arXiv subjects

Christophe Berthod

Publications and source records attributed to Christophe Berthod.

At least 19 recordsLinked to original sources

arXiv2026

Drosophila of phonon-mediated superconductivity: Full Eliashberg theory of the jellium model

We present a full numerical solution of the Migdal--Eliashberg equations for the jellium model of phonon-mediated superconductivity. We find very low critical temperatures below 1~K, in contrast to earlier claims that the jellium model for hydrogen solids might reach room-temperature superconductivity. Our results suggest that full momentum and frequency dependence of the gap function and normal self-energy should be taken into account for accurate $T_c$ estimates.

cond-mat.supr-con↗

arXiv2025

Angular momentum of vortex-core Majorana zero modes

Majorana zero modes (MZMs) are highly sought-after states with a possible application in quantum computation. Here, we show that vortex-core MZMs can carry a nontrivial angular momentum. This establishes new `flavors' of Majorana modes, independent of the Chern classification of topological superconductors. The MZM angular momentum is explicitly calculated for a microscopic model of a $d+id$ superconductor placed on a three-dimensional topological insulator ($d+id+\phantom{}$Dirac model) using both exact diagonalization and the Chebyshev expansion. We classify all possible quantum numbers of MZMs depending on the windings of the order parameter and underlying normal state. The topological protection of the MZM is set by the bulk gap, quasiparticle poisoning by trivial in-gap states, and its localization length. All these severely limit the stability of MZMs in the $d+id+\phantom{}$Dirac model, in contrast to earlier claims. Nevertheless, the possibility of having different flavors of MZM - in the form of angular momentum or something else - can provide a unique path forward for the study of MZMs.

cond-mat.supr-con↗

arXiv2025

Piecewise: Flexible piecewise functions for fast integral transforms in Julia

A piecewise function of a real variable x returns a value computed from a rule that can be different in each interval of the values of x. The Julia module Piecewise provides an implementation of piecewise functions, where the user is free to choose the rules. A mechanism allows for fitting a piecewise function made of user-defined formulas to a real function of a real variable. With appropriately chosen formulas, various integral transforms of the piecewise function become directly available without relying on quadratures. The module Piecewise defines seven formula that enable the fast calculation of the moments of the piecewise function. The module PiecewiseHilbert supplements these formula with methods enabling a fast Hilbert transform. The module PiecewiseLorentz extends some of these formula to enable what we call a Lorentz transform.

cs.MS↗

arXiv2025

Extraction of the self energy and Eliashberg function from angle resolved photoemission spectroscopy using the xARPES code

Angle-resolved photoemission spectroscopy is a powerful experimental technique for studying anisotropic many-body interactions through the electron spectral function. Existing attempts to decompose the spectral function into non-interacting dispersions and electron-phonon, electron-electron, and electron-impurity self-energies rely on linearization of the bands and manual assignment of self-energy magnitudes. Here, we show how self-energies can be extracted consistently for curved dispersions. We extend the maximum-entropy method to Eliashberg-function extraction with Bayesian inference, optimizing the parameters describing the dispersions and the magnitudes of electron-electron and electron-impurity interactions. We compare these novel methodologies with state-of-the-art approaches on model data, then demonstrate their applicability with two high-quality experimental data sets. With the first set, we identify the phonon modes of a two-dimensional electron liquid on TiO$_2$-terminated SrTiO$_3$. With the second set, we obtain unprecedented agreement between two Eliashberg functions of Li-doped graphene extracted from separate dispersions. We release these functionalities in the novel Python code xARPES.

cond-mat.mtrl-sci↗

arXiv2025

Universal low-density power laws of the dc conductivity and Hall constant in the self-consistent Born approximation

The dc conductivity tensor of two-dimensional one-band metals with weak pointlike disorder and magnetic field is studied in the self-consistent Born approximation, with special emphasis on the regime of low carrier density. In this theory, the Kubo conductivity is a functional of the electron dispersion and local (momentum-independent) electron self-energy, which is itself a causal functional of the dispersion and disorder strength. We obtain exact closed expressions for the asymptotic low-density conductivities at zero temperature in the form of power laws of the density and disorder strength with universal exponents. The crossover to the semiclassical regime of high density is studied numerically, as well as the temperature dependence. Our model and results may be relevant to interpret linear magneto-transport experiments performed in the metallic regime of gated two-dimensional semiconductors.

