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Christoph Schmid

Publications and source records attributed to Christoph Schmid.

At least 19 recordsLinked to original sources
arXiv2026

Tailoring the properties of YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ thin films by 30 keV He$^+$ irradiation: An enabling route to superconducting device nanopatterning

Focused helium ion beam (He-FIB) irradiation with 30 keV ions is a key tool for nanoscale patterning and defect engineering in high transition temperature (Tc) cuprate superconducting devices, yet its usable fluence window is constrained by the competing requirements of reliable superconductivity suppression and minimal structural degradation. In this work, we provide a comprehensive dataset on the effects of large-area 30 keV He+ ion exposure on the electric transport and superconducting properties of epitaxial YBa2Cu3O7 (YBCO) thin films. X-ray diffraction shows a fluence-driven loss of crystalline order accompanied by an out-of-plane lattice expansion and an orthorhombic-to-tetragonal transition, culminating at predominant amorphization at the highest fluence of 1 x 10^16 cm^-2. Raman spectra exhibit increasing disorder while lacking signatures of oxygen depletion, indicating that irradiation mainly generates oxygen-related Frenkel defects rather than changing the carrier concentration. Consistently, with increasing fluence, the normal-state resistivity \rho_N(T) at temperature T above Tc increases strongly, while d \rho_N/d T remains nearly unchanged at moderate fluence. The suppression of Tc is accurately described by Abrikosov-Gor'kov pair breaking and reaches complete quenching of superconductivity at 4.5 x 10^15 cm^-2. The anisotropic upper critical fields decrease approximately exponentially with increasing fluence, the vortex activation energy is reduced, and the anisotropy drops, in contrast to oxygen-depleted YBCO. Hall-angle analysis confirms a nearly constant carrier density but a systematic increase in defect scattering and reduced mobility, consistent with a crossover toward the dirty limit at high fluence. These results establish quantitative fluence thresholds and a practical operational window for He-FIB nanopatterning of YBCO quantum circuits.

cond-mat.supr-con↗
arXiv2026

Structural Changes and Transport Properties of $\mathrm{YBa_2Cu_3O_7}$ Locally Modified by a He$^+$ Focused Ion Beam

Irradiation of a material with ions can cause various defects that can lead to structural phase transitions and the modification of the material's properties. Here we study the irradiation of the epitaxyally grown thin films of the high-temperature superconductor $\mathrm{YBa_2Cu_3O_7}$ with $30\,\mathrm{keV}$ He$^{+}$ ions which leads to the expansion of the crystal lattice, decrease of the critical temperature $T_c$ and eventually transition to an insulator. Fabrication of such insulating regions with a focused He-Ion beam with a spot size of $\sim 10\,\mathrm{nm}$ is a powerful technique for fabrication of superconducting nano-devices. Using low-temperature resistivity measurements, diffraction with a nanofocused X-ray beam and atomic force microscopy, we investigated how the structure and the electric transport properties of $\mathrm{YBa_2Cu_3O_7}$ depend on the irradiation dose in a range $10$--$100\,\mathrm{ions/nm^2}$ and on the lateral size of the irradiated area in a range $30$--$5000\,\mathrm{nm}$.

cond-mat.supr-con↗
arXiv2026

Dually tunable YBCO coplanar waveguide resonators based on helium-ion-generated Josephson inductances

Superconducting microwave circuits with and without Josephson inductances are the Swiss Army knife for many experiments and technologies from quantum information science to astrophysical particle detectors. Despite a large variety of existing circuit types, thin film materials and Josephson junction technologies, a flexible and reliable platform for high-magnetic-field and high-temperature applications is yet to be found. In this manuscript, we investigate coplanar waveguide cavities made of the high-temperature cuprate superconductor YBa$_2$Cu$_3$O$_7$ (YBCO), integrated with Josephson inductances and quantum interferometers that are generated by the controlled local irradiation of the YBCO with a focused helium ion beam. We obtain strongly flux-tunable microwave resonators, which not only display periodic interferometer oscillations of resonance frequency and decay rate, but also a superimposed Fraunhofer-like modulation pattern. The latter originates from the magnetic field tuning of the individual Josephson junction critical currents due to the out-of-plane junction barriers. It allows adjusting resonance frequency and flux responsivity independently of each other, potentially enabling tunable microwave circuits with low sensitivity to external magnetic-field noise over a broad range of frequencies. Finally, we investigate the temperature dependence of the cavities, show that they have promising characteristics up to 14$\,$K, and present a model for the junction-induced cavity losses.

