  Coherent caloritronics, the thermal counterpart of coherent electronics, has
drawn growing attention since the discovery of heat interference in 2012.
Thermal interferometers, diodes, transistors and nano-valves have been
theoretically proposed and experimentally demonstrated by exploiting the
quantum phase difference between two superconductors coupled through a
Josephson junction. So far, the quantum-phase modulator has been realized in
the form of a superconducting quantum interference device (SQUID) or a
superconducting quantum interference proximity transistor (SQUIPT). Thence, an
external magnetic field is necessary in order to manipulate the heat transport.
Here, we theoretically propose the first on-chip fully thermal caloritronic
device: the phase-tunable temperature amplifier. Taking advantage of a recent
thermoelectric effect discovered in spin-split superconductors coupled to a
spin-polarized system, by a temperature gradient we generate the magnetic flux
controlling the transport through a temperature biased SQUIPT. By employing
commonly used materials and a geometry compatible with state-of-the-art
nano-fabrication techniques, we simulate the behavior of the temperature
amplifier and define a number of figures of merit in full analogy with voltage
amplifiers. Notably, our architecture ensures infinite input thermal impedance,
maximum gain of about 11 and efficiency reaching the 95%. This device concept
could represent a breakthrough in coherent caloritronic devices, and paves the
way for applications in radiation sensing, thermal logics and quantum
information.
