Creating atomically precise quantum architectures with high digital fidelity and desired quantum states is an important goal in a new era of quantum technology. The strategy of creating these quantum nanostructures mainly relies on atom-by-atom, molecule-by-molecule manipulation or molecular assembly through non-covalent interactions, which thus lack sufficient chemical robustness required for on-chip quantum device operation at elevated temperature. Here, we report a bottom-up synthesis of covalently linked organic quantum corrals (OQCs) with atomic precision to induce the formation of topology-controlled quantum resonance states, arising from a collective interference of scattered electron waves inside the quantum nanocavities. Individual OQCs host a series of atomic orbital-like resonance states whose orbital hybridization into artificial homo-diatomic and hetero-diatomic molecular-like resonance states can be constructed in Cassini oval-shaped OQCs with desired topologies corroborated by joint ab initio and analytic calculations. Our studies open up a new avenue to fabricate covalently linked large-sized OQCs with atomic precision to engineer desired quantum states with high chemical robustness and digital fidelity for future practical applications.

Centre for Advanced 2D Materials National University of Singapore Singapore 117543 Singapore

Department of Chemistry National University of Singapore Singapore 117543 Singapore

Institute of Physics Czech Academy of Sciences Prague 16200 Czech Republic

Regional Centre of Advanced Technologies and Materials Palacký University Olomouc 78371 Czech Republic

Yale NUS College 16 College Avenue West Singapore 138527 Singapore

Zobrazit více v PubMed

Crommie MF, Lutz CP, Eigler DM. Confinement of electrons to quantum corrals on a metal surface. Science. 1993;262:218–220. doi: 10.1126/science.262.5131.218. PubMed DOI

Manoharan HC, Lutz CP, Eigler DM. Quantum mirages formed by coherent projection of electronic structure. Nature. 2000;403:512–515. doi: 10.1038/35000508. PubMed DOI

Fiete GA, Heller EJ. Colloquium: Theory of quantum corrals and quantum mirages. Rev. Mod. Phys. 2003;75:933–948. doi: 10.1103/RevModPhys.75.933. DOI

Moon CR, Mattos LS, Foster BK, Zeltzer G, Manoharan HC. Quantum holographic encoding in a two-dimensional electron gas. Nat. Nanotechnol. 2009;4:167–172. doi: 10.1038/nnano.2008.415. PubMed DOI

Heller EJ, Crommie MF, Lutz CP, Eigler DM. Scattering and absorption of surface electron waves in quantum corrals. Nature. 1994;369:464–466. doi: 10.1038/369464a0. DOI

Braun KF, Rieder KH. Engineering electronic lifetimes in artificial atomic structures. Phys. Rev. Lett. 2002;88:096801. doi: 10.1103/PhysRevLett.88.096801. PubMed DOI

Stilp, F. et al. Very weak bonds to artificial atoms formed by quantum corrals. Science372,1196–1200 (2021). PubMed

Moon CR, et al. Quantum phase extraction in isospectral electronic nanostructures. Science. 2008;319:782–787. doi: 10.1126/science.1151490. PubMed DOI

Gomes KK, Mar W, Ko W, Guinea F, Manoharan HC. Designer Dirac fermions and topological phases in molecular graphene. Nature. 2012;483:306–310. doi: 10.1038/nature10941. PubMed DOI

Paavilainen S, Ropo M, Nieminen J, Akola J, Räsänen E. Coexisting honeycomb and Kagome characteristics in the electronic band structure of molecular graphene. Nano Lett. 2016;16:3519–3523. doi: 10.1021/acs.nanolett.6b00397. PubMed DOI

Slot MR, et al. Experimental realization and characterization of an electronic Lieb lattice. Nat. Phys. 2017;13:672–676. doi: 10.1038/nphys4105. PubMed DOI PMC

