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Tristan Cren

Publications and source records attributed to Tristan Cren.

At least 19 recordsLinked to original sources
arXiv2026

Doping-controlled topological superconducting transition in misfit layer compounds

Achieving topological superconductivity is a key goal in quantum physics, offering a path to fault-tolerant quantum computers. A central challenge in this field is to continuously drive a material through a topological quantum phase transition to directly observe the evolution from trivial to topological superconductivity. However, finding a robust platform that allows such extreme and precise tuning remains a challenge. Here, we demonstrate a doping-controlled phase transition from a conventional to a topological superconducting state in the bulk misfit layer compound (LaxPb1-xSe)1.14(NbSe2)2. We reveal a non-monotonic phase diagram characterized by two distinct superconducting regimes separated by a non-superconducting phase at a precise doping. In the highly doped regime, the superconducting phase becomes remarkably sensitive to non-magnetic disorder, and orientation-selective in-gap modes emerge at atomic step edges. Supported by Bogoliubov-de Gennes calculations, these emergent spatial signatures are consistent with a time-reversal-symmetric crystalline-topological order parameter. Our results establish misfit compounds as a platform to engineering topological superconductivity.

cond-mat.supr-con↗
arXiv2026

Doping tunable charge density waves in misfit layer compounds

The ability to tune charge density waves (CDWs) through external control knobs, such as doping, pressure or strain is crucial for exploring the phase diagram of two dimensional (2D) or quasi-2D materials. Yet, controlling CDWs critical temperature and ordering vector remains a challenge for current experimental techniques. In this work, we establish misfit layer compound heterostructures as a reliable platform to manipulate CDWs in transition metal dichalcogenides. By combining ab initio calculations with low-temperature scanning tunneling microscopy, we show how to achieve doping tunable control over NbSe2 CDW by chemically alloying in the rocksalt subunit. Crucially, we prove that tuning the La Pb ratio in the misfit family (LaxPb1xSe)1.14(NbSe2)2 enables stabilization of different CDW orders, such as 2x2 or 3x3 patterns, and even coexisting phases. This work paves the way for engineering transition metal dichalcogenides with tailored charge density waves within misfit heterostructures.

cond-mat.mtrl-sci↗
arXiv2026

Tuning the Charge Transfer of Transition Metal Dichalcogenides via Misfit Layer Compounds

Misfit layer compounds (MLCs) are a versatile platform for exploring the electronic phase diagram of two dimensional (2D) materials beyond the limits of conventional gating techniques. This work demonstrates the precise tunability of electron doping in NbSe2 monolayers through chemical alloying within the rocksalt layer of (LaxPb1xSe)1.14(NbSe2)2 heterostructures. By combining first principles density functional theory (DFT) calculations with angle resolved photoemission spectroscopy (ARPES), we prove that the rocksalt unit acts as an universal electron donor. We show that varying the La Pb ratio results in a rigid Fermi level shift, still preserving the NbSe2 electronic structure. Crucially, photon energy dependent ARPES confirms that the NbSe2 layers nearly maintain their intrinsic 2D character and orbital identity within the three dimensional misfit. This study establishes MLCs as a reliable platform for engineering emergent states in 2D transition metal dichalcogenides through precise stoichiometric control.

cond-mat.mtrl-sci↗
arXiv2026

Antiferromagnetic stripe phase and large-gap insulating ground state of the correlated $\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) single atomic layer

The one-third monolayer Sn layer on Si(111) has long been considered a benchmark system for exploring two-dimensional Mott physics, owing to its narrow bandwidth and sizable on-site Coulomb repulsion. Previous experiments suggested the emergence of a low-temperature Mott insulating phase with an energy gap of only a few tens of meV, while theory predicted a possible antiferromagnetic ordering that remained experimentally elusive. Here, by combining low-temperature scanning tunneling microscopy/spectroscopy with first-principles calculations, we reveal that the $\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) surface undergoes a transition below 30K into a robust insulating state characterized by a remarkably large gap of about 440 $\pm$ 120 meV at 4K, five to ten times larger than previously reported. Quasiparticle interference imaging uncovers a well-defined $2\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) superstructure, providing direct evidence for a two-dimensional stripe-like antiferromagnetic order. Ab initio calculations reveal that the silicon substrate stabilizes this phase through strong nonlocal tin-tin interactions, highlighting the decisive role of substrate-driven correlations in the $\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) system.

cond-mat.str-el↗
arXiv2025

Moiré pattern multiplicity driven by electronic effects in two-dimensional CrCl3/Au heterostructures

