arXiv subjects

Luke C. Rhodes

Publications and source records attributed to Luke C. Rhodes.

At least 19 recordsLinked to original sources

arXiv2026

Engineering correlated phases through manipulation of Van Hove singularities

Controlling the ordered phases of correlated electron systems remains a central challenge in quantum materials design. Divergences in the electronic density of states, known as Van Hove singularities (VHSs), are one obvious route to such control. It is clear from recent work that the exact functional form of these divergences can profoundly affect which phases are realized; a full picture, however, remains elusive. In this work, we use both the hot-spot parquet renormalization group and the truncated-unity functional renormalization group to theoretically study the emergent correlated states of a two-dimensional square-lattice Hubbard model with VHSs at or near the Fermi level. By varying a single hopping parameter, $t_3$, we are able to change the strength of the VHS divergence in the density of states from logarithmic (for $t_3 < t_{3c}$) to power-law (for $t_3 = t_{3c}$). Further increase of $t_3$ ($t_3 > t_{3c}$) causes each original Van Hove point to split into two, both of the conventional logarithmic type. We show that which of these regimes we are in strongly influences the predicted ordered states. We also study the dependence on doping, and find that the ferromagnetic state that occurs at Van Hove filling in these models is unstable to very small shifts in the Fermi level, often giving way to distinct ordered states depending on whether the model is electron- or hole-doped. These results highlight the importance of tuning VHS properties to control ordered states in correlated materials, and offer design rules to engineer these phases in novel systems.

cond-mat.str-el↗

arXiv2026

Quasiparticle interference as a tool to study quantum materials

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 <100$μ$eV 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.

cond-mat.str-el↗

arXiv2026

How to measure loop currents in scanning tunneling microscopy

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$_2$RuO$_4$. 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$_2$RuO$_4$. 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.

cond-mat.str-el↗

arXiv2026

Revealing Hund superdispersion with tunneling spectroscopy

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$_2$RuO$_4$. 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.

cond-mat.str-el↗

arXiv2025

Determining the superconducting order parameter of UPt$_3$ using scanning tunneling microscopy

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.

cond-mat.supr-con↗

arXiv2025

calcQPI: A versatile tool to simulate quasiparticle interference

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 $k$-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.

cond-mat.str-el↗

arXiv2025

Emergent exchange-driven giant magnetoelastic coupling in a correlated itinerant ferromagnet

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$_4$Ru$_3$O$_{10}$. 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.

cond-mat.str-el↗

arXiv2025

Electronic structure of monolayer-CrTe$_2$: an antiferromagnetic 2D van der Waals material

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 $U=2.5\mathrm{eV}$ is accounted for.

cond-mat.mtrl-sci↗

arXiv2025

Probing moiré electronic structures through quasiparticle interference

Moiré 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 stabilise new 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 tunnelling microscopy (STM) can overcome many of these challenges but requires detailed modelling 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 moiré lattice on the electronic structure as well as it's interaction at a defect. These calculations reveal that while the moiré 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 moiré lattice systems.

cond-mat.str-el↗

arXiv2025

On the engineering of higher-order Van Hove singularities in two dimensions

The properties of correlated electron materials are often intricately linked to Van Hove singularities (VHS) in the vicinity of the Fermi energy. The class of these VHS is of great importance, with higher-order ones -- with power-law divergence in the density of states -- leaving frequently distinct signatures in physical properties. We use a new theoretical method to detect and analyse higher-order VHS (HOVHS) in two-dimensional materials and apply it to the electronic structure of the surface layer of Sr$_2$RuO$_4$. We then constrain a low energy model of the VHS of the surface layer of Sr$_2$RuO$_4$ against angle-resolved photoemission spectroscopy and quasiparticle interference data to analyse the VHS near the Fermi level. We show how these VHS can be engineered into HOVHS.

