Since the discovery of high-temperature superconductivity in nickelate superconductors, it is an open question how closely the superconducting state resembles that of cuprate superconductors. One salient feature of the phase diagram of the high-temperature cuprate superconductors is stripe order. Despite their prevalence, real-space imaging has been limited to the charge sector. Here we use spin-polarised scanning tunnelling microscopy to visualize the local magnetic and charge distribution emerging due to a stripe order in the trilayer nickelate La_4Ni_3O_10. The stripe order exhibits a four unit cell periodicity, closely resembling that seen in cuprates, and opens a near-complete ∼66meV gap at the Fermi level. Crucially, discrete phase slips can be triggered by tunneling electrons above a ∼ 20meV threshold, allowing imaging of stripe dynamics at the atomic scale. These results highlight the importance of correlation physics driving stripe-like orders in lanthanum nickelates with striking similarities to the cuprates.

In cuprate superconductors, electron-electron repulsion results in characteristic spectroscopic features known as `waterfalls', where the sharp quasiparticle dispersion transitions into broad Hubbard bands. However, in multi-orbital systems, the additional Hund coupling results in behavior that defies the conventional Mott–Hubbard paradigm, creating qualitatively distinct `superdispersive' features in the spectral function. Here, we use tunneling spectroscopy to reveal this signature of Hund physics in Sr_2RuO_4. By combining density functional theory, dynamical mean-field theory, and continuum local density of states calculations, we show that the experimental features are in excellent agreement with theoretical predictions and intimately linked to the non-monotonous energy dependence of the real part of the self-energy in a Hund metal. Our results provide direct experimental evidence for Hund-induced spectroscopic features and open a new route to probing correlation effects in quantum materials.

The properties of strongly correlated electron materials exhibit a surprising sensitivity to small lattice distortions, providing an opportunity for their tuning by selective distortion driving, usually achieved by optical excitations. Using inelastic electron tunneling in scanning tunneling microscopy, we demonstrate that at the surface of a strongly correlated electron material, we can drive vibrational excitations out of equilibrium, by studying the dynamics of localized modes on the Pd-terminated surface of the delafossite oxide PdCrO2. This surface forms a tiling of hydrogen clusters of varying sizes and shapes upon hydrogen adsorption. Our findings reveal that vibrational excitations in the clusters exhibit longer lifetimes than on typical metal surfaces. Detailed analysis of the spectroscopy data reveals signatures of non-equilibrium effects in the excitations which we attribute to the extended lifetimes of these modes. Theoretical calculations support that the long-lived nature of the excitations is related to the unique properties of the substrate.

We investigate the electronic structure at the surface of the correlated oxide Ca_3Ru_2O_7, a low-symmetry ruthenate oxide which hosts an unconventional polar-metal phase. From a combination of angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy measurements, we demonstrate that the surface hosts an insulating phase, a distinct departure from metallicity within the bulk. Utilizing quantitative low-energy electron diffraction in conjunction with electronic structure calculations, we show how this results from a combined surface structure relaxation and the impact of marked electronic correlations in this system. Our findings highlight the proximity of Ca_3Ru_2O_7 to an insulating metallic state, and illustrate how subtle structural distortions can control its emergent electronic phases.

The emergence of loop current phases, where spontaneous loops of orbital currents give rise to a weak local magnetic moments, has been proposed to exist in a number of quantum materials based on measurements that pick up weak signatures of time reversal symmetry breaking or small magnetic moment order. The most prominent example is as an explanation of the pseudogap phase on the underdoped side of the phase diagram of the high-temperature cuprate superconductors, but more recently, it has been proposed to occur in Kagome materials and at the surface layer of Sr_2RuO_4. Experimental results have, however, been inconclusive so far, some detecting signatures that can be understood as emerging due to loop current phases, whilst others have not detected any significant proof. One of the techniques that should be able to pick up local signatures of loop current orders is low temperature scanning tunneling microscopy and spectroscopy (STM/STS), however firm predictions of how to detect them are missing. Here, we provide specific predictions for how loop current orders in a square lattice can be seen in spectroscopic maps, using models of the cuprate high-temperature superconductors and of the surface layer of Sr_2RuO_4. We find that, besides lifting degeneracies at the specific ordering vector of the loop current order, a finite spin polarisation emerges when spin-orbit coupling is present, signatures of which can be detected in spin-polarised STM.