Moiré patterns are a central motif in van der Waals heterostructures arising from the superposition of two-dimensional (2D) incommensurate lattices. These patterns reveal a wealth of correlated effects, influencing electronic, magnetic, and structural phenomena. While diffraction techniques typically resolve multiple moiré wave-vectors corresponding to the incommensurate nature of the underlying lattices, Scanning Tunneling Microscopy (STM) often reveals only a dominant superperiod. In this work, we address this apparent discrepancy through an STM study of a twisted monolayer of CrCl3 on Au(111). We observe the coexistence of several moiré patterns at a fixed twist angle, whose relative intensity depends on the tunneling bias. Fourier analysis of STM data uncovers hidden higher-order moiré components not visible in STM topographic images, while spectroscopy maps reveal that the spectral weight of each pattern varies with electron energy. Our results establish that STM selectively probes on the same area distinct moiré modulations depending on electronic confinement, providing a unified framework that reconciles real space and reciprocal space observations of complex moiré superstructures.

cond-mat.other↗
arXiv2025

Upper critical field and pairing symmetry of Ising superconductors

Motivated by the fact that the measured critical field $H_{c2}$ in various transition metal dichalcogenide (TMD) superconductors is poorly understood, we reexamine its scaling behavior with temperature and spin-orbit coupling (SOC). By computing the spin-susceptibility in a multipocket system, we find that segments of the Fermi Surface (FS) at which the SOC has nodal points can have a contribution orders of magnitude larger than the remaining FS, hence setting the $H_{c2}$, assuming the presence of a conventional singlet superconducting order parameter. Nodal lines of an Ising SOC in the Brillouin zone are imposed by symmetry, so they cause such nodal points whenever they intersect an FS pocket, which is indeed the case in monolayer NbSe$_2$ and TaS$_2$, but not in gated MoS$_2$ and WS$_2$. Our analysis reinterprets existing measurements, concluding that a dominant singlet-order parameter on pockets with SOC nodes is consistent with the $H_{c2}(T)$ data for all monolayer Ising superconductors, in contrast to previous contradictory pairing assumptions. Finally, we predict a doping-dependent experimental signature of our theory.

cond-mat.supr-con↗
arXiv2025

Anderson transition symmetries at the band-edge of a correlated Sn/Si monolayer

Anderson localization is predicted to enhance the critical temperature of disordered superconductors. Despite a huge body of theoretical work based on non-linear sigma models, experiments are lacking to understand correlated electrons in disordered potentials. In this study, we investigate a tin monolayer on silicon, a material known for its likely antiferromagnetic Mott-correlated groundstate. We analyze the statistical properties of tunneling conductance maps of increasingly localized states as we approach the edge of the valence band. Using multifractal analysis, we show that the system follows an exact symmetry relation based on the algebraic structure of nonlinear sigma-models (NLsMs). We anticipate that this symmetry may be broken in specific - e.g. chiral electronic phases. Finally, we point out that multifractal analysis can equally be applied to universal conductance fluctuations in magneto-transport experiments, thus providing a powerful tool to probe the underlying symmetries of disordered electronic phases.

cond-mat.mes-hall↗
arXiv2025

Superconducting and spin-density wave phases probed by scanning tunneling spectroscopy in the organic conductor $\mathrm{(TMTSF)_{2}ClO_{4}}$

By scanning tunneling microscopy (STM) we have probed the local quasi-particle density of states (DOS) of the Bechgaard salt organic superconductor $\mathrm{(TMTSF)_{2}ClO_{4}}$ in slowly cooled single crystals cleaved under ultrahigh vacuum conditions. In well STM imaged crystallographic surface planes, the local DOS has been probed for different surface areas at temperatures above and below the critical temperature of superconducting or insulating spin-density wave states. While a rather homogeneous superconducting state is expected in the bulk from previous studies, depending on the degree of disorder introduced by cleavage in the anion lattice, an inhomogeneous granular state is predominantly observed at the surface. A pronounced linear V-shape profile of the local DOS is observed from intermediate to the lowest energy scale in the less disordered superconducting surface areas. This supports the existence of an unconventional d-wave like order parameter with nodes at low energy, which is preceded by more energetic fluctuations attributed to quantum criticality of the material. At higher energy disorder combined to correlations deplete further the DOS. By contrast a non-linear U-shape characterizes the local low energy DOS profile for the more disordered and insulating surface areas of the spin-density wave state. The experimental results are compared quantitatively with those predicted by the renormalization group theory of the quasi-one dimensional electron gas model and its description of the superconducting and spin-density wave states that are interlinked by quantum criticality in the Bechgaard salts.

cond-mat.supr-con↗
arXiv2025

Misfit layer superconductors, tuneable bulk heterostructures with strong 2D effects

