On the nature of quasiparticle interference in three dimensions

Quasiparticle Interference (QPI) imaging is a powerful tool for the study of the low energy electronic structure of quantum materials. However, the measurement of QPI by scanning tunneling microscopy (STM) is restricted to surfaces and is thus inherently constrained to two dimensions. This has proved immensely successful for the study of materials that exhibit a quasi-two-dimensional electronic structure, yet it raises questions about how to interpret QPI in materials that have a highly three dimensional electronic structure. In this paper we address this question and establish the methodology required to simulate and understand QPI arising from three dimensional systems as measured by STM. We calculate the continuum surface Green's function in the presence of a defect, which captures the role of the surface and the vacuum decay of the wave functions. We find that defects at different depths from the surface will produce unique sets of scattering vectors for three dimensional systems, which nevertheless can be related to the three-dimensional electronic structure of the bulk material. We illustrate the consequences that the three-dimensionality of the electronic structure has on the measured QPI for a simple cubic nearest-neighbour tight-binding model, and then demonstrate application to a real material using a realistic model for PbS. Our method unlocks the use of QPI imaging for the study of quantum materials with three dimensional electronic structures and introduces a framework to generically account for $k_z$-dispersions within QPI simulations

Symmetry, spin and orbital character of a van-Hove singularity in proximity to a Lifshitz transition in Sr4_4Ru3_3O10_{10}

The physics of strongly correlated electron materials is often governed by Van Hove singularities (VHss) in the vicinity of the Fermi energy. The divergence of the density of states generated by the VHss can promote electron-electron interactions and the emergence of new phases such as superconductivity, ferromagnetism, metamagnetism, nematicity and density wave orders. The shape and intensity of this divergence depends sensitively on the order and symmetry of the VHs, and hence a detailed understanding of the low-energy electronic structure is essential to understand the role of VHss in emergent phases. A family of materials with a large diversity of emergent phases that can be related to VHss close to the Fermi energy is the Ruddlesden-Popper series of the strontium ruthenates. Here we study the low-energy electronic structure at the surface of ferromagnetic Sr$_4$Ru$_3$O$_{10}$ by scanning tunneling microscopy and spectroscopy at millikelvin temperatures. We identify multiple VHss close to the Fermi energy and establish their spin character. Using quasiparticle interference we extract the orbital character and symmetry of the VHs closest to the Fermi energy, enabling us to identify a new mechanism for a field-induced Lifshitz transition facilitated by spin-orbit coupling as the origin of the metamagnetic behaviour in Sr$_4$Ru$_3$O$_{10}$.Comment: 25 pages, 5 figures and supplementary materia

Spin-orbit coupling induced Van Hove singularity in proximity to a Lifshitz transition in Sr4Ru3O10

Funding: CAM, MN and PW gratefully acknowledge funding from the Engineering and Physical Sciences Research Council through EP/R031924/1 and EP/S005005/1, IB through the International Max Planck Research School for Chemistry and Physics of Quantum Materials and LCR from a fellowship from the Royal Commission of the Exhibition of 1851. RA, RF and AV thank the EU’s Horizon 2020 research and innovation program under Grant Agreement No. 964398 (SUPERGATE).Van Hove singularities (VHss) in the vicinity of the Fermi energy often play a dramatic role in the physics of strongly correlated electron materials. The divergence of the density of states generated by VHss can trigger the emergence of new phases such as superconductivity, ferromagnetism, metamagnetism, and density wave orders. A detailed understanding of the electronic structure of these VHss is therefore essential for an accurate description of such instabilities. Here, we study the low-energy electronic structure of the trilayer strontium ruthenate Sr4Ru3O10, identifying a rich hierarchy of VHss using angle-resolved photoemission spectroscopy and millikelvin scanning tunneling microscopy. Comparison of k-resolved electron spectroscopy and quasiparticle interference allows us to determine the structure of the VHss and demonstrate the crucial role of spin-orbit coupling in shaping them. We use this to develop a minimal model from which we identify a new mechanism for driving a field-induced Lifshitz transition in ferromagnetic metals.Peer reviewe

Spin-orbit coupling induced Van Hove singularity in proximity to a Lifshitz transition in Sr₄Ru₃O₁₀

Van Hove singularities (VHss) in the vicinity of the Fermi energy often play a dramatic role in the physics of strongly correlated electron materials. The divergence of the density of states generated by VHss can trigger the emergence of new phases such as superconductivity, ferromagnetism, metamagnetism, and density wave orders. A detailed understanding of the electronic structure of these VHss is therefore essential for an accurate description of such instabilities. Here, we study the low-energy electronic structure of the trilayer strontium ruthenate Sr4Ru3O10, identifying a rich hierarchy of VHss using angle-resolved photoemission spectroscopy and millikelvin scanning tunneling microscopy. Comparison of k-resolved electron spectroscopy and quasiparticle interference allows us to determine the structure of the VHss and demonstrate the crucial role of spin-orbit coupling in shaping them. We use this to develop a minimal model from which we identify a new mechanism for driving a field-induced Lifshitz transition in ferromagnetic metals.<br/

Spin-orbit coupling induced Van Hove singularity in proximity to a Lifshitz transition in Sr₄Ru₃O₁₀

Van Hove singularities (VHss) in the vicinity of the Fermi energy often play a dramatic role in the physics of strongly correlated electron materials. The divergence of the density of states generated by VHss can trigger the emergence of new phases such as superconductivity, ferromagnetism, metamagnetism, and density wave orders. A detailed understanding of the electronic structure of these VHss is therefore essential for an accurate description of such instabilities. Here, we study the low-energy electronic structure of the trilayer strontium ruthenate Sr4Ru3O10, identifying a rich hierarchy of VHss using angle-resolved photoemission spectroscopy and millikelvin scanning tunneling microscopy. Comparison of k-resolved electron spectroscopy and quasiparticle interference allows us to determine the structure of the VHss and demonstrate the crucial role of spin-orbit coupling in shaping them. We use this to develop a minimal model from which we identify a new mechanism for driving a field-induced Lifshitz transition in ferromagnetic metals.<br/