Apparent Reversal of Molecular Orbitals Reveals Entanglement

Abstract

The frontier orbital sequence of individual dicyanovinyl-substituted oligothiophene molecules is studied by means of scanning tunneling microscopy. On NaCl=Cuð111Þ, the molecules are neutral, and the two lowest unoccupied molecular states are observed in the expected order of increasing energy. On NaCl=Cuð311Þ, where the molecules are negatively charged, the sequence of two observed molecular orbitals is reversed, such that the one with one more nodal plane appears lower in energy. These experimental results, in open contradiction with a single-particle interpretation, are explained by a manybody theory predicting a strongly entangled doubly charged ground state. DOI: 10.1103/PhysRevLett.119.056801 For the use of single molecules as devices, engineering and control of their intrinsic electronic properties is all important. In this context, quantum effects such as electronic interference have recently shifted into the focus [1][2][3][4][5][6][7]. Most intriguing in this respect are electron correlation effects [8][9][10][11][12][13][14], which are intrinsically strong in molecules due to their small size [15][16][17][18][19].In general, Coulomb charging energies strongly depend on the localization of electrons and hence, on the spatial extent of the orbitals they occupy. Therefore, the orbital sequence of a given molecule can reverse upon electron attachment or removal if some of the frontier orbitals are strongly localized while others are not, like in, e.g., phthalocyanines [20][21][22][23][24]. Coulomb interaction may also lead to much more complex manifestations such as quantum entanglement of delocalized molecular orbitals.Here, we show that the energy spacing of the frontier orbitals in a single molecular wire of individual dicyanovinyl-substituted quinquethiophene (DCV5T) can be engineered to achieve near degeneracy of the two lowest-lying unoccupied molecular orbitals, leading to a strongly entangled ground state of DCV5T 2− . These orbitals are the lowest two of a set of particle-in-a-box-like states and differ only by one additional nodal plane across the center of the wire. Hence, according to the fundamental oscillation theorem of the Sturm-Liouville theory, their sequence has to be set with an increasing number of nodal planes, which is one of the basic principles of quantum mechanics [25,26]. This is evidenced and visualized from scanning tunneling microscopy (STM) and spectroscopy (STS) of DCV5T on ultrathin insulating films. Upon lowering the substrate's work function, the molecule becomes charged, leading to a reversal of the sequence of the two orbitals. The fundamental oscillation theorem seems strikingly violated since the state with one more nodal plane appears lower in energy. This contradiction can be solved, though, by considering intramolecular correlation leading to a strong entanglement in the ground state of DCV5T 2− . The experiments were carried out with a home-built combined STM and atomic force microscopy (AFM) using a qPlus sensor [27] operated in ultrahigh vacuum at a temperat...

Advances and challenges in single-molecule electron transport

“…This has a strong impact on the relative weight and phase of the interfering poles in the many-body Green's function and therefore crucially enters QI. Observation of this rather striking effect in STM experiments was reported by Yu et al (2017).…”

“…Much less is known for situations where states interfere that consist of a few Slater determinants instead of just a single one. One would expect that many-body QI should be a frequent encounter in molecular systems, but so far it has been identified only in exceptional cases (Yu et al, 2017).…”

Non-covalent control of spin-state in metal-organic complex by positioning on N-doped graphene

“…These types of images are typically attributed to single particle HOMO and LUMO signatures in the d I /d V 36 . However, according to recent studies on similar molecular systems 37 , 38 , these resonances should not be directly interpreted as such. Instead, they reflect the many body spectral functions of electron tunneling processes in and out of the molecule.…”

Coherent vortex dynamics in a strongly interacting superfluid on a silicon chip

“…Furthermore, while the experiments reported here were performed with a relatively small number of vortices, theÅngström-scale of the vortex core in helium-4 will enable the future research on the dynamics of ensembles of thousands of vortices, a regime well outside current capabilities with cold atom and exciton-polariton superfluids [41]. This could allow emergent phenomena in two-dimensional turbulence to be explored, such as the inverse energy cascade [41,50] and anomalous hydrodynamics [51,52]…”