arXiv subjects

Christoph Renner

Publications and source records attributed to Christoph Renner.

At least 19 recordsLinked to original sources

arXiv2026

Tuning competing electronic phases in monolayer VSe$_2$ via interface hybridization

Competing electronic phases in two-dimensional transition metal dichalcogenides constitute a fertile platform for uncovering emergent ground states and elucidating the control parameters that govern the correlated electron phases. Among these materials, vanadium diselenide is particularly compelling: while the bulk hosts a well-established charge density wave (CDW), monolayers exhibit markedly different electronic behavior. Here, we identify three distinct electronic regimes in mechanically exfoliated VSe$_2$ flakes on Au(111) substrates, where interfacial hybridization, charge transfer, and strain act as primary tuning parameters of electronic order. Monolayers strongly coupled to gold show complete suppression of the CDW, accompanied by the emergence of moir\'e modulations. In contrast, bilayers preserve the in-plane $4a \times 4a$ CDW characteristic of the bulk limit. Strained, electronically decoupled monolayers formed in suspended membrane and bubble regions stabilize a $\sqrt{3}a\times\sqrt{7}a$ CDW phase, underscoring the reversible role of substrate interaction and hybridization.

cond-mat.other↗

arXiv2026

Towards a full-scale version of Yakhot's model of strong turbulence

We present first elements of an extension of Yakhot's model of strong turbulence towards small scales. The analysis is based on an empirically observed relation for even order structure functions which extends from the inertial into the dissipation range. With this relation and Kolmogorov's four-fifth law, models for structure functions of orders two and three can be derived that replicate expected small scale limits and describe the transition from dissipative to inertial range scaling regimes correctly. An additional length scale parameter is introduced by the extension. It marks the crossover point from the inertial to the dissipation range and can be expressed as a function of the Reynolds number. In combination with a recently proposed large-scale extension of Yakhot's model, we ultimately obtain full-scale models for structure functions of second and third order. These expressions are closed--form, do not contain free parameters and are in good agreement with experimental data from the smallest dissipative scales up to the system scale.

physics.flu-dyn↗

arXiv2025

Vortex core spectroscopy links pseudogap and Lifshitz critical point in a cuprate superconductor

Understanding how superconductivity competes with other electronic phases in cuprates requires direct access to the hidden non-superconducting low temperature phase, for which Abrikosov vortices provide a unique local probe. We map the doping- and field-dependent evolution of vortex-core states in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ across a broad doping range spanning the Fermi-surface Lifshitz transition. High-resolution scanning tunneling spectroscopy reveals a striking transformation of the vortex-core spectrum from unconventional, pseudogap-like signatures at moderate doping to more BCS-like behavior beyond a critical doping $p^* \approx 0.21$. This crossover aligns with the pseudogap endpoint and the onset of Fermi-surface reconstruction, indicating a direct link between pseudogap physics and vortex electronic structure. Our findings highlight the vortex core as a sensitive local probe of the cuprate ground state.

cond-mat.supr-con↗

arXiv2025

Coupling between magnetism and band structure in a 2D semiconductor

Van der Waals semiconducting magnets exhibit a cornucopia of physical phenomena originating from the interplay of their semiconducting and magnetic properties. However, a comprehensive understanding of how semiconducting processes and magnetism are coupled is lacking. We address this question by performing scanning tunneling spectroscopy (STS) measurements on the magnetic semiconductor CrPS$_4$, and by comparing the results to photoluminescence experiments and density functional theory (DFT) calculations. Below the magnetic transition, STS exhibit multiple features absent in the paramagnetic state, caused by the proliferation of electronic bands due to spin splitting with a large ($\simeq 0.5$ eV) exchange energy. The energetic differences between the band edges determined by STS match all observed photoluminescence transitions, which also proliferate in the magnetic state. DFT calculations quantitatively predict the relative positions of all detected bands, explain which pairs of bands lead to radiative transitions, and also reproduce the measured spatial dependence of electronic wavefunctions. Our results reveal how all basic optoelectronic processes observed in CrPS$_4$ can be understood in terms of the evolution of the electronic band structure when entering the magnetic state, and allow us to conclude that individual bands are fully spin-polarized over a broad energy interval.

