ABSTRACT
Two-dimensional electronic states at surfaces are often observed in simple wide-band metals such as Cu or Ag (refs. 1-4). Confinement by closed geometries at the nanometre scale, such as surface terraces, leads to quantized energy levels formed from the surface band, in stark contrast to the continuous energy dependence of bulk electron bands2,5-10. Their energy-level separation is typically hundreds of meV (refs. 3,6,11). In a distinct class of materials, strong electronic correlations lead to so-called heavy fermions with a strongly reduced bandwidth and exotic bulk ground states12,13. Quantum-well states in two-dimensional heavy fermions (2DHFs) remain, however, notoriously difficult to observe because of their tiny energy separation. Here we use millikelvin scanning tunnelling microscopy (STM) to study atomically flat terraces on U-terminated surfaces of the heavy-fermion superconductor URu2Si2, which exhibits a mysterious hidden-order (HO) state below 17.5 K (ref. 14). We observe 2DHFs made of 5f electrons with an effective mass 17 times the free electron mass. The 2DHFs form quantized states separated by a fraction of a meV and their level width is set by the interaction with correlated bulk states. Edge states on steps between terraces appear along one of the two in-plane directions, suggesting electronic symmetry breaking at the surface. Our results propose a new route to realize quantum-well states in strongly correlated quantum materials and to explore how these connect to the electronic environment.
ABSTRACT
This work presents a Green's function approach, originally implemented in graphene with well-defined edges, to the surface of a strong 3D topological insulator with a sequence of proximitized superconducting (S) and ferromagnetic (F) surfaces. This consists of the derivation of the Green's functions for each region by the asymptotic solutions method and their coupling by a tight-binding Hamiltonian with the Dyson equation to obtain the full Green's functions of the system. These functions allow the direct calculation of the momentum-resolved spectral density of states, the identification of subgap interface states and the derivation of the differential conductance for a wide variety of configurations of the junctions. We illustrate the application of this method for some simple systems with two and three regions, finding the characteristic chiral state of the quantum anomalous Hall effect at the NF interfaces, and chiral Majorana modes at the NS interfaces. Finally, we discuss some geometrical effects present in three-region junctions such as weak Fabry-Pérot resonances and Andreev bound states.
ABSTRACT
This work presents a novel approach to describing spectral properties of graphene layers with well-defined edges. We microscopically analyze the boundary problem for the continuous Bogoliubov-de Gennes-Dirac equations and derive the Green functions for normal and superconducting graphene layers. Importing the idea used in tight-binding models of a microscopic hopping that couples different regions, we are able to set up and solve an algebraic Dyson equation describing a graphene-superconductor junction. For this coupled system we analytically derive the Green functions and use them to calculate the local density of states and the spatial variation of the induced pairing correlations in the normal region. Signatures of specular Andreev reflections are identified.