Atomically thin layered materials are systems with zero limit bulk-to-surface ratio. Their physical properties are determined by two-dimensionality and strongly affected by interfacing with other systems. Therefore, they represent an accessible platform for the abundance of quantum effects that can be engineered by combining them into vertical stacks. Two types of layered systems are considered here - artificially prepared (exfoliated) van der Waals nanostructures, and naturally layered systems showing quasi 2D behaviour already in a bulk form. A special class of naturally layered materials is misfit structures combining atomic layers of hexagonal transition metal dichalcogenides and slabs of tetragonal ionic rare-earth monochalcogenides in the same superlattice. Both types of layered systems feature a new state of quantum matter, the Ising superconductivity extremely resilient to external magnetic field. A giant electron doping, natural to the misfit structures, can lead to topological superconductivity. Both systems can also be assembled into heterostructures combining different constituents. Layered 2D heterostructures have a large number of implications for many potential applications in solid-state devices.

cond-mat.supr-con↗
arXiv2024

Anisotropy of Yu-Shiba-Rusinov states in NbSe$_2$

The spatial structure of in-gap Yu-Shiba-Rusinov (YSR) bound states induced by a magnetic impurity in a superconductor is the essential ingredient for the possibility of engineering collective impurity states. Recently, a saddle-point approximation [Phys. Rev. B 105, 144503] revealed how the spatial form of a YSR state is controlled by an anisotropic exponential decay length, and an anisotropic prefactor, which depends on the Fermi velocity and Fermi-surface curvature. Here we analyze scanning tunnel microscope (STM) data on YSR states in NbSe$_2$, focusing on a key issue that the exponential decay length predicted theoretically from the small superconducting gap is much larger than the observed extent of YSR states. We confirm that the exponential decay can be neglected in the analysis of the anisotropy. Instead, we extract the anisotropic prefactor directly from the data, matching it to the theoretical prediction, and we establish that the theoretical expression for the prefactor alone captures the characteristic flower-like shape of the YSR state. Surprisingly, we find that up to linear order in the superconducting gap the anisotropic prefactor that determines the shape of YSR states is the same as the anisotropic response to the impurity in the underlying normal metal. Our work points out the correct way to analyze STM data on impurities in small-gap superconductors, and reveals the importance of the normal band structure's curvature and Fermi velocity in designing multi-impurity in-gap states in superconductors.

cond-mat.supr-con↗
arXiv2024

NbSe$_{2}$'s charge density wave collapse in the (LaSe)$_{1.14}$(NbSe$_{2}$)$_{2}$ misfit layer compound

Misfit layer compounds, heterostructures composed by a regular alternating stacking of rocksalt monochalcogenides bilayers and few-layer transition metal dichalchogenides, are an emergent platform to investigate highly doped transition metal dichalcogenides. Among them, (LaSe)$_{1.14}$(NbSe$_2$)$_2$ displays Ising superconductivity, while the presence of a charge density wave (CDW) in the material is still under debate. Here, by using polarized Raman spectroscopy and first-principles calculations, we show that NbSe$_2$ undergoes a doping-driven collapse of the CDW ordering within the misfit, and no signature of the CDW is detected down to 8~K. We provide a complete experimental and theoretical description of the lattice dynamics of this misfit compound. We show that the vibrational properties are obtained from those of the two subunits, namely the LaSe unit and the NbSe$_2$ bilayer, in the presence of a suitable field-effect doping, and then highlight the 2D nature of the lattice dynamics of NbSe$_2$ within the (LaSe)$_{1.14}$(NbSe$_2$)$_2$ 3D structure.

cond-mat.mtrl-sci↗
arXiv2024

Higher order topological defects in a moiré lattice

Topological defects are ubiquitous, they manifest in a wide variety of systems such as liquid crystals, magnets or superconductors. The recent quest for nonabelian anyons in condensed matter physics stimulates the interest for topological defects since they can be hosted in vortices in quantum magnets or topological superconductors. In addition to these vortex defects, in this study we propose to investigate edge dislocations in 2D magnets as new building blocks for topological physics since they can be described as vortices in the structural phase field. Here we demonstrate the existence of higher order topological dislocations within the higher order moiré pattern of the van der Waals 2D magnet CrCl3 deposited on Au(111). Surprizingly, these higher order dislocations arise from ordinary simple edge dislocations in the atomic lattice of CrCl3. We provide a theoretical framework explaining the higher order dislocations as vortex with a winding Chern number of 2. We expect that these original defects could stabilize some anyons either in a 2D quantum magnet or within a 2D superconductor coupled to it.

cond-mat.mes-hall↗
arXiv2023

Misfit layer compounds as ultra-tunable field effect transistors: from charge transfer control to emergent superconductivity