Quasiparticle interference (QPI) is a powerful tool to characterize the symmetry of the superconducting order parameter in unconventional superconductors, by mapping the spatial dependence of elastic tunneling of electrons between the tip of a scanning tunneling microscope and a sample. Here, we consider the influence of inelastic tunneling on quasi-particle interference, exemplarily for the iron-based superconductor LiFeAs. We clearly observe replica features in both experimental QPI maps and the dispersion extracted from QPI, which from comparison with theoretical model calculations can be attributed to inelastic tunneling. Analysis of the QPI dispersion shows that the inelastic mode that gives rise to these replica features exhibits a resonance between 8 and 10 meV. Comparison of the energy scale of the resonance energy estimated from QPI with inelastic neutron scattering indicates that the replica features arise from interaction with spin fluctuations.

To understand the properties of quantum materials a detailed knowledge of the material's low energy electronic structure is key. Details of the electronic structure drive the ground state through electronic instabilities, electronic correlation effects, new electronic orders or just the absence of electronic states near the Fermi energy - making a realistic and detailed understanding crucial to be able to control and design properties of quantum materials. The past 25 years have seen a significant improvement in experimental techniques to observe the true electronic structure, in particular in techniques such as Angle resolved photoemission spectroscopy (ARPES) where energy resolutions of 2meV are routinely achievable now, which however is limited to zero magnetic field and only provides information about the occupied states. Scanning tunneling microscopy (STM) achieves a significantly better energy resolution <100μeV and can operate at temperatures well below 50mK and in magnetic fields. While per se a real-space technique, by imaging quasiparticle interference (QPI) STM can also provide information about the electronic structure. This technique has been used over the past decades to study a wide range of quantum materials to understand correlated electron behaviour. Recent theoretical progress now enables routine modelling of QPI, a key requirement to interpret the complex data. Here, we review the principles of QPI, its origin, experimental detection, and the physical insight gained from the study of QPI and possible future directions for this technique.

Quasiparticle interference imaging (QPI) provides a route to characterize electronic structure from real space images acquired using scanning tunneling microscopy. It emerges due to scattering of electrons at defects in the material. The QPI patterns encode details of the k k -space electronic structure and its spin and orbital texture. Recovering this information from a measurement of QPI is non-trivial, requiring modelling not only of the dominant scattering vectors, but also the overlap of the wave functions with the tip of the microscope. While, in principle, it is possible to model QPI from density functional theory (DFT) calculations, for many quantum materials it is more desirable to model the QPI from a tight-binding model, where inaccuracies of the DFT calculation can be corrected. Here, we introduce an efficient code to simulate quasiparticle interference from tight-binding models using the continuum Green’s function method.

Chromium ditelluride, CrTe2, is an attractive candidate van der Waals material for hosting 2D magnetism. However, how the room-temperature ferromagnetism of the bulk evolves as the sample is thinned to the single-layer limit has proved controversial. This, in part, reflects its metastable nature, vs. a series of more stable self-intercalation compounds with higher relative Cr:Te stoichiometry. Here, exploiting a recently developed method for enhancing nucleation in molecular-beam epitaxy growth of transition-metal chalcogenides, we demonstrate the selective stabilisation of high-coverage CrTe2 and Cr2+εTe3 epitaxial monolayers. Combining X-ray magnetic circular dichroism, scanning tunnelling microscopy, and temperature-dependent angle-resolved photoemission, we demonstrate that both compounds order magnetically with a similar TC. We find, however, that monolayer CrTe2 forms as an antiferromagnetic metal, while monolayer Cr2+εTe3 hosts an intrinsic ferromagnetic semiconducting state. This work thus demonstrates that control over the self-intercalation of metastable Cr-based chalcogenides provides a powerful route for tuning both their metallicity and magnetic structure, establishing the CrxTey system as a flexible materials class for future 2D spintronics.

Superconductivity, a state in which electrical currents can flow without resistance, occurs because of pairing of electrons into quasiparticles with integer spin S. In practically all known superconducting materials, these pairs form a singlet with S=0. Finding a material that has triplet pairing, S=1, would have profound fundamental and technological implications. UPt_3 has been a key candidate material for spin-triplet superconductivity. Because of a lack of direct evidence for the pairing symmetry, the nature of the superconducting pairing remains under debate. Here, we use ultra-low temperature scanning tunneling microscopy to resolve this question. Our data reveals a zero-bias Andreev bound state within the gap for a surface normal to the c-axis of UPt_3. The superconducting origin of the features is confirmed through vortex imaging. For triplet pairing, such an Andreev state is fragile against Rashba spin-splitting, whereas for singlet pairing it remains robust, classifying UPt_3 as a spin-singlet superconductor with a chiral order parameter.

