We report on an apparent low-energy nanoscale electronic inhomogeneity in FeSe$_{0.4}$Te$_{0.6}$ due to the distribution of selenium and tellurium atoms revealed through unsupervised machine learning. Through an unsupervised clustering algorithm, characteristic spectra of selenium- and tellurium-rich regions are identified. The inhomogeneity linked to these spectra can clearly be traced in the differential conductance and is detected both at energy scales of a few electron volts as well as within a few millielectronvolts of the Fermi energy. By comparison with ARPES, this inhomogeneity can be linked to an electron-like band just above the Fermi energy. It is directly correlated with the local distribution of selenium and tellurium. There is no clear correlation with the magnitude of the superconducting gap, however the height of the coherence peaks shows significant correlation with the intensity with which this band is detected, and hence with the local chemical composition.
We use scanning tunneling microscopy (STM) and quasiparticle interference (QPI) imaging to investigate the low-energy orbital texture of single-layer FeSe/SrTiO$_3$. We develop a $T$-matrix model of multi-orbital QPI to disentangle scattering intensities from Fe $3d_{xz}$ and $3d_{yz}$ bands, enabling the use of STM as a nanoscale detection tool of nematicity. By sampling multiple spatial regions of a single-layer FeSe/SrTiO$_3$ film, we quantitatively exclude static $xz/yz$ orbital ordering with domain size larger than $δr^2$ = 20 nm $\times$ 20 nm, $xz/yz$ Fermi wave vector difference larger…
In a material prone to a nematic instability, anisotropic strain in principle provides a preferred symmetry-breaking direction for the electronic nematic state to follow. This is consistent with experimental observations, where electronic nematicity and structural anisotropy typically appear hand-in-hand. In this work, we discover that electronic nematicity can be locally decoupled from the underlying structural anisotropy in strain-engineered iron-selenide (FeSe) thin films. We use heteroepitaxial molecular beam epitaxy to grow FeSe with a nanoscale network of modulations that give rise to sp…
Structural phase separation in the form of partially disordered stripes, with characteristic length scales in the nanometer range, is observed for superconducting BaPb$_{1-x}$Bi$_x$O$_3$. The evolution of the superconducting coherence length with composition relative to the size of these stripes suggests an important role of the nanostructure in determining the shape of the superconducting dome. It is proposed that the maximum $T_c$ is determined by a kind of "optimal inhomogeneity", characterized by a crossover from an inhomogeneous macroscopic superconductor to a granular superconductor for …
While stripe phases with broken rotational symmetry of charge density appear in many complex correlated systems, the heterogeneity of spatial ordering and dynamics remains elusive. This missing info is at the heart of understanding the structure and function relation in quantum complex materials. We focus here on the spatial heterogeneity of the motion of charge density wave (CDW) at nanoscale in the archetypal case of La$_{2-x}$Sr$_x$NiO$_{4+y}$ perovskite at low temperature. We report compelling evidence that the unconventional increasing motion of CDW at T < 50K is related with the decreasi…
We have studied the superexchange interaction $J_{ij}$ in doped $2D$ cuprates. The AFM interaction strongly depends on the state of the lattice of a CuO$_2$ layer surrounded by two LaO rock salt layers. In a static $U$ and $D$ stripe nanostructure, the homogeneous AFM interaction is impossible due to the $U/D/U...$ periodic stripe sequence and $T_N=0$. In a dynamic stripe nanostructure, the ideal CuO$_2$ layer with nonlocal effects and the homogeneous AFM interaction are restored. However the interaction $J_{ij}$ decreases by the exponential factor due to partial dynamic quenching. The meaning…
The notion of spontaneous formation of an inhomogeneous superconducting state is at the heart of most theories attempting to understand the superconducting state in the presence of strong disorder. Using scanning tunneling spectroscopy and high resolution scanning transmission electron microscopy, we experimentally demonstrate that under the competing effects of strong homogeneous disorder and superconducting correlations, the superconducting state of a conventional superconductor, NbN, spontaneously segregates into domains. Tracking these domains as a function of temperature we observe that t…
We calculate ground-state energies and density distributions of Hubbard superlattices characterized by periodic modulations of the on-site interaction and the on-site potential. Both density-matrix renormalization group and density-functional methods are employed and compared. We find that small variations in the on-site potential $v_i$ can simulate, cancel, or even overcompensate effects due to much larger variations in the on-site interaction $U_i$. Our findings highlight the importance of nanoscale spatial inhomogeneity in strongly correlated systems, and call for reexamination of model cal…
Topological insulators are a class of band insulators with non-trivial topology, a result of band inversion due to the strong spin-orbit coupling. The transition between topological and normal insulator can be realized by tuning the spin-orbit coupling strength, and has been observed experimentally. However, the impact of chemical disorders on the topological phase transition was not addressed in previous studies. Herein, we report a systematic scanning tunneling microscopy/spectroscopy and first-principles study of the topological phase transition in single crystals of In doped Bi$_2$Se$_3$. …
