| Summary: | Clathrates are a materials class with an extremely low phonon thermal conductivity, which is a key ingredient for a high thermoelectric conversion efficiency. Here, we present a study on the type-I clathrate La<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>1.2</mn></mrow></msub></semantics></math></inline-formula>Ba<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>6.8</mn></mrow></msub></semantics></math></inline-formula>Au<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>5.8</mn></mrow></msub></semantics></math></inline-formula>Si<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow></mrow><mrow><mn>38.8</mn></mrow></msub><msub><mo>□</mo><mrow><mn>1.4</mn></mrow></msub></mrow></semantics></math></inline-formula> directed at lowering the phonon thermal conductivity even further by forming mesoscopic wires out of it. Our hypothesis is that the interaction of the low-energy rattling modes of the guest atoms (La and Ba) with the acoustic modes, which originate mainly from the type-I clathrate framework (formed by Au and Si atoms, with some vacancies □), cuts off their dispersion and thereby tilts the balance of phonons relevant for thermal transport to long-wavelength ones. Thus, size effects are expected to set in at relatively long length scales. The structuring was carried out using a top-down approach, where the wires, ranging from 1260 nm to 630 nm in diameter, were cut from a piece of single crystal using a focused ion beam technique. Measurements of the thermal conductivity were performed with a self-heating <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mi>ω</mi></mrow></semantics></math></inline-formula> technique down to 80 K. Indeed, they reveal a reduction of the room-temperature phonon thermal conductivity by a sizable fraction of ∼40 % for our thinnest wire, thereby confirming our hypothesis.
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