Superconductivity often occurs close to broken-symmetry parent states and is especially common in doped magnetic insulators 1 . When twisted close to a magic relative orientation angle near !°, bilayer graphene has flat moiré superlattice minibands that have emerged as a rich and highly tunable source of strong correlation physics 2-5 , notably the appearance of superconductivity close to interaction-induced insulating states. Here we report on the fabrication of bilayer graphene devices with exceptionally uniform twist angles. We show that the reduction in twist angle disorder reveals insulating states at all integer occupancies of the four-fold spin/valley degenerate flat conduction and valence bands, i.e. at moiré band filling factors # = %, ±!, ±(, ±), and superconductivity below critical temperatures as high as ~ 3 K close to -2 filling. We also observe three new superconducting domes at much lower temperatures close to the # = % and # = ±! insulating states. Interestingly, at # = ±! we find states with non-zero Chern numbers. For # = −! the insulating state exhibits a sharp hysteretic resistance enhancement when a perpendicular magnetic field above 3.6 tesla is applied, consistent with a field driven phase transition. Our study shows that symmetry-broken states, interaction driven insulators, and superconducting domes are common across the entire moiré flat bands, including near charge neutrality.

Heat capacity is an invaluable quantity in condensed matter physics and yet has been completely inaccessible in two-dimensional (2D) van der Waals (vdW) materials, owing to their ultrafast thermal relaxation times and the lack of suitable nanoscale thermometers. Here, we demonstrate a novel thermal relaxation calorimetry scheme that allows the first measurements of the electronic heat capacity of graphene. It is enabled by combining a radio frequency Johnson noise thermometer, which can measure the electronic temperature with a sensitivity of ∼20 mK/Hz 1/2 , and a photomixed optical heater that modulates T e with a frequency of up to Ω = 0.2 THz. This allows record sensitive measurements of the electronic heat capacity C e < 10 −19 J/K and the fastest measurement of electronic thermal relaxation time τ e < 10 −12 s yet achieved by a calorimeter. These features advance heat capacity metrology into the realm of nanoscale and lowdimensional systems and provide an avenue for the investigation of their thermodynamic quantities.

Photodetectors based on nano-structured superconducting thin films are currently some of the most sensitive quantum sensors and are key enabling technologies in such broad areas as quantum information, quantum computation and radio-astronomy. However, their broader use is held back by the low operation temperatures which require expensive cryostats. Here, we demonstrate a high-T c superconducting photodetector, which shows orders of magnitude improved performance characteristics of any superconducting detector operated above 77 K, with a responsivity of 9.61 × 104 V W−1, theoretically achievable noise equivalent power of 15.9 fW Hz1/2 and nanosecond relaxation times. At 15 K the detector reaches an ultra-high performance of 2.33 × 107 V W−1 and 55.2 aW Hz1/2. It is based on van der Waals heterostructures of the high temperature superconductor Bi2Sr2CaCu2O8+δ , which are shaped into nano-wires with ultra-small form factor using focused helium ion beam irradiation. To highlight the versatility of the detector we demonstrate its fabrication and operation on a telecom grade SiN waveguide chip. Our detector significantly relaxes the demands of practical applications of superconducting detectors and displays its possible potential for photonics based quantum applications.

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