
The bulk conduction band of Si has six equivalent valleys. Strain in Si/SiGe heterostructures partially lifts the sixfold valley degeneracy by raising the energy of the four inplane valleys. It is known that large electric fields can lift the degeneracy of the remaining two lowlying valleys. However, the measured valley splittings range from 10 – 300 μeV, suggesting that microscopic details such as interface roughness and disorder impact the valley splitting. In this lecture I will describe how microwave spectroscopy can be applied to probe valley states in silicon nanostructures [1]. In the first experiment, a cavity coupled Si double quantum dot is probed using microwave frequency photons. The transmission of the photons through the microwave cavity displays signatures that are consistent with the valley degree of freedom and the data can be modeled using cavity inputoutput theory [2]. We also use LandauZener interferometry to probe the lowlying energy level structure of a silicon double quantum dot. The observed LandauZener interference pattern persists down to low driving frequencies of 50 MHz, suggesting relatively longlived charge coherence. Lowlying valley states result in a unique LandauZener interference pattern that is in contrast with measurements on conventional twolevel charge qubits [3]. These new probes of valley states have high energy resolution and may be applied to other low energy degrees of freedom.
1. Burkard and Petta, PRB 94, 195305 (2016).
2. Mi, Peterfalvi, Burkard, and Petta, PRL 119, 176803 (2017).
3. Mi, Kohler, and Petta, PRB 98, 161404(R) (2018).