlined by a black contour. The map was acquired at $+ 110 pm$ with respect to the set point $I_{set} = 1 nA$ , $V_{set} = 50 mV$ , with a bias modulation $V_{rms} = 20 mV$ . (b) LDOS map for the same energy simulated using the muffin-tin model. The $p$ -like orbitals and the sign of the wave function are indicated in black. (c) Band structure along the high symmetry directions of the Brillouin zone (see inset) as calculated by a muffin-tin approach. The three lowest $s$ -like bands are indicated in green, the six $p$ -orbital bands in blue. (d) Bloch-type wave function along the purple dashed line in the muffin-tin simulation in (b). The wave function exhibits a positive maximum or negative minimum between the sites, while it is zero at the artificial-atom sites (corner and edges).
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Figure 2
(a) Differential-conductance map above a symmetric Lieb-like lattice acquired at $V = 70 mV$ , shown for part of the lattice (see SM [40] for entire lattice). The CO molecules are encircled in red and $p_{x}$ - and $p_{y}$ -like orbitals (black) are indicated in one unit cell (blue dashed box). The map was acquired after stabilization at $I_{set} = 1 nA$ , $V_{set} = 70 mV$ , with a bias modulation $V_{rms} = 10 mV$ . (b) LDOS map for the same energy simulated using the muffin-tin model.
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Figure 3
(a),(b) Differential-conductance maps acquired at $V = + 50 mV$ and $V = - 50 mV$ , respectively, above an asymmetric Lieb-like lattice with more spacing in the $y$ direction (pink arrow) than in the $x$ direction (cyan arrow). A part of the lattice is shown. The maps were acquired after stabilization at $I_{set} = 1 nA$ , $V_{set} = + 50$ and $- 50 mV$ , respectively, with a bias modulation $V_{rms} = 5 mV$ . (c),(d) Same as (a),(b), calculated using the muffin-tin model.
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Figure 4
(a) Schematic of $p$ orbitals (blue) in a honeycomb arrangement of artificial-atom sites (green). (b) Decomposition of a $p_{x}$ orbital into a $σ$ and $π$ bond. The rotation $\cos (60 °) = 1 / 2$ and $\cos (- 30 °) = \sqrt{3} / 2$ give the prefactors for these rotations, respectively. (c) Differential-conductance map acquired at $V = - 80 mV$ above a honeycomb lattice, shown for a part of the lattice. Several artificial-atom sites (green), the $σ$ -bond overlap of the $p$ -like orbitals (black contours), and CO molecules (red contours) are indicated. The map was acquired at $- 6 pm$ with respect to the set point $I_{set} = 1 nA$ , $V_{set} = 150 mV$ , with a bias modulation $V_{rms} = 10 mV$ . (d) The corresponding LDOS map simulated using the muffin-tin model.
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