cond-mat.str-el↗

arXiv2024

Superconductivity in metallic hydrogen

Superconductivity, the lossless flow of electric current, occurs typically at very low temperatures. A possible exception is highly pressurized hydrogen, for which room temperature superconductivity has been predicted. However, as a result of various approximations used, conflicting theoretical predictions exist for the temperatures where superconductivity is expected to occur in highly pressurized hydrogen. Here we avoid those approximations and exploit the ``jellium'' model proposed in 1966 by De Gennes, where superconductivity involves the combination of Coulomb repulsion between the electrons and Coulomb attraction between the protons and the electrons. We confirm that metallic hydrogen should indeed exhibit superconductivity, but this is limited to temperatures far below previous estimates. We also find that the superconducting order develops over an energy range significantly exceeding the characteristic phonon energy, and that the phase of the order parameter flips 180 degrees at the characteristic phonon energy above and below the Fermi energy.

cond-mat.supr-con↗

arXiv2024

Hall response of locally correlated two-dimensional electrons at low density

We study the Hall constant in a homogeneous two-dimensional fluid of correlated electrons immersed in a perpendicular magnetic field, with special focus on the regime of low carrier density. The model consists of a one-band tight-binding model and a momentum-independent causal self-energy, representing interaction-induced correlations effects that are restricted to be local in space. We write general gauge-invariant equations for the conductivity tensor at first order in the magnetic field and solve them numerically (analytically when possible) in a minimal model of anisotropic square lattice with constant self-energy. Our results show that deviations from the universal behavior of the Hall constant, as observed in the semiclassical regime, appear upon entering the quantum regime, where the Fermi energy and interaction are comparable energy scales.

cond-mat.str-el↗

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

Can dd excitations mediate pairing ?

The Cu-$3d$ states in the high-$T_c$ cuprates are often described as a single band of $3d_{x^2-y^2}$ states, with the other four $3d$ states having about 2 to 3 eV higher energy due to the lower-than-octahedral crystal field at the copper sites. However, excitations to these higher energy states observed with RIXS show indications of strong coupling to doped holes in the $3d_{x^2-y^2}$ band. This relaunches a decades-old question of the possible role of the orbital degrees of freedom that once motivated Bednorz and Müller to search for superconductivity in these systems. Here we explore a direction different from the Jahn-Teller electron-phonon coupling considered by Bednorz and Müller, namely the interaction between holes mediated by $dd$ excitations.

cond-mat.supr-con↗

arXiv2023

Electronic structure of few-layer black phosphorus from $μ$-ARPES

Black phosphorus (BP) stands out among two-dimensional (2D) semiconductors because of its high mobility and thickness dependent direct band gap. However, the quasiparticle band structure of ultrathin BP has remained inaccessible to experiment thus far. Here we use a recently developed laser-based micro-focus angle resolved photoemission ($μ$-ARPES) system to establish the electronic structure of 2-9 layer BP from experiment. Our measurements unveil ladders of anisotropic, quantized subbands at energies that deviate from the scaling observed in conventional semiconductor quantum wells. We quantify the anisotropy of the effective masses and determine universal tight-binding parameters which provide an accurate description of the electronic structure for all thicknesses.

cond-mat.mes-hall↗

arXiv2023

Theory of spin-polarized high-resolution electron energy loss spectroscopy from nonmagnetic surfaces with a large spin-orbit coupling

The scattering theory of low-energy (slow) electrons has been developed by Evans and Mills [Phys. Rev. B 5, 4126 (1972)]. The formalism is merely based on the electrostatic Coulomb interaction of the scattering electrons with the charge-density fluctuations above the surface and can describe most of the interesting features observed in the high-resolution electron energy-loss spectroscopy experiments. Here we extend this theory by including the spin-orbit coupling in the scattering process. We discuss the impact of this interaction on the scattering cross section. In particular, we discuss cases in which a spin-polarized electron beam is scattered from nonmagnetic surfaces with a strong spin-orbit coupling. We show that under some assumptions one can derive an expression for the scattering cross section, which can be used for numerical calculations of the spin-polarized spectra recorded by spin-polarized high-resolution electron energy-loss spectroscopy experiments.

cond-mat.str-el↗

arXiv2022

Direct probing of a large spin-orbit coupling in the FeSe superconducting monolayer on STO: Evidence for nontrivial topological states