cond-mat.str-el↗

arXiv2024

Magic angle of Sr$_2$RuO$_4$: Optimizing correlation-driven superconductivity

Understanding of unconventional superconductivity is crucial for engineering materials with specific order parameters or elevated superconducting transition temperatures. However, for many materials, the pairing mechanism and symmetry of the order parameter remain unclear: reliable and efficient methods of predicting the order parameter and its response to tuning parameters are lacking. Here, we investigate the response of superconductivity in Sr$_2$RuO$_4$ to structural distortions via the random phase approximation (RPA) and functional renormalization group (FRG), starting from realistic models of the electronic structure. Our results suggest that RPA misses the interplay of competing fluctuation channels. FRG reproduces key experimental findings. We predict a magic octahedral rotation angle, maximizing the superconducting $T_c$ and a dominant $d_{x^2-y^2}$ pairing symmetry. To enable experimental verification, we provide calculations of the phase-referenced Bogoliubov Quasiparticle Interference imaging. Our work demonstrates a designer approach to tuning unconventional superconductivity with relevance and applicability for a wide range of quantum materials.

cond-mat.supr-con↗

arXiv2024

Structural routes to stabilise superconducting La$_3$Ni$_2$O$_7$ at ambient pressure

The bilayer perovskite La$_3$Ni$_2$O$_7$ 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 Ac$_3$Ni$_2$O$_7$ and Ba-doped La$_3$Ni$_2$O$_7$ as potential candidates for a high temperature superconducting nickelate at ambient pressure.

cond-mat.supr-con↗

arXiv2024

Spin-orbit coupling induced Van Hove singularity in proximity to a Lifshitz transition in Sr$_4$Ru$_3$O$_{10}$

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 new 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 Sr$_4$Ru$_3$O$_{10}$, 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 new mechanism for driving a field-induced Lifshitz transition in ferromagnetic metals.

cond-mat.str-el↗

arXiv2023

Compass-like manipulation of electronic nematicity in Sr$_3$Ru$_2$O$_7$

Electronic nematicity has been found in a wide range of strongly correlated electron materials, resulting in the electronic states having a symmetry that is lower than that of the crystal that hosts them. One of the most astonishing examples is Sr$_3$Ru$_2$O$_7$, in which a small in-plane component of a magnetic field induces significant resistivity anisotropy. The direction of this anisotropy follows the direction of the in-plane field. The microscopic origin of this field-induced nematicity has been a long-standing puzzle, with recent experiments suggesting a field-induced spin density wave driving the anisotropy. Here, we report spectroscopic imaging of a field-controlled anisotropy of the electronic structure at the surface of Sr$_3$Ru$_2$O$_7$. We track the electronic structure as a function of the direction of the field, revealing a continuous change with the angle. This continuous evolution suggests a mechanism based on spin-orbit coupling resulting in compass-like control of the electronic bands. The anisotropy of the electronic structure persists to temperatures about an order of magnitude higher compared to the bulk, demonstrating novel routes to stabilize such phases over a wider temperature range.

cond-mat.str-el↗

arXiv2023

Magnetic-Field Tunable Intertwined Checkerboard Charge Order and Nematicity in the Surface Layer of Sr$_2$RuO$_4$

In strongly correlated electron materials, the electronic, spin, and charge degrees of freedom are closely intertwined. This often leads to the stabilization of emergent orders that are highly sensitive to external physical stimuli promising opportunities for technological applications. In perovskite ruthenates, this sensitivity manifests in dramatic changes of the physical properties with subtle structural details of the RuO$_6$ octahedra, stabilizing enigmatic correlated ground states, from a hotly debated superconducting state via electronic nematicity and metamagnetic quantum criticality to ferromagnetism. Here, it is demonstrated that the rotation of the RuO$_6$ octahedra in the surface layer of Sr$_2$RuO$_4$ generates new emergent orders not observed in the bulk material. Through atomic-scale spectroscopic characterization of the low-energy electronic states, four van Hove singularities are identified in the vicinity of the Fermi energy. The singularities can be directly linked to intertwined nematic and checkerboard charge order. Tuning of one of these van Hove singularities by magnetic field is demonstrated, suggesting that the surface layer undergoes a Lifshitz transition at a magnetic field of ~32T. The results establish the surface layer of Sr$_2$RuO$_4$ as an exciting 2D correlated electron system and highlight the opportunities for engineering the low-energy electronic states in these systems.

