Designing quantum matter in two dimensions

Experimental condensed matter research is experiencing a paradigm shift. In the past, the need for 3D crystalline samples with a specific structure and doping imposed strict requirements for achieving the desired properties. Now, it is possible to create tunable 2D samples in the lab, overcoming the previous limitations and accelerating the research. In this thesis, I will demonstrate how we utilized the molecular beam epitaxy (MBE) technique to design and fabricate van der Waals (vdW) heterostructures. The vdW nature of the MBE-grown materials enabled us to combine physical properties of different materials without altering them. I will showcase how we engineered two phases of matter that are central to condensed matter physics, and probed them using scanning tunneling microscope. The first is heavy fermions, which we artificially created by combining magnetic and metallic vdW materials. Here, a lattice of magnetic moments in 1T-TaS2 couples via the Kondo exchange coupling to conduction electrons in 1H-TaS2, resulting in the emergence of Kondo lattice physics. The flat band of Kondo lattice hybridized with the dispersive electrons, leading to a gap at the Fermi level of 1H-TaS2. In this special case of separated magnetic moments and conduction electrons, we reproduce the expected observables in the spectral function: Kondo peak on the side of magnetic lattice and heavy-fermion hybridization gap on the side of conduction electrons. The second is unconventional superconductivity, which we attempted to achieve in two different systems: a monolayer vdW material and a vdW heterostructure composed of a superconductor and a magnet. We observe strong signatures of nodal superconductivity in 1H-TaS2: V-shaped spectral gap, many-body fluctuations and a pseudogap, which is the first evidence of unconventional superconductivity in a monolayer vdW material. We also create topological superconductivity in a heterostructure of magnetic CrBr3 and superconducting 2H-NbSe2, and observe the edge state and the Shiba bands. Futhermore, we show that the topology of this system arises from the moiré pattern. These results highlight the benefits of the designer approach and open new opportunities in their respective fields.