In condensed-matter physics spin-orbit coupling (SOC) is a fundamental physical interaction, which describes how the electrons' spin couples to their orbital motion. It is the source of a vast variety of fascinating phenomena in solids such as topological phases of matter, quantum spin Hall states, and many other exotic quantum states. Although in most theoretical descriptions of the phenomenon of high-temperature superconductivity SOC has been neglected, including this interaction can, in principle, revise the microscopic picture of superconductivity in these compounds. Not only the interaction leading to Cooper pairing but also the symmetry of the order parameter and the topological character of the involved states can be determined by SOC. Here by preforming energy-, momentum-, and spin-resolved spectroscopy experiments with an unprecedented resolution we demonstrate that while probing the dynamic charge response of the FeSe monolayer on strontium titanate, a prototype two dimensional high-temperature superconductor using slow electrons, the scattering cross-section shows a considerable spin asymmetry. We unravel the origin of the observed spin asymmetry by developing a model in which SOC is taken into consideration. Our analysis indicates that SOC in this two dimensional superconductor is rather strong. We anticipate that such a strong SOC can have several serious consequences on the electronic structures and can lead to the formation of topological states. Moreover, a sizable SOC can compete with other pairing scenarios and is crucial for the mechanism of high-temperature superconductivity.

cond-mat.supr-con↗

arXiv2021

Theory of cross quantum capacitance

Impressive progress in the control of atomically thin crystals is now enabling the realization of gated structures in which two electrodes are separated by atomic scale distances. The electrical capacitance of these structures is determined by phenomena that are not relevant in capacitors with larger electrode separation. With the aim to analyze these phenomena, we use linear response theory to develop a systematic description of capacitance for two coupled electron liquids, accounting for the wave nature of electrons, as well as for the effect of both intra and interlayer Coulomb interactions. Our theory leads to a general expression for the electrical capacitance in terms of both intra and interlayer electronic polarizabilities. The intralayer polarizability is directly related to the conventional expression for the quantum capacitance, whereas the interlayer polarizability term accounts for interaction-induced correlations between charges hosted by opposite capacitor plates. We refer to this latter term as to the cross quantum capacitance. We discuss the implications of the general expression for the capacitance, show that it leads to established results when the effect of interlayer correlations is negligible, and that the intra and interlayer polarizabilities play a comparable role for capacitors with very small electrode separation. Using two different approaches, we calculate the capacitance in specific cases, and find that the interlayer polarizability can be either positive or negative, so that the cross quantum capacitance can either increase or decrease the total capacitance. We conclude by showing that the cross quantum capacitance term can lead to a non-monotonic evolution of the total capacitance with increasing separation between the capacitor plates, which would represent an unambiguous manifestation of the cross quantum capacitance if observed experimentally.

cond-mat.mes-hall↗

arXiv2020

Role of a higher dimensional interaction in stabilizing charge density waves in quasi-1D NbSe$_3$ revealed by angle-resolved photoemission spectroscopy

We revisit charge density wave (CDW) behavior in the archetypal quasi-one-dimensional (quasi-1D) material NbSe$_3$ by high-resolution angle-resolved photoemission spectroscopy measurements utilizing a microfocused laser with a photon energy of 6.3 eV. We present a detailed view of the electronic structure of this complex multiband system and unambiguously resolve CDW gaps at the Fermi level ($E_F$). By employing a tight-binding model, we argue that these gaps are the result of interband coupling between electronic states that reside predominantly on distinct 1D chains within the material. Two such localized states are found to couple to an electronic state that extends across multiple 1D chains, highlighting the importance of a higher-dimensional interaction in stabilizing the CDW ordering in this material. In addition, the temperature evolution of intrachain gaps caused by the CDW periodicities far below $E_F$ deviate from the behavior expected for a Peierls-type mechanism driven by nesting; the upper and lower bands of the renormalized CDW dispersions maintain a fixed peak-to-peak distance while the gaps are gradually removed at higher temperatures. This points toward a gradual loss of long-range phase coherence as the dominant effect in reducing the CDW order parameter, which may correspond to the loss of coherence between the coupled chains. Furthermore, one of the gaps is observed above the bulk and surface CDW transition temperatures, implying the persistence of short-range incoherent CDW order. The influence of such higher-dimensional interactions likely plays an important role in a range of low-dimensional systems.

cond-mat.str-el↗

arXiv2019

Band filling and cross quantum capacitance in ion gated semiconducting transition metal dichalcogenide monolayers

