How to measure the entropy of a mesoscopic system via thermoelectric transport.

Entropy is a fundamental thermodynamic quantity indicative of the accessible degrees of freedom in a system. While it has been suggested that the entropy of a mesoscopic system can yield nontrivial information on emergence of exotic states, its measurement in such small electron-number system is a daunting task. Here we propose a method to extract the entropy of a Coulomb-blockaded mesoscopic system from transport measurements. We prove analytically and demonstrate numerically the applicability of the method to such a mesoscopic system of arbitrary spectrum and degeneracies. We then apply our procedure to measurements of thermoelectric response of a single quantum dot, and demonstrate how it can be used to deduce the entropy change across Coulomb-blockade valleys, resolving, along the way, a long-standing puzzle of the experimentally observed finite thermoelectric response at the apparent particle-hole symmetric point.

Shielded cantilever with on-chip interferometer circuit for THz scanning probe impedance microscopy.

We have realized a microstrip based terahertz (THz) near field cantilever that enables quantitative measurements of the impedance of the probe tip at THz frequencies (0.3 THz). A key feature is the on-chip balanced hybrid coupler that serves as an interferometer for passive signal cancellation to increase the readout circuit sensitivity despite extreme impedance mismatch at the tip. We observe distinct changes in the reflection coefficient of the tip when brought into contact with different dielectric (Si, SrTiO3) and metallic samples (Au). By comparing finite element simulations, we determine the sensitivity of our THz probe to be well below 0.25 fF. The cantilever further allows for topography imaging in a conventional atomic force microscope mode. Our THz cantilever removes several critical technology challenges and thus enables a shielded cantilever based THz near field microscope.

Transport regimes of a split gate superconducting quantum point contact in the two-dimensional LaAlO3/SrTiO3 superfluid.

One of the hallmark experiments of quantum transport is the observation of the quantized resistance in a point contact in GaAs/AlGaAs heterostructures. Being formed with split gate technology, these structures represent in an ideal manner equilibrium reservoirs which are connected only through a few electron mode channel. It has been a long standing goal to achieve similar experimental conditions also in superconductors. Here we demonstrate the formation of a superconducting quantum point contact (SQPC) with split gate technology in a two-dimensional superconductor, utilizing the unique gate tunability of the superfluid at the LaAlO3/SrTiO3 interface. When the constriction is tuned through the action of metallic split gates we identify three regimes of transport: First, SQPC for which the supercurrent is carried only by a few quantum transport channels. Second, superconducting island strongly coupled to the equilibrium reservoirs. Third, charge island with a discrete spectrum weakly coupled to the reservoirs.

Three-terminal energy harvester with coupled quantum dots.

Rectification of thermal fluctuations in mesoscopic conductors is the key idea behind recent attempts to build nanoscale thermoelectric energy harvesters to convert heat into useful electric power. So far, most concepts have made use of the Seebeck effect in a two-terminal geometry, where heat and charge are both carried by the same particles. Here, we experimentally demonstrate the working principle of a new kind of energy harvester, proposed recently, using two capacitively coupled quantum dots. We show that, due to the novel three-terminal design of our device, which spatially separates the heat reservoir from the conductor circuit, the directions of charge and heat flow become decoupled. This enables us to manipulate the direction of the generated charge current by means of external gate voltages while leaving the direction of heat flow unaffected. Our results pave the way for a new generation of multi-terminal nanoscale heat engines.