Twisted van der Waals (vdW) heterostructures have recently emerged as an attractive platform to study tunable correlated electron systems. However, the quantum mechanical nature of vdW heterostructures makes their theoretical and experimental exploration laborious and expensive. Here we present a simple platform to mimic the behavior of twisted vdW heterostructures using acoustic metamaterials comprising of interconnected air cavities in a steel plate. Our classical analog of twisted bilayer graphene shows much of the same behavior as its quantum counterpart, including mode localization at a magic angle of about 1.1 degrees. By tuning the thickness of the interlayer membrane, we reach a regime of strong interactions more than three times higher than the feasible range of twisted bilayer graphene under pressure. In this regime, we find the magic angle as high as 6.01 degrees, corresponding to a far denser array of localized modes in real space and further increasing their interaction strength. Our results broaden the capabilities for cross-talk between quantum mechanics and acoustics, as vdW metamaterials can be used both as simplified models for exploring quantum systems and as a means for translating interesting quantum effects into acoustics.
The van der Waals heterostructures are a fertile frontier for discovering emergent phenomena in condensed matter systems. They are constructed by stacking elements of a large library of two-dimensional materials, which couple together through van der Waals interactions. However, the number of possible combinations within this library is staggering, and fully exploring their potential is a daunting task. Here we introduce van der Waals metamaterials to rapidly prototype and screen their quantum counterparts. These layered metamaterials are designed to reshape the flow of ultrasound to mimic electron motion. In particular, we show how to construct analogues of all stacking configurations of bilayer and trilayer graphene through the use of interlayer membranes that emulate van der Waals interactions. By changing the membrane's density and thickness, we reach coupling regimes far beyond that of conventional graphene. We anticipate that van der Waals metamaterials will explore, extend, and inform future electronic devices. Equally, they allow the transfer of useful electronic behavior to acoustic systems, such as flat bands in magic-angle twisted bilayer graphene, which may aid the development of super-resolution ultrasound imagers.
The Kondo insulator SmB6 has emerged as a primary candidate for exotic quantum phases, due to the predicted formation of strongly correlated, low-velocity topological surface states and corresponding high Fermi-level density of states. However, measurements of the surface-state velocity in SmB6 differ by orders of magnitude, depending on the experimental technique used. Here we reconcile two techniques, scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES), by accounting for surface band bending on polar terminations. Using spatially resolved scanning tunneling spectroscopy, we measure a band shift of ∼20 meV between full-Sm and half-Sm terminations, in qualitative agreement with our density-functional theory calculations of the surface charge density. Furthermore, we reproduce the apparent high-velocity surface states reported by ARPES by simulating their observed spectral function as an equal-weight average over the two band-shifted domains that we image by STM. Our results highlight the necessity of local measurements to address inhomogeneously terminated surfaces or fabrication techniques to achieve uniform termination for meaningful large-area surface measurements of polar crystals such as SmB6.
A point charge near the surface of a topological insulator (TI) with broken time-reversal symmetry is predicted to generate an image magnetic charge in addition to an image electric charge. We use scanning tunneling spectroscopy to study the image potential states (IPSs) of the topological semimetal Sb(111) surface. We observe five IPSs with discrete energy levels that are well described by a one-dimensional model. The spatial variation of the IPS energies and lifetimes near surface step edges shows the first local signature of resonant interband scattering between IPSs, which suggests that image charges too may interact. Our work motivates the exploration of the TI surface geometry necessary to realize and manipulate a magnetic charge.
The interplay between strong electron interactions and band topology is a new frontier in the search for exotic quantum phases. The Kondo insulator SmB6 has emerged as a promising platform because its correlation-driven bulk gap is predicted to host topological surface modes entangled with f electrons, spawning heavy Dirac fermions1,2,3,4. Unlike the conventional surface states of non-interacting topological insulators, heavy Dirac fermions are expected to harbour spontaneously generated quantum anomalous Hall states5, non-Abelian quantum statistics6,7, fractionalization8 and topological order6,7,8. However, the small energy scales required to probe heavy Dirac fermions have complicated their experimental realization. Here we use high-energy-resolution spectroscopic imaging in real and momentum space on SmB6. On cooling below 35 K, we observe the opening of an insulating gap that expands to 14 meV at 2 K. Within the gap, we image the formation of linearly dispersing surface states with effective masses reaching 410 ± 20 me (where me is the mass of the electron). Our results demonstrate the presence of correlation-driven heavy surface states in SmB6, in agreement with theoretical predictions1,2,3,4. Their high effective mass translates to a large density of states near zero energy, which magnifies their susceptibility to the anticipated novel orders and their potential utility.
Scanning tunneling microscopy/spectroscopy (STM/S) is a powerful experimental tool to understand the electronic structure of materials at the atomic scale, with energy resolution down to the microelectronvolt range. Such resolution requires a low-vibration laboratory, low-noise electronics, and a cryogenic environment. Here, we present a thorough enumeration and analysis of various noise sources and their contributions to the noise floor of STM/S measurements. We provide a comprehensive recipe and an interactive python notebook to input and evaluate noise data, and to formulate a custom step-by-step approach for optimizing the signal-to-noise ratio in STM/S measurements.
