arXiv subjects

Christoph Renner

Publications and source records attributed to Christoph Renner.

27 records · Page 2Linked to original sources

arXiv2018

Holographic imaging of the complex charge density wave order parameter

The charge density wave (CDW) in solids is a collective ground state combining lattice distortions and charge ordering. It is defined by a complex order parameter with an amplitude and a phase. The amplitude and wavelength of the charge modulation are readily accessible to experiment. However, accurate measurements of the corresponding phase are significantly more challenging. Here we combine reciprocal and real space information to map the full complex order parameter based on topographic scanning tunneling microscopy (STM) images. Our technique overcomes limitations of earlier Fourier space based techniques to achieve distinct amplitude and phase images with high spatial resolution. Applying this analysis to transition metal dichalcogenides provides striking evidence that their CDWs consist of three individual charge modulations whose ordering vectors are connected by the fundamental rotational symmetry of the crystalline lattice. Spatial variations in the relative phases of these three modulations account for the different contrasts often observed in STM topographic images. Phase images further reveal topological defects and discommensurations, a singularity predicted by theory for a nearly commensurate CDW. Such precise real space mapping of the complex order parameter provides a powerful tool for a deeper understanding of the CDW ground state whose formation mechanisms remain largely unclear.

cond-mat.str-el↗

arXiv2018

Hole Transport in Exfoliated Monolayer MoS$_2$

Ideal monolayers of common semiconducting transition metal dichalcogenides (TMDCs) such as MoS$_2$, WS$_2$, MoSe$_2$, and WSe$_2$ possess many similar electronic properties. As it is the case for all semiconductors, however, the physical response of these systems is strongly determined by defects in a way specific to each individual compound. Here we investigate the ability of exfoliated monolayers of these TMDCs to support high-quality, well-balanced ambipolar conduction, which has been demonstrated for WS$_2$, MoSe$_2$, and WSe$_2$, but not for MoS$_2$. Using ionic-liquid gated transistors we show that, contrary to WS$_2$, MoSe$_2$, and WSe$_2$, hole transport in exfoliated MoS$_2$ monolayers is systematically anomalous, exhibiting a maximum in conductivity at negative gate voltage (V$_G$) followed by a suppression of up to 100 times upon further increasing V$_G$. To understand the origin of this difference we have performed a series of experiments including the comparison of hole transport in MoS$_2$ monolayers and thicker multilayers, in exfoliated and CVD-grown monolayers, as well as gate-dependent optical measurements (Raman and photoluminescence) and scanning tunneling imaging and spectroscopy. In agreement with existing {\it ab-initio} calculations, the results of all these experiments are consistently explained in terms of defects associated to chalcogen vacancies that only in MoS$_2$ monolayers -- but not in thicker MoS$_2$ multilayers nor in monolayers of the other common semiconducting TMDCs -- create in-gap states near the top of the valence band that act as strong hole traps. Our results demonstrate the importance of studying systematically how defects determine the properties of 2D semiconducting materials and of developing methods to control them.

cond-mat.mes-hall↗

arXiv2017

Observation of Caroli-de Gennes-Matricon Vortex States in YBa$_2$Cu$_3$O$_{7-δ}$

The copper oxides present the highest superconducting temperature and properties at odds with other compounds, suggestive of a fundamentally different superconductivity. In particular, the Abrikosov vortices fail to exhibit localized states expected and observed in all clean superconductors. We have explored the possibility that the elusive vortex-core signatures are actually present but weak. Combining local tunneling measurements with large-scale theoretical modeling, we positively identify the vortex states in YBa$_2$Cu$_3$O$_{7-δ}$. We explain their spectrum and the observed variations thereof from one vortex to the next by considering the effects of nearby vortices and disorder in the vortex lattice. We argue that the superconductivity of copper oxides is conventional, but the spectroscopic signature does not look so because the superconducting carriers are a minority.

cond-mat.supr-con↗

arXiv2017

Dimensional cross-over of the charge density wave order parameter in thin exfoliated 1T-VSe$_2$

The capability to isolate one to few unit-cell thin layers from the bulk matrix of layered compounds opens fascinating prospects to engineer novel electronic phases. However, a comprehensive study of the thickness dependence and of potential extrinsic effects are paramount to harness the electronic properties of such atomic foils. One striking example is the charge density wave (CDW) transition temperature in layered dichalcogenides whose thickness dependence remains unclear in the ultrathin limit. Here we present a detailed study of the thickness and temperature dependences of the CDW in VSe$_2$ by scanning tunnelling microscopy (STM). We show that mapping the real-space CDW periodicity over a broad thickness range unique to STM provides essential insight. We introduce a robust derivation of the local order parameter and transition temperature based on the real space charge modulation amplitude. Both quantities exhibit a striking non-monotonic thickness dependence that we explain in terms of a 3D to 2D dimensional crossover in the FS topology. This finding highlights thickness as a true tuning parameter of the electronic ground state and reconciles seemingly contradicting thickness dependencies determined in independent transport studies.

