Yigal Meir

In recent years many candidate setups have been proposed to support exotic quasi-particles, such as Majorana fermions (MFs), which may be relevant for quantum computing, but whether these  particles  have  been  observed  experimentally is currently a topic of a vivid debate. Entropy measurements can unambiguously separate these quasi-particles from other, simpler excitations. The entropy of a MFs is, for example, log2/2 (in units of the Boltzman constant), a fractional value that cannot be attributed to a localzed excitation. However, standard entropy measurements applicable to bulk systems cannot be utilized in measuring the additional entropy of a mesoscopic device, which may be due to less than a single electron in the device. In this talk I will describe recent theoretical and experimental progress in performing such measurements, either using thermopower and/or using the Maxwell relations [1,2]. Particular examples will be single and double quantum dots in the Coulomb blockade regime. Lastly I will show how the formalism has been generalized to deduce the entropy from conductance measurements, and, applying it to a setup where two and three-channel Kondo physics have been observed, yields the fractional entropy of a single MF and a single Fibonacci anyon [3].  Lastly I will discuss the backaction of the measurement and discuss the possibility of measuring entanglement entropy [4].

1. Direct entropy measurement in a mesoscopic quantum system, N. Hartman, et al.,  Nature Physics 14, 1083 (2018).
2. How to measure the entropy of a mesoscopic system via thermoelectric transport, Y. Kleeorin et al., Nature Comm. 10 , 5801 (2019)
3. Fractional Entropy of Multichannel Kondo Systems from Conductance-Charge Relations, C. Han et al., Phys. Rev. Lett. 128, 146803 (2022).
4. Realistic protocol to measure entanglement at finite temperatures, C. Han, Y. Meir and E. Sela, Phys. Rev. Lett., in press.