Misfit layer compounds are heterostructures composed of rocksalt units stacked with few layers transition metal dichalcogenides. They host Ising superconductivity, charge density waves and good thermoelectricity. The design of misfits emergent properties is, however, hindered by the lack of a global understanding of the electronic transfer among the constituents. Here, by performing first principles calculations, we unveil the mechanism controlling the charge transfer and demonstrate that rocksalt units are always donor and dichalcogenides acceptors. We show that misfits behave as a periodic arrangement of ultra-tunable field effect transistors where a charging as large as 6\times10^{14} e^-cm^{-2} can be reached and controlled efficiently by the La-Pb alloying in the rocksalt. Finally, we identify a strategy to design emergent superconductivity and demonstrate its applicability in (LaSe)_{1.27}(SnSe_2)_2. Our work paves the way to the design synthesis of misfit compounds with tailored physical properties.

cond-mat.mtrl-sci↗
arXiv2023

Local density of state fluctuations in 2D superconductor as a probe of quantum diffusion

The interplay of superconductivity and disorder generates a wealth of complex phenomena. In particular, the peculiar structure of diffusive electronic wavefunctions is predicted to increase the superconducting critical temperature in some range of disorder. In this work, we use an epitaxial monolayer of lead showing a simple band structure and homogenous structural disorder as a model system of a 2D superconductor in the weak-antilocalization regime. Then, we perform an extensive study of the emergent fluctuations of local density of states (LDOS) and spectral energy gap in this material and compare them with both analytical results and numerical solution of the attractive Hubbard model. We show that mesoscopic LDOS fluctuations allow to probe locally both the elastic and inelastic scattering rates which are notoriously difficult to measure in transport measurements.

cond-mat.supr-con↗
arXiv2023

Protection of Ising spin-orbit coupling in bulk misfit superconductors

Low-dimensional materials have remarkable properties that are distinct from their bulk counterparts. A paradigmatic example is Ising superconductivity that occurs in monolayer materials such as NbSe2 which show a strong violation of the Pauli limit. In monolayers, this occurs due to a combination of broken inversion symmetry and spin-orbit coupling that locks the spins of the electrons out-of-plane. Bulk NbSe2 is centrosymmetric and is therefore not an Ising superconductor. We show that bulk misfit compound superconductors, (LaSe)1.14(NbSe2) and (LaSe)1.14(NbSe2)2, comprised of monolayers and bilayers of NbSe2, exhibit unexpected Ising protection with a Pauli-limit violation comparable to monolayer NbSe2, despite formally having inversion symmetry. We study these misfit compounds using complementary experimental methods in combination with first-principles calculations. We propose theoretical mechanisms of how the Ising protection can survive in bulk materials. We show how some of these mechanisms operate in these bulk compounds due to a concerted effect of charge-transfer, defects, reduction of interlayer hopping, and stacking. This highlights how Ising superconductivity can, unexpectedly, arise in bulk materials, and possibly enable the design of bulk superconductors that are resilient to magnetic fields.

cond-mat.supr-con↗
arXiv2020

Misfit layer compounds: a platform for heavily-doped two-dimensional transition metal dichalcogenides

Transition metal dichalcogenides (TMDs) display a rich variety of instabilities such as spin and charge orders, Ising superconductivity and topological properties. Their physical properties can be controlled by doping in electric double-layer field-effect transistors (FET). However, for the case of single layer NbSe$_2$, FET doping is limited to $\approx 1\times 10^{14}$ cm$^{-2}$, while a somewhat larger charge injection can be obtained via deposition of K atoms. Here, by performing ARPES, STM, quasiparticle interference measurements, and first principles calculations we show that a misfit compound formed by sandwiching NbSe$_2$ and LaSe layers behaves as a NbSe$_2$ single layer with a rigid doping of $0.55-0.6$ electrons per Nb atom or $\approx 6\times 10^{14}$ cm$^{-2}$. Due to this huge doping, the $3\times3$ charge density wave is replaced by a $2\times2$ order with very short coherence length. As a tremendous number of different misfit compounds can be obtained by sandwiching TMDs layers with rock salt or other layers, our work paves the way to the exploration of heavily doped 2D TMDs over an unprecedented wide range of doping.

cond-mat.mtrl-sci↗
arXiv2020

Unveiling odd-frequency pairing around a magnetic impurity in a superconductor

We study the unconventional superconducting correlations caused by a single isolated magnetic impurity in a conventional s-wave superconductor. Due to the local breaking of time-reversal symmetry, the impurity induces unconventional superconductivity which is even in both space and spin variables but odd under time inversion. We derive an exact proportionality relation between the even-frequency component of the local electron density of states and the imaginary part of the odd-frequency local pairing function. By applying this relation to scanning tunneling microscopy spectra taken on top of magnetic impurities immersed in a Pb/Si(111) monolayer, we show experimental evidence of the occurrence of the odd-frequency pairing in these systems and explicitly extract its superconducting function from the data.

cond-mat.supr-con↗