We have found a quantitative connection between the evolution of the inhomogeneous nanoscale electronic gaps (INSEG) state detected in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ by scanning tunneling microscopy/spectroscopy (STM/S) and the two universal, the upper and the lower, pseudogaps in high-temperature cuprate superconductors (HTCS). When the doping and temperature dependent INSEG map were analyzed by using our proposed hole-scale, we find that the two pseudogaps are connected to two specific coverages of the CuO$_2$ plane by INSEG: the 50\% and 100\% coverages of the CuO$_2$ planes by INSEG corresp…
The results of a computer analysis of a simple 2D quantum mechanical tunnelling model are reported. These suggest that the spatial dependence of the superconducting energy gap observed by Scanning Tunnelling Spectroscopy (STS) studies of single crystals of the high Tc superconductor Bi:2212 is not necessarily caused by nanoscale inhomogeneity. Instead the spatial dependence of the STS data could arise from the momentum (k) dependence of the energy gap, which is a defining feature of a d-wave superconductor. It is possible that this viewpoint could be exploited to obtain k-dependent information…
In several strongly correlated electron systems, defects, charge and local lattice distortions are found to show complex inhomogeneous spatial distributions. There is growing evidence that such inhomogeneity plays a fundamental role in unique functionality of quantum complex materials. La1.72Sr0.28NiO4 is a prototypical strongly correlated material showing spin striped order associated with lattice and charge modulations. In this work we present the spatial distribution of the spin organization by applying micro X-ray diffraction to La1.72Sr0.28NiO4, mapping the spin-density-wave order below t…
We use scanning tunneling microscopy to determine the surface structure and dopant distribution in Pr$_x$Ca$_{1-x}$Fe$_2$As$_2$, the highest-$T_c$ member of the 122 family of iron-based superconductors. We identify the cleaved surface termination by mapping the local tunneling barrier height, related to the work function. We image the individual Pr dopants responsible for superconductivity, and show that they do not cluster, but in fact repel each other at short length scales. We therefore suggest that the low volume fraction high-$T_c$ superconducting phase is unlikely to originate from Pr in…
A microscopic theory is presented for the observed electronic disorder in superconducting Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. The essential phenomenology is shown to be consistent with the existence of two types of interstitial oxygen dopants: those serving primarily as charge reserviors and those close to the apical plane contributing both carriers and electrostatic potential to the CuO$_2$ plane. The nonlinear screening of the latter produces nanoscale variations in the doped hole concentration, leading to electronic inhomogeneity. Based on an unrestricted Gutzwiller approximation of the extended…
We report the nanoscale conductivity imaging of correlated electronic states in angle-aligned WSe2/WS2 heterostructures using microwave impedance microscopy. The noncontact microwave probe allows us to observe the Mott insulating state with one hole per moiré unit cell that persists for temperatures up to 150 K, consistent with other characterization techniques. In addition, we identify for the first time a Mott insulating state at one electron per moiré unit cell. Appreciable inhomogeneity of the correlated states is directly visualized in the hetero-bilayer region, indicative of local disord…
The interplay of different electronic phases underlies the physics of unconventional superconductors. One of the most intriguing examples is a high-Tc superconductor FeTe1-xSex: it undergoes both a topological transition, linked to the electronic band inversion, and an electronic nematic phase transition, associated with rotation symmetry breaking, around the same critical composition xc where superconducting Tc peaks. At this regime, nematic fluctuations and symmetry-breaking strain could have an enormous impact, but this is yet to be fully explored. Using spectroscopic-imaging scanning tunne…
Nanoscale electronic variations in altermagnetic $α$-MnTe
School of Engineering & Applied Sciences, Harvard University（哈佛大学本科院）；Department of Physics, Harvard University（哈佛大学物理系）；Materials Science & Technology Division, Physical Sciences Directorate, Oak Ridge National Lab（橡树岭国家实验室物理科学部材料科学与技术分部）
Singular spin fluctuations in the strange-metal phase of La2-xSrxCuO4
Univ. Grenoble Alpes, CNRS, Univ. Toulouse, INSA-T（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，图卢兹大学，国立应用科学学院）；LNCMI-EMFL, UPR3228（强磁场中心欧洲磁力实验室）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Beijing National Laboratory for Condensed Matter Physics（北京凝聚态物理国家研究中心）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory（布鲁克海文国家实验室凝聚态物理与材料科学部）
Replacing a magnetic atom by a spinless atom in a heavy fermion compound generates a quantum state often referred to as a 'Kondo-hole'. No experimental imaging has been achieved of the atomic-scale electronic structure of a Kondo-hole, or of their destructive impact (Lawrence JM, et al. (1996) Kondo hole behavior in Ce0. 97La0. 03Pd3. Phys Rev B 53:12559-12562; Bauer ED, et al. (2011) Electronic inhomogeneity in a Kondo lattice. Proc Natl Acad Sci. 108:6857-6861) on the hybridization process between conduction and localized electrons which generates the heavy fermion state. Here we report visu…
Surface probes such as scanning tunneling microscopy (STM) have detected complex patterns at the nanoscale, indicative of electronic inhomogeneity, in a variety of high temperature superconductors. In cuprates, the pattern formation is associated with the pseudogap phase, a precursor to the high temperature superconducting state. Symmetry breaking (i.e. from C4 to C2) in the form of electronic nematicity has recently been implicated as a unifying theme of the pseudogap phase,[1] however the fundamental physics governing the nanoscale pattern formation has not yet been identified. Here we use u…