Pennec Y, et al. Supramolecular gratings for tuneable confinement of electrons on metal surfaces. Nat. Nanotechnol. 2007;2:99–103. doi: 10.1038/nnano.2006.212. PubMed DOI

Klappenberger F, et al. Dichotomous array of chiral quantum corrals by a self-assembled nanoporous kagomé network. Nano Lett. 2009;9:3509–3514. doi: 10.1021/nl901700b. PubMed DOI

Lobo-Checa J, et al. Band formation from coupled quantum dots formed by a nanoporous network on a copper surface. Science. 2009;325:300–303. doi: 10.1126/science.1175141. PubMed DOI

Klappenberger F, et al. Tunable quantum dot arrays formed from self-assembled metal-organic networks. Phys. Rev. Lett. 2011;106:026802. doi: 10.1103/PhysRevLett.106.026802. PubMed DOI

Wyrick J, et al. Do two-dimensional “noble gas atoms” produce molecular honeycombs at a metal surface? Nano Lett. 2011;11:2944–2948. doi: 10.1021/nl201441b. PubMed DOI

Wang S, et al. Tuning two-dimensional band structure of Cu(111) surface-state electrons that interplay with artificial supramolecular architectures. Phys. Rev. B. 2013;88:245430. doi: 10.1103/PhysRevB.88.245430. DOI

Kepčija N, Huang TJ, Klappenberger F, Barth JV. Quantum confinement in self-assembled two-dimensional nanoporous honeycomb networks at close-packed metal surfaces. J. Chem. Phys. 2015;142:101931. doi: 10.1063/1.4913244. PubMed DOI

Müller K, Enache M, Stöhr M. Confinement properties of 2D porous molecular networks on metal surfaces. J. Phys. Condens. Matter. 2016;28:153003. doi: 10.1088/0953-8984/28/15/153003. PubMed DOI

Zhang YQ, Björk J, Barth JV, Klappenberger F. Intermolecular hybridization creating nanopore orbital in a supramolecular hydrocarbon sheet. Nano Lett. 2016;16:4274–4281. doi: 10.1021/acs.nanolett.6b01324. PubMed DOI

Piquero-Zulaica I, et al. Precise engineering of quantum dot array coupling through their barrier widths. Nat. Commun. 2017;8:787. doi: 10.1038/s41467-017-00872-2. PubMed DOI PMC

Su J, et al. On-surface synthesis and characterization of [7]Triangulene quantum ring. Nano Lett. 2021;21:861–867. doi: 10.1021/acs.nanolett.0c04627. PubMed DOI

Telychko M, et al. Ultrahigh-yield on-surface synthesis and assembly of circumcoronene into a chiral electronic Kagome-honeycomb lattice. Sci. Adv. 2021;7:eabf0269. doi: 10.1126/sciadv.abf0269. PubMed DOI PMC

Fan Q, et al. Surface-assisted organic synthesis of hyperbenzene nanotroughs. Angew. Chem. Int. Ed. 2013;52:4668–4672. doi: 10.1002/anie.201300610. PubMed DOI

Summerfield A, et al. Ordering, flexibility and frustration in arrays of porphyrin nanorings. Nat. Commun. 2019;10:2932. doi: 10.1038/s41467-019-11009-y. PubMed DOI PMC

Kaiser K, et al. An sp-hybridized molecular carbon allotrope, cyclo[18]carbon. Science. 2019;365:1299–1301. doi: 10.1126/science.aay1914. PubMed DOI

Fan C, et al. On-surface synthesis of giant conjugated macrocycles. Angew. Chem. Int. Ed. 2021;60:1–5. doi: 10.1002/anie.202015604. PubMed DOI

Reinert F, Nicolay G, Schmidt S, Ehm D, Hüfner S. Direct measurements of the L-gap surface states on the (111) face of noble metals by photoelectron spectroscopy. Phys. Rev. B. 2001;63:115415. doi: 10.1103/PhysRevB.63.115415. DOI