In cuprates, the strong correlations in proximity to the antiferromagnetic Mott insulating state give rise to an array of unconventional phenomena beyond high temperature superconductivity. Developing a complete description of the ground state evolution is crucial to decoding the complex phase diagram. Here we use the structure of broken translational symmetry, namely d-form factor charge modulations in (Bi,Pb)2(Sr,La)2CuO6+δ, as a probe of the ground state reorganization that occurs at the transition from truncated Fermi arcs to a large Fermi surface. We use real space imaging of nanoscale electronic inhomogeneity as a tool to access a range of dopings within each sample, and we definitively validate the spectral gap Δ as a proxy for local hole doping. From the Δ-dependence of the charge modulation wavevector, we discover a commensurate to incommensurate transition that is coincident with the Fermi surface transition from arcs to large hole pocket, demonstrating the qualitatively distinct nature of the electronic correlations governing the two sides of this quantum phase transition. Furthermore, the doping dependence of the incommensurate wavevector on the overdoped side is at odds with a simple Fermi surface driven instability.
We present a new method for nanoscale thermal imaging of insulating thin films using atomic force microscopy (AFM). By sweeping the voltage applied to a conducting AFM tip in contact mode, we measure the local current through a VO2 film. We fit the resultant current-voltage curves to a Poole-Frenkel conduction model to extract the local temperature of the film using fundamental constants and known film properties. As the local voltage is further increased, the nanoscale region of VO2 undergoes an insulator-to-metal transition. Immediately preceding the transition, we find the average electric field to be 32 MV/m, and the average local temperature to be at least 335 K, close to the bulk transition temperature of 341 K, indicating that Joule heating contributes to the transition. Our thermometry technique enables local temperature measurement of any film dominated by the Poole-Frenkel conduction mechanism, and provides the opportunity to extend our technique to materials that display other conduction mechanisms.
We propose a scheme for the use of magnetic force microscopy to manipulate Majorana zero modes emergent in vortex cores of topological superconductors in the Fe(Se,Te) family. We calculate the pinning forces necessary to drag two vortices together and the resulting change in current and charge density of the composite fermion. A possible algorithm for measuring and altering Majorana pair parity is demonstrated.
Topological metamaterials have robust properties engineered from their macroscopic arrangement, rather than their microscopic constituency. They are promising candidates for creating next-generation technologies due to their protected dissipationless boundary modes. They can be designed by starting from Dirac metamaterials with either symmetry-enforced or accidental degeneracy. The latter case provides greater flexibility in the design of topological switches, waveguides, and cloaking devices, because a large number of tuning parameters can be used to break the degeneracy and induce a topological phase. However, the design of a topological logic element--a switch that can be controlled by the output of a separate switch--remains elusive. Here we numerically demonstrate a topological logic gate for ultrasound by exploiting the large phase space of accidental degeneracies in a honeycomb lattice. We find that a degeneracy can be broken by six physical parameters, and we show how to tune these parameters to create a phononic switch between a topological waveguide and a trivial insulator that can be triggered by ultrasonic heating. Our design scheme is directly applicable to photonic crystals and may guide the design of future electronic topological transistors.
The long-sought Majorana fermion is expected to manifest in a topological-superconductor heterostructure as a zero bias conductance peak (ZBCP). As one promising platform for such heterostructures, we investigate the cleaved surface of the topological semimetal Sb(111) using scanning tunneling microscopy and spectroscopy. Remarkably, we find a robust ZBCP on some terraces of the cleaved surface, although no superconductor is present. Using quasiparticle interference imaging, Landau level spectroscopy and density functional theory, we show that the ZBCP originates from a van Hove singularity pushed up to the Fermi level by a sub-surface stacking fault. Amidst the sprint to stake claims on new Majorana fermion systems, our finding highlights the importance of using a local probe together with detailed modeling to check thoroughly for crystal imperfections that may give rise to a trivial ZBCP unrelated to Majorana physics.
The pseudogap (PG) state and its related intra-unit-cell symmetry breaking remain the focus in the research of cuprate superconductors. Although the nematicity has been studied in Bi2Sr2CaCu2O8+δ, especially underdoped samples, its behavior in other cuprates and different doping regions is still unclear. Here we apply a scanning tunneling microscope to explore an overdoped (Bi, Pb)2Sr2CuO6+δ with a large Fermi surface (FS). The establishment of a nematic order and its real-space distribution is visualized as the energy scale approaches the PG.
Epitaxial engineering of solid state heterointerfaces is a leading avenue to realizing enhanced or novel electronic states of matter. As a recent example, bulk FeSe is an unconventional superconductor with a modest transition temperature (Tc) of 9 K. However, when a single atomic layer of FeSe is grown on SrTiO3, its Tc can skyrocket by an order of magnitude to 65 K or 109 K. Since this discovery in 2012, efforts to reproduce, understand, and extend these findings continue to draw both excitement and scrutiny. In this review, we first present a critical survey of experimental measurements performed using a wide range of techniques. We then turn to the open question of microscopic mechanisms of superconductivity. We examine contrasting indications for both phononic (conventional) and magnetic/orbital (unconventional) means of electron pairing, as well as speculations about whether they could work cooperatively to boost Tc in a monolayer of FeSe.