quant-ph↗
arXiv2025

YBa$_2$Cu$_3$O$_7$ nano-constriction Josephson junctions and SQUIDs fabricated by focused helium-ion-beam irradiation

By focused $30\,\mathrm{keV}$ He ion beam irradiation, epitaxially grown YBa$_2$Cu$_3$O$_7$ (YBCO) thin films can be driven from the superconducting to the insulating state with increasing irradiation dose. A properly chosen dose suppresses superconductivity down to $4\,\mathrm{K}$, while crystallinity is still preserved. With this approach we create areas of normal-conducting YBCO that can be used to define resistively shunted constriction-type Josephson junctions (cJJs) on the nanometer scale. We also demonstrate that the fabricated cJJs can be incorporated in direct current superconducting quantum interference devices and can be used as detector junctions in THz antennas.

cond-mat.supr-con↗
arXiv2024

Non-volatile multi-state electrothermal resistive switching in a strongly correlated insulator thin-film device

Strongly correlated insulators, such as Mott or charge-transfer insulators, exhibit a strong temperature dependence in their resistivity. Consequently, self-heating effects can lead to electrothermal instabilities in planar thin film devices of these materials. When the electrical bias current exceeds a device-specific threshold, the device can switch from a high- to a low-resistance state through the formation of metallic filaments. However, since the current and temperature redistribution effects that create these filaments are sustained by local Joule heating, a reduction of the bias current below a second (lower) threshold leads to the disappearance of filaments, and the device switches back into the high-resistance state. Hence, electrothermal resistive switching is usually volatile. Here, on the contrary, we report on non-volatile resistive switching in a planar $\mathrm{NdNiO}_3$ thin-film device. By combining electrical transport measurements with optical wide-field microscopy, we provide evidence for a metallic filament that persists even after returning the bias current to zero. We attribute this effect to the pronounced hysteresis between the cooling and heating branches in the resistance vs. temperature dependence of the device. At least one hundred intermediate resistance states can be prepared, which are persistent as long as the base temperature is kept constant. Further, the switching process is non-destructive, and thermal cycling can reset the device to its pristine state.

physics.app-ph↗
arXiv2024

YBa$_2$Cu$_3$O$_7$ Josephson diode operating as a high-efficiency ratchet

Using a focused He$^+$ beam for nanopatterning and writing of Josephson barriers we fabricated specially shaped Josephson junctions of in-line geometry in YBa$_2$Cu$_3$O$_7$ thin film microbridges with an asymmetry ratio of critical currents of opposite polarities (non-reciprocity ratio) $\approx 7$ at optimum magnetic field. Those Josephson diodes were subsequently used as ratchets to rectify an applied ac current into a dc voltage. We also demonstrate the operation of such a ratchet in the loaded regime, where it produces a nonzero dc output power and yields a thermodynamic efficiency of up to $75\,\mathrm{\%}$. The ratchet shows record figures of merit: an output dc voltage of up to $212\,\mathrm{\mu V}$ and an output power of up to $0.2\,\mathrm{nW}$. The device has an essential area $\approx 1\,\mathrm{\mu m^2}$. For rectification of quasistatic Gaussian noise, the figures of merit are more modest, however the efficiency can be as high as for the deterministic ac drives within some regimes. Since the device is based on YBa$_2$Cu$_3$O$_7$, it can operate at temperatures up to $\sim40\,\mathrm{K}$, where more noise is available for rectification.

cond-mat.supr-con↗
arXiv2024

Vortex matching at 6 T in YBa$_2$Cu$_3$O$_{7-δ}$ thin films by imprinting a 20 nm-periodic pinning array with a focused helium ion beam