cond-mat.str-el↗

arXiv2016

Revisiting the vortex-core tunnelling spectroscopy in YBa$_2$Cu$_3$O$_{7-δ}$

The observation by scanning tunnelling spectroscopy (STS) of Abrikosov vortex cores in the high-temperature superconductor YBa$_2$Cu$_3$O$_{7-δ}$ (Y123) has revealed a robust pair of electron-hole symmetric states at finite subgap energy. Their interpretation remains an open question because theory predicts a different signature in the vortex cores, characterised by a strong zero-bias conductance peak. We present STS data on very homogeneous Y123 at 0.4 K revealing that the subgap features do not belong to vortices: they are actually observed everywhere along the surface with high spatial and energy reproducibility, even in the absence of magnetic field. Detailed analysis and modelling show that these states remain unpaired in the superconducting phase and belong to an incoherent channel which contributes to the tunnelling signal in parallel with the superconducting density of states.

cond-mat.supr-con↗

arXiv2014

Surface transport and band gap structure of exfoliated 2H-MoTe$_2$ crystals

Semiconducting transition metal dichalcogenides (TMDs) have emerged as materials that can be used to realize two-dimensional (2D) crystals possessing rather unique transport and optical properties. Most research has so far focused on sulfur and selenium compounds, while tellurium-based materials attracted little attention so far. As a first step in the investigation of Te-based semiconducting TMDs in this context, we have studied MoTe$_2$ crystals with thicknesses above 4 nm, focusing on surface transport and a quantitative determination of the gap structure. Using ionic-liquid gated transistors, we show that ambipolar transport at the surface of the material is reproducibly achieved, with hole and electron mobility values between 10 and 30 cm$^2$/Vs at room temperature. The gap structure is determined through three different techniques: ionic-liquid gated transistors and scanning tunneling spectroscopy, that allow the measurement of the indirect gap ($E_{ind}$), and optical transmission spectroscopy on crystals of different thickness, that enables the determination of both the direct ($E_{dir}$) and the indirect gap. We find that at room temperature $E_{ind}$ = 0.88 eV and $E_{dir}$ = 1.02 eV. Our results suggest that thin MoTe$_2$ layers may exhibit a transition to a direct gap before mono-layer thickness. They should also drastically extend the range of direct gaps accessible in 2D semiconducting TMDs.

cond-mat.mes-hall↗

arXiv2011

Imaging Oxygen Defects and their Motion at a Manganite Surface

Manganites are technologically important materials, used widely as solid oxide fuel cell cathodes: they have also been shown to exhibit electroresistance. Oxygen bulk diffusion and surface exchange processes are critical for catalytic action, and numerous studies of manganites have linked electroresistance to electrochemical oxygen migration. Direct imaging of individual oxygen defects is needed to underpin understanding of these important processes. It is not currently possible to collect the required images in the bulk, but scanning tunnelling microscopy could provide such data for surfaces. Here we show the first atomic resolution images of oxygen defects at a manganite surface. Our experiments also reveal defect dynamics, including oxygen adatom migration, vacancy-adatom recombination and adatom bistability. Beyond providing an experimental basis for testing models describing the microscopics of oxygen migration at transition metal oxide interfaces, our work resolves the long-standing puzzle of why scanning tunnelling microscopy is more challenging for layered manganites than for cuprates.

cond-mat.str-el↗

arXiv2006

Scanning tunneling spectroscopy of high-temperature superconductors

Tunneling spectroscopy played a central role in the experimental verification of the microscopic theory of superconductivity in the classical superconductors. Initial attempts to apply the same approach to high-temperature superconductors were hampered by various problems related to the complexity of these materials. The use of scanning tunneling microscopy/spectroscopy (STM/STS) on these compounds allowed to overcome the main difficulties. This success motivated a rapidly growing scientific community to apply this technique to high-temperature superconductors. This paper reviews the experimental highlights obtained over the last decade. We first recall the crucial efforts to gain control over the technique and to obtain reproducible results. We then discuss how the STM/STS technique has contributed to the study of some of the most unusual and remarkable properties of high-temperature superconductors: the unusual large gap values and the absence of scaling with the critical temperature; the pseudogap and its relation to superconductivity; the unprecedented small size of the vortex cores and its influence on vortex matter; the unexpected electronic properties of the vortex cores; the combination of atomic resolution and spectroscopy leading to the observation of periodic local density of states modulations in the superconducting and pseudogap states, and in the vortex cores.

cond-mat.supr-con↗

arXiv1999

How to quantify deterministic and random influences on the statistics of the foreign exchange market

It is shown that prize changes of the US dollar - German Mark exchange rates upon different delay times can be regarded as a stochastic Marcovian process. Furthermore we show that from the empirical data the Kramers-Moyal coefficients can be estimated. Finally, we present an explicite Fokker-Planck equation which models very precisely the empirical probabilitiy distributions.

physics.data-an↗