We report a detailed three-step roadmap for the fabrication and characterization of bulk Cr tips for spin-polarized scanning tunneling microscopy. Our strategy uniquely circumvents the need for ultra-high vacuum preparation of clean surfaces or films. First, we demonstrate the role of ex situ electrochemical etch parameters on Cr tip apex geometry, using scanning electron micrographs of over 70 etched tips. Second, we describe the suitability of the in situ cleaved surface of the layered antiferromagnet La1.4Sr1.6Mn2O7 to evaluate the spin characteristics of the Cr tip, replacing the ultra-high vacuum-prepared test samples that have been used in prior studies. Third, we outline a statistical algorithm that can effectively delineate closely spaced or irregular cleaved step edges, to maximize the accuracy of step height and spin-polarization measurements.
Helium ion beams (HIB) focused to subnanometer scales have emerged as powerful tools for high-resolution imaging as well as nanoscale lithography, ion milling, or deposition. Quantifying irradiation effects is an essential step toward reliable device fabrication, but most of the depth profiling information is provided by computer simulations rather than the experiment. Here, we demonstrate the use of atomic force microscopy (AFM) combined with scanning near-field optical microscopy (SNOM) to provide three-dimensional (3D) dielectric characterization of high-temperature superconductor devices fabricated by HIB. By imaging the infrared dielectric response obtained from light demodulation at multiple harmonics of the AFM tapping frequency, we find that amorphization caused by the nominally 0.5 nm HIB extends throughout the entire 26.5 nm thickness of the cuprate film and by ∼500 nm laterally. This unexpectedly widespread damage in morphology and electronic structure can be attributed to a helium depth distribution substantially modified by the internal device interfaces. Our study introduces AFM-SNOM as a quantitative tomographic technique for noninvasive 3D characterization of irradiation damage in a wide variety of nanoscale devices.
Measurement instruments and fabrication tools with spatial resolution on the atomic scale require facilities that mitigate the impact of vibration sources in the environment. One approach to protection from vibration in a building's foundation is to place the instrument on a massive inertia block, supported on pneumatic isolators. This opens the questions of whether or not a massive floating block is susceptible to acoustic forces, and how to mitigate the effects of any such acoustic buffeting. Here this is investigated with quantitative measurements of vibrations and sound pressure, together with finite element modeling. It is shown that a particular concern, even in a facility with multiple acoustic enclosures, is the excitation of the lowest fundamental acoustic modes of the room by infrasound in the low tens of Hz range, and the efficient coupling of the fundamental room modes to a large inertia block centered in the room.
We use scanning tunneling microscopy (STM) and quasiparticle interference (QPI) imaging to investigate the low-energy orbital texture of single-layer FeSe/SrTiO3. We develop a T-matrix model of multiorbital QPI to disentangle scattering intensities from Fe 3dxz and 3dyz bands, enabling the use of STM as a nanoscale detection tool of nematicity. By sampling multiple spatial regions of a single-layer FeSe/SrTiO3 film, we quantitatively exclude static xz/yz orbital ordering with domain size larger than $δ$r2=20nm×20nm, xz/yz Fermi wave vector difference larger than $δ$k=0.014$π$, and energy splitting larger than $δ$E=3.5meV. The lack of detectable ordering pinned around defects places qualitative constraints on models of fluctuating nematicity.
The properties of iron-based superconductors (Fe-SCs) can be varied dramatically with the introduction of dopants and atomic defects. As a pressing example, FeSe, parent phase of the highest-Tc Fe-SC, exhibits prevalent defects with atomic-scale “dumbbell” signatures as imaged by scanning tunneling microscopy (STM). These defects spoil superconductivity when their concentration exceeds 2.5%. Resolving their chemical identity is a prerequisite to applications such as nanoscale patterning of superconducting/nonsuperconducting regions in FeSe as well as fundamental questions such as the mechanism of superconductivity and the path by which the defects destroy it. We use STM and density functional theory to characterize and identify the dumbbell defects. In contrast to previous speculations about Se adsorbates or substitutions, we find that an Fe-site vacancy is the most energetically favorable defect in Se-rich conditions and reproduces our observed STM signature. Our calculations shed light more generally on the nature of Se capping, the removal of Fe vacancies via annealing, and their ordering into a √5 × √5 superstructure in FeSe and related alkali-doped compounds.
Topological materials host protected surface states with locked spin and momentum degrees of freedom. The helical Dirac character of the surface states, of tremendous scientific interest, stems from the interplay of the bulk band structure and surface Rashba spin-orbit interaction. The semimetal Sb offers a pristine platform to examine the Rashba origins of the Dirac-like topological surface states. Here we present an overview of our momentum-resolved scanning tunneling spectroscopy studies of Sb, over an extended (300 meV) energy range, revealing several features characteristic of the emergence of the Dirac-like surface states from a conventional Rashba-type parabolic dispersion. Our work provides a conceptual framework to create and investigate tunable Rashba states with topological properties.