Quantifying Many-Body Effects by High-Resolution Fourier Transform Scanning Tunneling Spectroscopy

Abstract

Many-body phenomena are ubiquitous in solids, as electrons interact with one another and the many excitations arising from lattice, magnetic, and electronic degrees of freedom. These interactions can subtly influence the electronic properties of materials ranging from metals, 1 exotic materials such as graphene, 2, 3 and topological insulators, 4 or they can induce new phases of matter, as in conventional 5 and unconventional superconductors, 6-9 heavy fermion systems, 10 and other systems of correlated electrons. As no single theoretical approach describes all such phenomena, the development of versatile methods for measuring manybody effects is key for understanding these systems. To date, angle-resolved photoemission spectroscopy (ARPES) has been the method of choice for accessing this physics by directly imaging momentum resolved electronic structure. 2-4, 6, 7, 9 Scanning tunneling microscopy/spectroscopy (STM/S), renown for its real-space atomic resolution capability, can also access the electronic structure in momentum space using Fourier transform scanning tunneling spectroscopy (FT-STS Non-interacting electrons in a crystal occupy quantum states with an infinite lifetime and band dispersion (k) set by the lattice potential. Interactions with the other electrons and elementary excitations of the system scatter the electrons, resulting in an altered dispersion relation E(k) and a finite lifetime. These many-body effects are encoded in the complex self-energyThe imaginary part Σ (k, E) determines the lifetime of the state and is related to the scattering rate. The real part Σ (k, E) shifts the electronic dispersionThe tools available for studying energy and momentum resolved selfenergy are limited. 15 For example, bulk transport and optical spectroscopies provide some access to k-integrated self-energies while ARPES accesses k-resolved information for only the occupied states. It is therefore important to develop a more extensive suite of versatile techniques, especially in the context of complex systems that remain poorly understood from a theoretical perspective.STM/STS accesses momentum space electronic structure by imaging real-space maps of the modulations in differential conductance (dI/dV ), which is proportional to the local density of states (LDOS) of the sample. These modulations arise from the interference of electrons scattered elastically by defects, and contain information about the initial and final momenta that are accessible by a Fourier transform of the real space map. As the electrons are dressed by interactions, the momentum space scattering intensity map is often referred to as the quasiparticle interference (QPI) map. The dominant intensities in a QPI map occur at scattering wave vectors linking constant energy segments of the band dispersion. By tracking the energy dependence of these peaks, the electronic dispersion E(k) can be obtained. This technique has been used to map coarse dispersions in many materials 16,17 and to examine scattering selection rules. 16,17 While the influenc...

Dispersing artifacts in FT-STS: a comparison of set point effects across acquisition modes

“…Simple 1-band systems can be analyzed directly, and this was first done for the surface states of noble metals [21,22,23,24,25] which have more recently been used to advance FT-STS as a probe for many-body effects [17,26]. However, more complicated systems require complementary information about the band structure, and the patterns observed can become extremely complex when scattering between multiple bands [3,19,27], and the possibility of selection rules for the allowed scattering processes [5,7,16,28], come into play.…”

Optical dielectric function of silver

“…[60][61][62] In the study of DC conductivity of metals, intrinsic effects can be determined after consideration of extrinsic effects from systematic studies under controlled temperature and impurity levels. [28,63,64] In contrast, the determination of the spectroscopic behavior of the dielectric function at optical frequencies is more involved.…”

Apparent Reversal of Molecular Orbitals Reveals Entanglement

“…In this context, quantum effects such as electronic interference have recently shifted into the focus [1][2][3][4][5][6][7]. Most intriguing in this respect are electron correlation effects [8][9][10][11][12][13][14], which are intrinsically strong in molecules due to their small size [15][16][17][18][19].In general, Coulomb charging energies strongly depend on the localization of electrons and hence, on the spatial extent of the orbitals they occupy. Therefore, the orbital sequence of a given molecule can reverse upon electron attachment or removal if some of the frontier orbitals are strongly localized while others are not, like in, e.g., phthalocyanines [20][21][22][23][24].…”