Controlled engineering of vortex pinning sites in copper-oxide superconductors is a critical issue in manufacturing devices based on magnetic flux quanta. To address this, we employed a focused He-ion beam (He-FIB) to irradiate thin YBa$_2$Cu$_3$O$_{7-δ}$ films and create ultradense hexagonal arrays of defects with lattice spacings as small as 20 nm. Critical current and magnetoresistance measurements demonstrate efficient pinning by an unprecedentedly high matching field of 6 T visible in a huge temperature range from the critical temperature $T_c$ down to 2 K. These results show that He-FIB irradiation provides excellent opportunities for the development and application of superconducting fluxonic devices based on Abrikosov vortices. In particular, our findings suggest that such devices can operate at temperatures far below $T_c$, where superconductivity is robust.

cond-mat.supr-con↗
arXiv2023

The Gravito-Maxwell Equations of General Relativity in the local reference frame of a GR-noninertial observer

We show that the acceleration-difference of neighboring free-falling particles (= geodesic deviation) measured in the local reference frame of a GR-noninertial observer is not given by the Riemann tensor. With the gravito-electric field of GR defined as the acceleration of free-falling quasistatic particles relative to the observer, the divergence of the gravito-electric field measured in the reference frame of a GR-noninertial observer is different from the Ricci curvature $R^0_{\,\,0}$. We derive our exact, explicit, and simple gravito-Gauss law for the divergence of the gravito-electric field in our new reference frame of a GR-noninertial observer with his LONB (Local Ortho-Normal Basis) and his LONB-connections in his time and 3-directions: the sources of the divergence of the gravito-electric field are contributed by all fields including the GR-gravitational fields, gravito-electric and gravito-magnetic. In the reference frame of a GR-inertial observer our gravito-Gauss law coincides with Einstein's $R^0_{\,\,0}$ equation, which does not have gravitational fields as sources. We derive the gravito-Ampere law, the gravito-Faraday law and the law for the divergence of the gravito-magnetic field. The densities of energy, momentum, and momentum-flow of GR-gravitational fields are local observables, but depend on observer with his local reference frame: these quantities are zero if measured by a GR-inertial observer. For a GR-noninertial observer the sources of gravitational energy, momentum, and momentum-flow densities have the opposite sign from the electromagnetic and matter sources. In the gravito-Gauss law the sources contributed by gravitational energy and momentum-flow densities have a repulsive effect on the gravitational acceleration-difference of particles.

gr-qc↗
arXiv2021

Semiconductor-Bloch Formalism: Derivation and Application to High-Harmonic Generation from Dirac Fermions

We rederive the semiconductor Bloch equations emphasizing the close link to the Berry connection. Our rigorous derivation reveals the existence of two further contributions to the current, in addition to the frequently considered intraband and polarization-related interband terms. The extra contributions become sizable in situations with strong dephasing or when the dipole-matrix elements are strongly wave-number dependent. We apply the formalism to high-harmonic generation for a Dirac metal. The extra terms add to the frequency-dependent emission intensity (high-harmonic spectrum) significantly at certain frequencies changing the total signal up to a factor of 10.

cond-mat.mes-hall↗
arXiv2016

Einstein's $R^{\hat{0} \hat{0}}$ equation for non-relativistic sources derived from Einstein's inertial motion and the Newtonian law for relative acceleration

With Einstein's inertial motion (free-falling and non-rotating relative to gyroscopes), geodesics for non-relativistic particles can intersect repeatedly, allowing one to compute the space-time curvature $R^{\hat{0} \hat{0}}$ exactly. Einstein's $R^{\hat{0} \hat{0}}$ for strong gravitational fields and for relativistic source-matter is identical with the Newtonian expression for the relative radial acceleration of neighboring free-falling test-particles, spherically averaged.--- Einstein's field equations follow from Newtonian experiments, local Lorentz-covariance, and energy-momentum conservation combined with the Bianchi identity.

gr-qc↗
arXiv2016

Einstein's equations from Einstein's inertial motion and Newton's law for relative acceleration