Moir & eacute; lattices are a general feature of bilayer structures, where an additional periodic superstructure is generated by either lattice mismatch or from a twist angle. They have been shown to stabilize exotic ground states, including unconventional superconductivity and Mott insulating phases, attributed to strong electron correlations. However, controlling these interactions requires a detailed understanding of the low-energy electronic structure, which is lacking so far. Probing the electronic structure is challenging due to sample inhomogeneity, the low characteristic energy scales involved, and small sample sizes. Through quasiparticle interference (QPI) imaging, scanning tunneling microscopy (STM) can overcome many of these challenges but requires detailed modeling to extract the k-space electronic structure. Here, we present realistic calculations of QPI in twisted bilayer structures, which accounts for the effect of the long-range moir & eacute; lattice on the electronic structure as well as its interaction at a defect. These calculations reveal that, while the moir & eacute; supercell significantly reduces the size of the Brillouin zone, the QPI scattering vectors retain characteristics of the individual monolayers with distinct perturbations from the twisted geometry that can be directly linked back to the electronic structure. The procedure introduced here provides a general framework to use QPI to determine the low-energy electronic structure in moir & eacute; lattice systems.

Knowledge of the electronic structure of quantum materials in the vicinity of the Fermi energy is key to understanding and tuning their properties and to making them useful for applications. While for bulk materials in single crystal form, spatially averaging techniques, such as angular resolved photoemission, now routinely reach sufficient energy and momentum resolution to achieve this, for thin film samples, intrinsic structural variation and inhomogeneity make it more challenging to gain a full understanding from spatially integrating techniques. Quasiparticle interference (QPI) provides a route to obtaining information about the electronic structure on a sub-millielectronvolt energy scale, with an energy resolution primarily limited by temperature. Efficient acquisition of QPI maps requires long hold times and low temperatures, ideally below 4 K in an ultra-high vacuum environment. Here, we introduce a 1 K-pot design that achieves efficient cooling with continuous feeding while not adding to the noise level and demonstrate its performance in scanning tunneling microscopy measurements.

The chemical and electronic properties of surfaces and interfaces are important for many technologically relevant processes, be it in information processing, where interfacial electronic properties are crucial for device performance, or in catalytic processes, which depend on the types and densities of active nucleation sites for chemical reactions. Quasi-periodic and nonperiodic crystalline surfaces offer new opportunities because of their inherent inhomogeneity, resulting in localisation and properties vastly different from those of surfaces described by conventional Bravais lattices. Here, we demonstrate the formation of a nonperiodic tiling structure on the surface of the frustrated antiferromagnet PdCrO2 due to hydrogen adsorption. The tiling structure exhibits no long-range periodicity but comprises few-atom hexagonally packed domains covering large terraces. Measurement of the local density of states by tunnelling spectroscopy reveals adsorption-driven modifications to the quasi-2D electronic structure of the surface layer, showing exciting opportunities arising from electron localisation.

The interaction between the electronic and structural degrees of freedom is central to several intriguing phenomena observed in condensed-matter physics. In magnetic materials, magnetic interactions couple to lattice degrees of freedom, resulting in magnetoelastic coupling, which is typically small and only detectable in macroscopic samples. Here we demonstrate a giant magnetoelastic coupling in the correlated itinerant ferromagnet Sr_4Ru_3O_10. We establish an effective control of magnetism in the surface layer and utilize it to probe the impact of magnetism on its electronic and structural properties. By using scanning tunnelling microscopy, we reveal subtle changes in the electronic structure dependent on ferromagnetic or antiferromagnetic alignment between the surface and subsurface layers. We further determine the consequences of the exchange force on the relaxation of the surface layer, which exhibits giant magnetostriction. Our results provide a direct measurement of the impact of exchange interactions and correlations on structural details in a quantum material, revealing how electronic correlations result in a strong electron-lattice coupling.

The interplay of electronic and structural degrees of freedom is at the heart of some of the most astonishing phenomena found in condensed matter physics, for example, the condensation of electron pairs into a macroscopically coherent ground state in superconductors. In magnetic materials, magnetic interactions couple to lattice degrees of freedom resulting in magnetoelastic coupling - an effect that is typically small and only detectable on macroscopic samples. Here, we demonstrate giant magnetoelastic coupling in the correlated itinerant ferromagnet Sr$_4$Ru$_3$O$_{10}$. We establish control of the magnetism in the surface layer and use this control to probe the impact of the magnetism on its electronic and structural properties. By using scanning tunneling microscopy (STM), we reveal subtle changes in the electronic structure dependent on ferromagnetic or antiferromagnetic alignment between the surface and subsurface layers. We determine the consequences of the exchange force on the relaxation of the surface layer, exhibiting a giant magnetostriction. Our results provide a direct measurement of the impact of exchange interactions and correlations on structural details in a quantum material, reveal how electronic correlations result in strong electron-lattice coupling and establish Sr$_4$Ru$_3$O$_{10}$ as a system to study magnetism in 2D.

