arXiv subjects

Robin Ohmann

Publications and source records attributed to Robin Ohmann.

3 recordsLinked to original sources

arXiv2020

Inducing the controlled rotation of single o MeO DMBI molecules anchored on Au(111)

A key step towards building single molecule machines is to control the rotation of molecules and nanostructures step by step on a surface. Here, we used the tunneling electrons coming from the tip of a scanning tunneling microscope to achieve the controlled directed rotation of complex o-MeO-DMBI molecules. We studied the adsorption of single o-MeO-DMBI molecules on Au(111) by scanning tunneling microscopy at low temperature. The enantiomeric form of the molecule on the surface can be determined by imaging the molecule by STM at high bias voltage. We observed by lateral manipulation experiments that the molecules chemisorb on the surface and are anchored on Au(111) with an oxygen-gold bond via their methoxy-group. Driven by inelastic tunneling electrons, o-MeO-DMBI molecules can controllably rotate, stepwise and unidirectional, either clockwise or counterclockwise depending on their enantiomeric form.

cond-mat.mes-hall↗

arXiv2010

Image potential states as quantum probe of graphene interfaces

Image potential states (IPSs) are electronic states localized in front of a surface in a potential well formed by the surface projected bulk band gap on one side and the image potential barrier on the other. In the limit of a two-dimensional solid a double Rydberg series of IPSs has been predicted which is in contrast to a single series present in three-dimensional solids. Here, we confirm this prediction experimentally for mono- and bilayer graphene. The IPSs of epitaxial graphene on SiC are measured by scanning tunnelling spectroscopy and the results are compared to ab-initio band structure calculations. Despite the presence of the substrate, both calculations and experimental measurements show that the first pair of the double series of IPSs survives, and eventually evolves into a single series for graphite. Thus, IPSs provide an elegant quantum probe of the interfacial coupling in graphene systems.

cond-mat.mes-hall↗

arXiv2008

Hopf algebras and the logarithm of the S-transform in free probability

Let k be a positive integer and let G_k denote the set of non-commutative k-variable distributions \mu such that \mu (X_1) = ... = \mu (X_k) = 1. G_k is a group under the operation of free multiplicative convolution. We identify G_k as the group of characters of a certain Hopf algebra Y_k. Then, by using the log map from characters to infinitesimal characters of Y_k, we introduce a transform LS_{\mu} for distributions \mu in G_k. The main property of the LS-transform is that it linearizes commuting products in G_k. For \mu in G_k, the transform LS_{\mu} is a power series in k non-commuting indeterminates; its coefficients can be computed from the coefficients of the R-transform of \mu by using summations over chains in the lattices NC(n) of non-crossing partitions. In the particular case k=1 one has that Y_1 is naturally isomorphic to the Hopf algebra Sym of symmetric functions, and that the LS-transform is very closely related to the logarithm of the S-transform of Voiculescu, by the formula LS(z) = - z log S(z). In this case the group G_1 can be identified as the group of characters of Sym, in such a way that the S-transform, its reciprocal 1/S and its logarithm log S relate in a natural sense to the sequences of complete, elementary and respectively power sum symmetric functions.

math.OA↗