Kevan SD, Gaylord RH. High-resolution photoemission study of the electronic structure of the noble-metal (111)surfaces. Phys. Rev. B. 1987;36:5809. doi: 10.1103/PhysRevB.36.5809. PubMed DOI

Liu M, et al. High-yield formation of graphdiyne macrocycles through on-surface assembling and coupling reaction. ACS Nano. 2018;12:12612–12618. doi: 10.1021/acsnano.8b07349. PubMed DOI

Fritton M, et al. The role of kinetics versus thermodynamics in surface-assisted Ullmann coupling on gold and silver surfaces. J. Am. Chem. Soc. 2019;141:4824–4832. doi: 10.1021/jacs.8b11473. PubMed DOI

Krug CK, Nieckarz D, Fan Q, Szabelski P, Gottfried JM. The Macrocycle versus chain competition in on-surface polymerization: insights from reactions of 1,3-dibromoazulene on Cu(111) Chem. Eur. J. 2020;26:7647–7656. doi: 10.1002/chem.202000486. PubMed DOI PMC

Zheng Y, et al. Designer spin order in diradical nanographenes. Nat. Commun. 2020;11:6076. doi: 10.1038/s41467-020-19834-2. PubMed DOI PMC

Zheng Y, et al. Engineering of magnetic coupling in nanographene. Phys. Rev. Lett. 2020;124:147206. doi: 10.1103/PhysRevLett.124.147206. PubMed DOI

Mishra S, et al. Topological defect-induced magnetism in a nanographene. J. Am. Chem. Soc. 2020;142:1147–1152. doi: 10.1021/jacs.9b09212. PubMed DOI

Steiner C, et al. Hierarchical on-surface synthesis and electronic structure of carbonyl-functionalized one- and two-dimensional covalent nanoarchitectures. Nat. Commun. 2017;8:14765. doi: 10.1038/ncomms14765. PubMed DOI PMC

Nguyen GD, et al. Atomically precise graphene nanoribbon heterojunctions from a single molecular precursor. Nat. Nanotechnol. 2017;12:1077–1082. doi: 10.1038/nnano.2017.155. PubMed DOI

Li J, et al. Survival of spin state in magnetic porphyrins contacted by graphene nanoribbons. Sci. Adv. 2018;4:eaaq0582. doi: 10.1126/sciadv.aaq0582. PubMed DOI PMC

Li J, et al. Uncovering the triplet ground state of triangular graphene nanoflakes engineered with atomic precision on a metal surface. Phys. Rev. Lett. 2020;124:177201. doi: 10.1103/PhysRevLett.124.177201. PubMed DOI

Song S, et al. Real-space imaging of a single-molecule monoradical reaction. J. Am. Chem. Soc. 2020;142:13550–13557. doi: 10.1021/jacs.0c05337. PubMed DOI

Hapala P, et al. Mechanism of high-resolution STM/AFM imaging with functionalized tips. Phys. Rev. B. 2014;90:085421. doi: 10.1103/PhysRevB.90.085421. PubMed DOI

Hapala P, Temirov R, Tautz FS, Jelínek P. Origin of high-resolution IETS-STM images of organic molecules with functionalized tips. Phys. Rev. Lett. 2014;113:226101. doi: 10.1103/PhysRevLett.113.226101. PubMed DOI

Krejčí O, Hapala P, Ondráček M, Jelínek P. Principles and simulations of high-resolution STM imaging with a flexible tip apex. Phys. Rev. B. 2017;95:045407. doi: 10.1103/PhysRevB.95.045407. DOI

Taber BN, et al. Quantum confinement of surface electrons by molecular nanohoop corrals. J. Phys. Chem. Lett. 2016;7:3073–3077. doi: 10.1021/acs.jpclett.6b01279. PubMed DOI

Ishii H, Sugiyama K, Ito E, Seki K. Energy level alignment and interfacial electronic structures at organic/metal and organic/organic interfaces. Adv. Mater. 1999;11:605–625. doi: 10.1002/(SICI)1521-4095(199906)11:8<605::AID-ADMA605>3.0.CO;2-Q. DOI

Braun S, Salaneck WR, Fahlman M. Energy-level alignment at organic/metal and organic/organic interfaces. Adv. Mater. 2009;21:1450–1472. doi: 10.1002/adma.200802893. DOI

Mahan, G. D. Many-Particle Physics. Physics of Solids and Liquids (Springer US, 2000).