Ionic liquid gated field-effect transistors (FETs) based on semiconducting transition metal dichalcogenides (TMDs) are used to study a rich variety of extremely interesting physical phenomena, but important aspects of how charge carriers are accumulated in these systems are not understood. We address these issues by means of a systematic experimental study of transport in monolayer MoSe$_2$ and WSe$_2$ as a function of magnetic field and gate voltage, exploring accumulated densities of carriers ranging from approximately 10$^{14}$ cm$^{-2}$ holes in the valence band to 4x10$^{14}$ cm$^{-2}$ electrons in the conduction band. We identify the conditions when the chemical potential enters different valleys in the monolayer band structure (the K and Q valley in the conduction band and the two spin-split K-valleys in the valence band) and find that an independent electron picture describes the occupation of states well. Unexpectedly, however, the experiments show very large changes in the device capacitance when multiple valleys are occupied that are not at all compatible with the commonly expected quantum capacitance contribution of these systems, $\textit{C}$$_Q$=$\textit{e}^2$/(d$μ$/d$\textit{n}$). This unexpected behavior is attributed to the presence of a cross quantum capacitance, which originates from screening of the electric field generated by charges on one plate from charges sitting on the other plate. Our findings therefore reveal an important contribution to the capacitance of physical systems that had been virtually entirely neglected until now. (short abstract due to size limitations - full abstract in the manuscript)

cond-mat.mtrl-sci↗

arXiv2018

Modulation of superconductivity by quantum confinement in doped strontium titanate

Quantum confinement in a thin-film geometry offers viable routes for tuning the critical properties of superconductors through modification of both density of states and pairing interaction. Low-density systems like doped strontium titanate are especially susceptible to these confinement-induced effects. In this paper, we show that the superconducting critical temperature $T_c$ is enhanced through quantum confinement in SrTiO$_3$/SrTi$_{1-x}$Nb$_x$O$_3$/SrTiO$_3$ heterostructures at $x=1\%$ concentration, by measuring resistivity transitions and the Hall carrier density for different thicknesses of the doped layer. We observe a nonmonotonic raise of $T_c$ with decreasing layer thickness at constant carrier density as estimated from the Hall effect. We analyze the results by solving a two-band model with a pairing interaction reproducing the density-dependent $T_c$ of doped SrTiO$_3$ in the bulk, that we confine to a potential well established self-consistently by the charged Nb dopants. The evolution of the theoretical $T_c$ with thickness agrees well with experiments. We point out the possible role of density inhomogeneities and suggest novel methods for engineering superconductivity in epitaxial thin films.

cond-mat.supr-con↗

arXiv2018

Signatures of nodeless multiband superconductivity and particle-hole crossover in the vortex cores of FeTe$_{0.55}$Se$_{0.45}$

Scanning tunneling experiments on single crystals of superconducting FeTe$_{0.55}$Se$_{0.45}$ have recently provided evidence for discrete energy levels inside vortices. Although predicted long ago, such levels are seldom resolved due to extrinsic (temperature, instrumentation) and intrinsic (quasiparticle scattering) limitations. We study a microscopic multiband model with parameters appropriate for FeTe$_{0.55}$Se$_{0.45}$. We confirm the existence of well-separated bound states and show that the chemical disorder due to random occupation of the chalcogen site does not affect significantly the vortex-core electronic structure. We further analyze the vortex bound states by projecting the local density of states on angular-momentum eigenstates. A rather complex pattern of bound states emerges from the multiband and mixed electron-hole nature of the normal-state carriers. The character of the vortex states changes from hole-like with negative angular momentum at low energy to electron-like with positive angular momentum at higher energy within the superconducting gap. We show that disorder in the arrangement of vortices most likely explains the differences found experimentally when comparing different vortices.

cond-mat.supr-con↗

arXiv2018

The Maunakea Spectroscopic Explorer Book 2018

(Abridged) This is the Maunakea Spectroscopic Explorer 2018 book. It is intended as a concise reference guide to all aspects of the scientific and technical design of MSE, for the international astronomy and engineering communities, and related agencies. The current version is a status report of MSE's science goals and their practical implementation, following the System Conceptual Design Review, held in January 2018. MSE is a planned 10-m class, wide-field, optical and near-infrared facility, designed to enable transformative science, while filling a critical missing gap in the emerging international network of large-scale astronomical facilities. MSE is completely dedicated to multi-object spectroscopy of samples of between thousands and millions of astrophysical objects. It will lead the world in this arena, due to its unique design capabilities: it will boast a large (11.25 m) aperture and wide (1.52 sq. degree) field of view; it will have the capabilities to observe at a wide range of spectral resolutions, from R2500 to R40,000, with massive multiplexing (4332 spectra per exposure, with all spectral resolutions available at all times), and an on-target observing efficiency of more than 80%. MSE will unveil the composition and dynamics of the faint Universe and is designed to excel at precision studies of faint astrophysical phenomena. It will also provide critical follow-up for multi-wavelength imaging surveys, such as those of the Large Synoptic Survey Telescope, Gaia, Euclid, the Wide Field Infrared Survey Telescope, the Square Kilometre Array, and the Next Generation Very Large Array.

astro-ph.IM↗