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To date, there are very few experimental techniques, if any, that aresuitable for the purpose of acquiring, with nanoscale lateral resolution,quantitative maps of the thermal expansivity of 2D materials and thin films,despite huge demand for nanoscale thermal management, for example in designingintegrated circuitry for power electronics. Besides, contactless analyticaltools for determining the thermal expansion coefficient (TEC) are highlydesirable, because probes in contact with the sample significantly perturb anythermal measurements. Here, we introduce {\omega}-2{\omega} near-fieldthermoreflectance imaging, as an all-optical and contactless approach to mapthe TEC at the nanoscale with precision. Testing of our technique is performedon nanogranular films of gold and multilayer graphene (ML-G) platelets. Ourmethod demonstrates that the TEC of Au is higher at the metal-insulatorinterface, with an average of (17.12 +/- 2.30)x10-6 K-1 in agreement withmacroscopic techniques. For ML-G, the average TEC was (-5.77 +/- 3.79)x10-6 K-1and is assigned to in-plane vibrational bending modes. A vibrational-thermaltransition from graphene to graphite is observed, where the TEC becomespositive as the ML thickness increases. Our nanoscale method demonstratesresults in excellent agreement with its macroscopic counterparts, as well assuperior capabilities to probe 2D materials and interfaces.

A contactless scanning near-field optical dilatometer imaging the thermal expansivity of inhomogeneous 2D materials and thin films at the nanoscale