cond-mat.mtrl-sci↗

arXiv2024

Doping Tunable CDW Phase Transition in Bulk 1T-ZrSe$_2$

Tuneable electronic properties in transition metal dichalcogenides (TMDs) are essential to further their use in device applications. Here, we present a comprehensive scanning tunnelling microscopy and spectroscopy study of a doping-induced charge density wave (CDW) in semiconducting bulk 1T-ZrSe$_2$. We find that atomic impurities which locally shift the Fermi level ($E_F$) into the conduction band trigger a CDW reconstruction concomitantly to the opening of a gap at $E_F$. Our findings shed new light on earlier photoemission spectroscopy and theoretical studies of bulk 1T-ZrSe$_2$, and provide a local understanding of the electron-doping mediated CDW transition observed in semiconducting TMDs.

cond-mat.str-el↗

arXiv2024

Empirical large-scale extension of Yakhot's model of strong turbulence

We propose an empirical extension of Yakhot's model of strong turbulence [V. Yakhot, Phys. Rev. E 57(2) (1998)] that correctly describes the statistics of longitudinal velocity increments not only in the inertial range but also for larger scales up to the system length scale L. Two additional parameters are introduced to the original equation for the probability density function of velocity increments. These parameters can be motivated by physical arguments and their values are fixed by large scale boundary conditions. The resultant model ensures correct convergence of structure functions at the system length scale, including vanishing slopes at L, and shows good agreement with experimental data.

physics.flu-dyn↗

arXiv2024

Feedback loop dependent charge density wave imaging by scanning tunneling spectroscopy

Scanning Tunneling Spectroscopy (STS) is a unique technique to probe the local density of states (LDOS) at the atomic scale by measuring the tunneling conductance between a sharp tip and a sample surface. However, the technique suffers of well-known limitations, the so-called set-point effect, which can potentially introduce artifacts in the measurements. We compare several STS imaging schemes applied to the LDOS modulations of the charge density wave state on atomically flat surfaces, and demonstrate that only constant-height STS is capable of mapping the intrinsic LDOS. In the constant-current STS, commonly used and easier-to-implement, the tip-sample distance variations imposed by the feedback loop result in set-point-dependent STS images and possibly mislead the identification of the CDW gap edges.

cond-mat.mtrl-sci↗

arXiv2023

Vortex-core spectroscopy of $d$-wave cuprate high-temperature superconductors

The mechanism of high-temperature superconductivity remains one of the great challenges of contemporary physics. Here, we review efforts to image the vortex lattice in copper oxide-based high-temperature superconductors and to measure the characteristic electronic structure of the vortex core of a $d$-wave superconductor using scanning tunneling spectroscopy.

cond-mat.supr-con↗

arXiv2023

Delusive chirality and periodic strain pattern in moir\'{e} systems

Geometric phase analysis (GPA) is a widely used technique for extracting displacement and strain fields from scanning probe images. Here, we demonstrate that GPA should be implemented with caution when several fundamental lattices contribute to the image, in particular in twisted heterostructures featuring moir\'e patterns. We find that in this case, GPA is likely to suggest the presence of chiral displacement and periodic strain fields, even if the structure is completely relaxed and without distortions. These delusive fields are subject to change with varying twist angles, which could mislead the interpretation of twist angle dependent properties.

cond-mat.mes-hall↗

arXiv2023

Twist angle dependent electronic properties of exfoliated single layer MoS$_2$ on Au(111)