Chen W, Madhavan V, Jamneala T, Crommie MF. Scanning tunneling microscopy observation of an electronic superlattice at the surface of clean gold. Phys. Rev. Lett. 1998;80:1469–1472. doi: 10.1103/PhysRevLett.80.1469. DOI

Bürgi L, Brune H, Kern K. Imaging of electron potential landscapes on Au(111) Phys. Rev. Lett. 2002;89:176801. doi: 10.1103/PhysRevLett.89.176801. PubMed DOI

Schouteden K, et al. Confinement of surface state electrons in self-organized Co islands on Au(111) N. J. Phys. 2008;10:43016. doi: 10.1088/1367-2630/10/4/043016. DOI

Schouteden K, Lievens P, Van Haesendonck C. Fourier-transform scanning tunneling microscopy investigation of the energy versus wave vector dispersion of electrons at the Au(111) surface. Phys. Rev. B. 2009;79:195409. doi: 10.1103/PhysRevB.79.195409. DOI

Hasegawa Y, Avouris P. Direct observation of standing wave formation at surface steps using scanning tunneling spectroscopy. Phys. Rev. Lett. 1993;71:1071. doi: 10.1103/PhysRevLett.71.1071. PubMed DOI

Petersen L, Laitenberger P, Lægsgaard E, Besenbacher F. Screening waves from steps and defects on Cu(111) and Au(111) imaged with STM: contribution from bulk electrons. Phys. Rev. B. 1998;58:7361–7366. doi: 10.1103/PhysRevB.58.7361. DOI

Petersen L, et al. Direct imaging of the two-dimensional Fermi contour: Fourier-transform STM. Phys. Rev. B. 1998;57:R6858. doi: 10.1103/PhysRevB.57.R6858. DOI

Gross L, et al. Scattering of surface state electrons at large organic molecules. Phys. Rev. Lett. 2004;93:056103. doi: 10.1103/PhysRevLett.93.056103. PubMed DOI

Seufert K, et al. Controlled interaction of surface quantum-well electronic states. Nano Lett. 2013;13:6130–6135. doi: 10.1021/nl403459m. PubMed DOI

Lewis JP, et al. Advances and applications in the FIREBALL ab initio tight-binding molecular-dynamics formalism. Phys. Status Solidi B Basic Res. 2011;248:1989–2007. doi: 10.1002/pssb.201147259. DOI

Becke AD. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A. 1988;38:3098–3100. doi: 10.1103/PhysRevA.38.3098. PubMed DOI

Grimme S, Ehrlich S, Goerigk L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 2011;32:1456–1465. doi: 10.1002/jcc.21759. PubMed DOI

Basanta MA, Dappe YJ, Jelínek P, Ortega J. Optimized atomic-like orbitals for first-principles tight-binding molecular dynamics. Comput. Mater. Sci. 2007;39:759–766. doi: 10.1016/j.commatsci.2006.09.003. DOI

Bezanson J, Edelman A, Karpinski S, Shah VB. Julia: a fresh approach to numerical computing. SIAM Rev. 2017;59:65. doi: 10.1137/141000671. DOI

Mahalingam, H. & Rodin, A. Visualizing designer quantum states in stable macrocycle quantum corrals. rodin-physics/au-polymer. 10.5281/zenodo.5497903 (2021). PubMed PMC

Visualizing designer quantum states in stable macrocycle quantum corrals