Magnetic van der Waals materials are an important building block to realize spintronic functionalities in heterostructures of two-dimensional (2D) materials. However, establishing their magnetic and electronic properties and the interrelationship between the magnetic ground state and electronic structure is often challenging because only a limited number of techniques can probe magnetism and electronic structure on length scales of tens to hundreds of nanometers. Chromium chalcogenides are a class of 2D magnetic materials for which a rich interplay between structure and magnetism has been predicted. Here, we combine angle-resolved photoemission and quasiparticle interference imaging to establish the electronic structure of a monolayer of CrTe 2 on graphite. From a comparison of model calculations with spectroscopic mapping using angle-resolved photoemission spectroscopy and scanning tunneling microscopy we establish the magnetic ground state and the low-energy electronic structure. We demonstrate that the band structure of monolayer CrTe 2 is captured well by density functional theory (DFT) in a DFT + U framework when a Coulomb repulsion of U = 2.5 eV is accounted for.

Magnetic van der Waals materials are an important building block to realize spintronic functionalities in heterostructures of two-dimensional (2D) materials. Yet, establishing their magnetic and electronic properties and the interrelationship between the magnetic ground state and electronic structure is often challenging because only a limited number of techniques can probe magnetism and electronic structure on length scales of tens to hundreds of nanometers. Chromium chalcogenides are a class of 2D magnetic materials for which a rich interplay between structure and magnetism has been predicted. Here, we combine angle-resolved photoemission and quasi-particle interference imaging to establish the electronic structure of a monolayer of CrTe_2 on graphite. From a comparison of model calculations with spectroscopic mapping using angle-resolved photoemission spectroscopy and scanning tunnelling microscopy we establish the magnetic ground state and the low energy electronic structure. We demonstrate that the band structure of monolayer CrTe_2 is captured well by density functional theory (DFT) in a DFT+U framework when a Coulomb repulsion of U=2.5eV is accounted for.

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 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 mechanism for driving a field-induced Lifshitz transition in ferromagnetic metals.

Chromium ditelluride, CrTe_2, is an attractive candidate van der Waals material for hosting 2D magnetism. However, how the room-temperature ferromagnetism of the bulk evolves as the sample is thinned to the single-layer limit has proved controversial. This, in part, reflects its metastable nature, vs. a series of more stable self-intercalation compounds with higher relative Cr:Te stoichiometry. Here, exploiting a recently-developed method for enhancing nucleation in molecular beam epitaxy growth of transition-metal chalcogenides, we demonstrate the selective stabilisation of high-coverage CrTe_2 and Cr_2+εTe_3 epitaxial monolayers. Combining X-ray magnetic circular dichroism, scanning tunnelling microscopy, and temperature-dependent angle-resolved photoemission, we demonstrate that both compounds order magnetically with a similar Tc. We find, however, that monolayer CrTe_2 forms as an anti-ferromagnetic metal, while monolayer Cr_2+εTe_3 hosts an intrinsic ferromagnetic semiconducting state. This work thus demonstrates that control over the self-intercalation of metastable Cr-based chalcogenides provides a powerful route for tuning both their metallicity and magnetic structure, establishing the Cr-Te system as a flexible materials class for future 2D spintronics.

The bilayer perovskite La3Ni2O7 has recently been found to enter a superconducting state under hydrostatic pressure at temperatures as high as 80 K. The onset of superconductivity is observed concurrent with a structural transition which suggests that superconductivity is inherently related to this specific structure. Here we perform density functional theory based structural relaxation calculations and identify several promising routes to stabilize the crystal structure which hosts the superconducting state at ambient pressure. We find that the structural transition is controlled almost entirely by a reduction of the b -axis lattice constant, which suggests that uniaxial compression along the [010] direction or in -plane biaxial compression are sufficient as tuning parameters to control this transition. Furthermore, we show that increasing the size of the A -site cations can also induce the structural transitions via chemical pressure and identify Ac3Ni2O7 and Ba-doped La3Ni2O7 as potential candidates for a high temperature superconducting nickelate at ambient pressure.