Synthetic materials and heterostructures obtained by the controlled stacking of exfoliated monolayers are emerging as attractive functional materials owing to their highly tunable properties. We present a detailed scanning tunneling microscopy and spectroscopy study of single layer MoS$_2$-on-gold heterostructures as a function of twist angle. We find that their electronic properties are determined by the hybridization of the constituent layers and are modulated at the moiré period. The hybridization depends on the layer alignment and the modulation amplitude vanishes with increasing twist angle. We explain our observations in terms of a hybridization between the nearest sulfur and gold atoms, which becomes spatially more homogeneous and weaker as the moiré periodicity decreases with increasing twist angle, unveiling the possibility of tunable hybridization of electronic states via twist angle engineering.

cond-mat.mes-hall↗

arXiv2022

Determining spin-orbit coupling in graphene by quasiparticle interference imaging

Inducing and controlling spin-orbit coupling (SOC) in graphene is key to create topological states of matter, and for the realization of spintronic devices. Placing graphene onto a transition metal dichalcogenide is currently the most successful strategy to achieve this goal, but there is no consensus as to the nature and the magnitude of the induced SOC. Here, we show that the presence of backscattering in graphene-on-WSe$_2$ heterostructures can be used to probe SOC and to determine its strength quantitatively, by imaging quasiparticle interference with a scanning tunneling microscope. A detailed theoretical analysis of the Fourier transform of quasiparticle interference images reveals that the induced SOC consists of a valley-Zeeman ($λ_{\text{vZ}}\approx 2$ meV) and a Rashba ($λ_\text{R}\approx 15$ meV) term, one order of magnitude larger than what theory predicts, but in excellent agreement with earlier transport experiments. The validity of our analysis is confirmed by measurements on a 30 degree twist angle heterostructure that exhibits no backscattering, as expected from symmetry considerations. Our results demonstrate a viable strategy to determine SOC quantitatively by imaging quasiparticle interference.

cond-mat.mes-hall↗

arXiv2022

Tunable biaxial strain device for low dimensional materials

Strain is attracting much interest as a mean to tune the properties of thin exfoliated two-dimensional materials and their heterostructures. Numerous devices to apply tunable uniaxial strain are proposed in the literature, but only few for biaxial strain where there is often a trade-off between maximum strain and uniformity, reversibility and device size. We present a compact device that allows the controlled application of uniform in-plane biaxial strain, with maximum deformation and uniformity comparable to those found in much larger devices. Its performance and strain uniformity over the sample area are modeled using finite element analysis and demonstrated by measuring the response of exfoliated 2H-MoS$_2$ to strain by Raman spectroscopy.

cond-mat.mtrl-sci↗

arXiv2021

Wang-MacDonald d-wave vortex cores observed in heavily overdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$

Low magnetic field scanning tunneling spectroscopy of individual Abrikosov vortices in heavily overdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ unveils a clear d-wave electronic structure of the vortex core, with a zero-bias conductance peak at the vortex center that splits with increasing distance from the core. We show that previously reported unconventional electronic structures, including the low energy checkerboard charge order in the vortex halo and the absence of a zero-bias conductance peak at the vortex center, are direct consequences of short inter-vortex distance and consequent vortex-vortex interactions prevailing in earlier experiments.

cond-mat.supr-con↗

arXiv2021

Multiband charge density wave exposed in a transition metal dichalcogenide

In the presence of multiple bands, well-known electronic instabilities may acquire new complexity. While multiband superconductivity is the subject of extensive studies, the possibility of multiband charge density waves (CDWs) has been largely ignored so far. Here, combining energy dependent scanning tunnelling microscopy (STM) topography with a simple model of the charge modulations and a self-consistent calculation of the CDW gap, we find evidence for a multiband CDW in 2H-NbSe$_2$. This CDW not only involves the opening of a gap on the inner band around the K-point, but also on the outer band. This leads to spatially out-of-phase charge modulations from electrons on these two bands, which we detect through a characteristic energy dependence of the CDW contrast in STM images.

cond-mat.str-el↗

arXiv2020

Insight into the charge density wave gap from contrast inversion in topographic STM images