cond-mat.str-el↗

arXiv2022

Atomic-scale imaging of emergent order at a magnetic-field-induced Lifshitz transition

The phenomenology and radical changes seen in materials properties traversing a quantum phase transition has captivated condensed matter research over past decades. Strong electronic correlations lead to novel electronic ground states, including magnetic order, nematicity and unconventional superconductivity. Providing a microscopic model for these requires detailed knowledge of the electronic structure in the vicinity of the Fermi energy, promising a complete understanding of the physics of the quantum critical point. Here, we demonstrate such a measurement at the surface of Sr$_3$Ru$_2$O$_7$. Our results show that, even in zero field, the electronic structure is strongly $C_2$ symmetric and that a magnetic-field drives both a Lifshitz transition and induces a charge-stripe order. We track the changes of the electronic structure as a function of field via quasi-particle interference imaging at ultralow temperatures. Our results provide a complete microscopic picture of the field-induced changes of the electronic structure across the Lifshitz transition.

cond-mat.str-el↗

arXiv2022

Strong surface termination dependence of the electronic structure of polar superconductor LaFeAsO revealed by nano-ARPES

The electronic structures of the iron-based superconductors have been intensively studied by using angleresolved photoemission spectroscopy (ARPES). A considerable amount of research has been focused on the LaFeAsO family, showing the highest transition temperatures, where previous ARPES studies have found much larger Fermi surfaces than bulk theoretical calculations would predict. The discrepancy has been attributed to the presence of termination-dependent surface states. Here, using photoemission spectroscopy with a sub-micron focused beam spot (nano-ARPES) we have successfully measured the electronic structures of both the LaO and FeAs terminations in LaFeAsO. Our data reveal very different band dispersions and core-level spectra for different surface terminations, showing that previous macro-focus ARPES measurements were incomplete. Our results give direct evidence for the surface-driven electronic structure reconstruction in LaFeAsO, including formation of the termination-dependent surface states at the Fermi level. This new experimental technique, which we have shown to be very powerful when applied to this prototypical compound, can now be used to study various materials with different surface terminations.

cond-mat.supr-con↗

arXiv2022

On the nature of quasiparticle interference in three dimensions

Quasiparticle Interference (QPI) imaging is a powerful tool for the study of the low energy electronic structure of quantum materials. However, the measurement of QPI by scanning tunneling microscopy (STM) is restricted to surfaces and is thus inherently constrained to two dimensions. This has proved immensely successful for the study of materials that exhibit a quasi-two-dimensional electronic structure, yet it raises questions about how to interpret QPI in materials that have a highly three dimensional electronic structure. In this paper we address this question and establish the methodology required to simulate and understand QPI arising from three dimensional systems as measured by STM. We calculate the continuum surface Green's function in the presence of a defect, which captures the role of the surface and the vacuum decay of the wave functions. We find that defects at different depths from the surface will produce unique sets of scattering vectors for three dimensional systems, which nevertheless can be related to the three-dimensional electronic structure of the bulk material. We illustrate the consequences that the three-dimensionality of the electronic structure has on the measured QPI for a simple cubic nearest-neighbour tight-binding model, and then demonstrate application to a real material using a realistic model for PbS. Our method unlocks the use of QPI imaging for the study of quantum materials with three dimensional electronic structures and introduces a framework to generically account for $k_z$-dispersions within QPI simulations.

cond-mat.str-el↗