Within the last three decades Scanning Probe Microscopy has been developed to a powerful tool for measuring surfaces and their properties on an atomic scale such that users can be found nowadays not only in academia but also in industry. This development is still pushed further by researchers, who continuously exploit new possibilities of this technique, as well as companies that focus mainly on the usability. However, although imaging has become significantly easier, the time required for a safe approach (without unwanted tip-sample contact) can be very time consuming, especially if the microscope is not equipped or suited for the observation of the tip-sample distance with an additional optical microscope. Here we show that the measurement of the absolute tip-sample capacitance provides an ideal solution for a fast and reliable pre-approach. The absolute tip-sample capacitance shows a generic behavior as a function of the distance, even though we measured it on several completely different setups. Insight into this behavior is gained via an analytical and computational analysis, from which two additional advantages arise: the capacitance measurement can be applied for observing, analyzing, and fine-tuning of the approach motor, as well as for the determination of the (effective) tip radius. The latter provides important information about the sharpness of the measured tip and can be used not only to characterize new (freshly etched) tips but also for the determination of the degradation after a tip-sample contact/crash.

The ability to manipulate single atoms has opened up the door to constructing interesting and useful quantum structures from the ground up. On the one hand, nanoscale arrangements of magnetic atoms are at the heart of future quantum computing and spintronic devices; on the other hand, they can be used as fundamental building blocks for the realization of textbook many-body quantum models, illustrating key concepts such as quantum phase transitions, topological order or frustration as a function of system size. Here, we use low-temperature scanning tunnelling microscopy to construct arrays of magnetic atoms on a surface, designed to behave like spin-1/2 XXZ Heisenberg chains in a transverse field, for which a quantum phase transition from an antiferromagnetic to a paramagnetic phase is predicted in the thermodynamic limit. Site-resolved measurements on these finite-size realizations reveal a number of sudden ground state changes when the field approaches the critical value, each corresponding to a new domain wall entering the chains. We observe that these state crossings become closer for longer chains, suggesting the onset of critical behaviour. Our results present opportunities for further studies on quantum behaviour of many-body systems, as a function of their size and structural complexity.