Charge density waves (CDWs) are understood in great details in one dimension, but they remain largely enigmatic in two dimensional systems. In particular, numerous aspects of the associated energy gap and the formation mechanism are not fully understood. Two long standing riddles are the amplitude and position of the CDW gap with respect to the Fermi level ($E_F$) and the frequent absence of CDW contrast inversion (CI) between opposite bias scanning tunneling microscopy (STM) images. Here, we find compelling evidence that these two issues are intimately related. Combining density functional theory and STM to analyse the CDW pattern and modulation amplitude in 1$T$-TiSe$_2$, we find that CI takes place at an unexpected negative sample bias because the CDW gap opens away from $E_F$, deep inside the valence band. This bias becomes increasingly negative as the CDW gap shifts to higher binding energy with electron doping. This study shows the importance of CI in STM images to identify periodic modulations with a CDW and to gain valuable insight into the CDW gap, whose measurement is notoriously controversial.

cond-mat.mes-hall↗

arXiv2019

Towards surface diffusion potential mapping on atomic length scale

The surface diffusion potential landscape plays an essential role in a number of physical and chemical processes such as self-assembly and catalysis. Diffusion energy barriers can be calculated theoretically for simple systems, but there is currently no experimental technique to systematically measure them on the relevant atomic length scale. Here, we introduce an atomic force microscopy based method to semiquantitatively map the surface diffusion potential on an atomic length scale. In this proof of concept experiment, we show that the atomic force microscope damping signal at constant frequency-shift can be linked to nonconservative processes associated with the lowering of energy barriers and compared with calculated single-atom diffusion energy barriers.

cond-mat.mes-hall↗

arXiv2019

Scanning Tunneling Microscopy of an Air Sensitive Dichalcogenide Through an Encapsulating Layer

Many atomically thin exfoliated 2D materials degrade when exposed to ambient conditions. They can be protected and investigated by means of transport and optical measurements if they are encapsulated between chemically inert single layers in the controlled atmosphere of a glove box. Here, we demonstrate that the same encapsulation procedure is also compatible with scanning tunneling microscopy (STM) and spectroscopy (STS). To this end, we report a systematic STM/STS investigation of a model system consisting of an exfoliated 2H-NbSe2 crystal capped with a protective 2H-MoS2 monolayer. We observe different electronic coupling between MoS2 and NbSe2, from a strong coupling when their lattices are aligned within a few degrees to 2 essentially no coupling for 30° misaligned layers. We show that STM always probes intrinsic NbSe2 properties such as the superconducting gap and charge density wave at low temperature when setting the tunneling bias inside the MoS2 band gap, irrespective of the relative angle between the NbSe2 and MoS2 lattices. This study demonstrates that encapsulation is fully compatible with STM/STS investigations of 2D materials.

cond-mat.mes-hall↗

arXiv2018

Energy-dependent spatial texturing of the charge order in $1T$-Cu$_x$TiSe$_2$

We report a detailed study of the microscopic effects of Cu intercalation on the charge density wave (CDW) in 1\textit{T}-Cu$_x$TiSe$_2$. Scanning tunneling microscopy and spectroscopy (STM/STS) reveal a unique, Cu driven spatial texturing of the charge ordered phase, with the appearance of energy dependent CDW patches and sharp $π$-phase shift domain walls ($π$DWs). The energy and doping dependencies of the patchwork are directly linked to the inhomogeneous potential landscape due to the Cu intercalants. They imply a CDW gap with unusual features, including a large amplitude, the opening below the Fermi level and a shift to higher binding energy with electron doping. Unlike the patchwork, the $π$DWs occur independently of the intercalated Cu distribution. They remain atomically sharp throughout the investigated phase diagram and occur both in superconducting and non-superconducting specimen. These results provide unique atomic-scale insight on the CDW ground state, questioning the existence of incommensurate CDW domain walls and contributing to understand its formation mechanism and interplay with superconductivity.

cond-mat.str-el↗