The Aharonov-Bohm effect and its applications to electron phase microscopy

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

The differential phase contrast uncertainty relation: Connection between electron dose and field resolution

Differential phase contrast (DPC) microscopy is a STEM imaging technique, which is used to measure magnetic and electric fields of mesoscopic and nanoscopic dimensions, i.e. interatomic distances (Chapman et al. 1978; Chapman et al. 1981; Chapman, 1984; Chapman et al. 1985; Chapman et al. 1997; Lohr et al. 2012; Shibata et al. 2015; Bauer et al. 2014; Carvalho et al. 2016; Lohr et al. 2016; Mueller-Caspary et al. 2019a,2019b; Mueller-Caspary et al. 2018; Mueller-Caspary et al. 2017; Mueller-Caspary et al. 2014; Winkler et al. 2020; Toyama et al. 2020). In this paper we will demonstrate that the electron dose per pixel deposited on the specimen is decisive to the precision and resolution of measurements of a field's local strength. Relations are given which connect a given electron dose per pixel to the fundamentally achievable precision to which the specimen's interaction with the electrons may be determined, taking into account quantum mechanical considerations. Vice versa, given a certain required precision, the required dose per pixel can be easily predicted for reliable measurements of a desired property. First, these relations are given for the case of a continuous, i.e. non-pixelated, detector followed by simulations which show that the same relations hold for pixelated detectors. Then, the achievable precision for detectors with different pixel counts in combination with different camera lengths is discussed and the maximum measurable field amplitude per set-up is determined. Finally, the effect of inhomogeneities within the diffraction disk is discussed and possible deviations from the derived relations are considered. We also demonstrate that Heisenberg's uncertainty relation determines the possible field resolution in differential phase contrast microscopy, and that the achievable local field resolution is a function of the applied electron dose per pixel.