We show that Einstein's $R^{\hat{0} \hat{0}}$ equation for nonrelativistic matter and strong gravitational fields is identical with Newton's equation for relative radial acceleration of neighbouring freefalling particles, spherically averaged. These laws are explicitely identical with primary observer's (1) space-time slicing by radial 4-geodesics, (2) radially parallel Local Ortho-Normal Bases, LONBs, (3) Riemann normal 3-coordinates. Hats on indices denote LONBs. General relativity follows from Newton's law of relative acceleration, Einstein's inertial motion, Lorentz covariance, and energy-momentum conservation combined with Bianchi identity. The gravitational field equation of Newton-Gauss and Einstein's $R^{\hat{0} \hat{0}}$ equation are identical and linear in gravitational field for an inertial primary observer.--- Einstein's equivalence between fictitious forces and gravitational forces is formulated as equivalence theorem in the equations of motion. With this, the gravitational field equation of 19th-century Newtonian physics and Einstein's equation for $R^{\hat{0} \hat{0}}$ are identical and bilinear in the gravitational forces for non-inertial primary observers.--- $R^{\hat{0} \hat{0}} = - div \vec{E}_g$ and $2 R^{\hat{i} \hat{0}} = - (curl \vec{B}_g)^{\hat{i}}$ hold exactly for inertial primary observers, if one uses our LONB's. The gravitational $\vec{E}_g, \vec{B}_g $ are measured exactly with quasistatic particles via $(d/dt) p_{\hat{i}}$ and $(d/dt) S_{\hat{i}}$ in correspondence with the electromagnetic $\vec{E}$ and $\vec{B}$. The $(\vec{E}_g, \vec{B}_g)$ are identical with the observer's Ricci connection along his worldline, $(ω_{\hat{a} \hat{b}})_{\hat{0}}$.

gr-qc↗
arXiv2014

Exact Dragging of Inertial Axes by Cosmic Energy-Currents on the Past Light-Cone

We prove exact rotational dragging of local inertial axes (= spin axes of gyroscopes) by arbitrary cosmic energy-currents on the past light-cone of the gyroscope for linear perturbations of Friedmann-Robertson-Walker cosmologies. Hence the principle formulated by Mach holds for arbitrary linear cosmological perturbations.

gr-qc↗
arXiv2012

Newton's superb theorem: An elementary geometric proof

Newton's "superb theorem" for the gravitational inverse-square-law force states that a spherically symmetric mass distribution attracts a body outside as if the entire mass were concentrated at the center. This theorem is crucial for Newton's comparison of the Moon's orbit with terrestrial gravity (the fall of an apple), which is evidence for the inverse-square-law. Newton's geometric proof in the Principia "must have left its readers in helpless wonder" according to S. Chandrasekhar and J.E. Littlewood. In this paper we give an elementary geometric proof, which is much simpler than Newton's geometric proof and more elementary than proofs using calculus.

physics.class-ph↗
arXiv2009

Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with $K = (\pm 1, 0)$

We show that the dragging of the axis directions of local inertial frames by a weighted average of the energy currents in the universe is exact for all linear perturbations of any Friedmann-Robertson-Walker (FRW) universe with K = (+1, -1, 0) and of Einstein's static closed universe. This includes FRW universes which are arbitrarily close to the Milne Universe, which is empty, and to the de Sitter universe. Hence the postulate formulated by E. Mach about the physical cause for the time-evolution of the axis directions of inertial frames is shown to hold in cosmological General Relativity for linear perturbations. The time-evolution of axis directions of local inertial frames (relative to given local fiducial axes) is given experimentally by the precession angular velocity of gyroscopes, which in turn is given by the operational definition of the gravitomagnetic field. The gravitomagnetic field is caused by cosmological energy currents via the momentum constraint. This equation for cosmological gravitomagnetism is analogous to Ampere's law, but it holds also for time-dependent situtations. In the solution for an open universe the 1/r^2-force of Ampere is replaced by a Yukawa force which is of identical form for FRW backgrounds with $K = (-1, 0).$ The scale of the exponential cutoff is the H-dot radius, where H is the Hubble rate, and dot is the derivative with respect to cosmic time. Analogous results hold for energy currents in a closed FRW universe, K = +1, and in Einstein's closed static universe.

astro-ph↗
arXiv2006

Cosmological gravitomagnetism and Mach's principle

The spin axes of gyroscopes experimentally define local non-rotating frames. But what physical cause governs the time-evolution of gyroscope axes? We consider linear perturbations of Friedmann-Robertson-Walker cosmologies with k=0. We ask: Will cosmological vorticity perturbations exactly drag the spin axes of gyroscopes relative to the directions of geodesics to quasars in the asymptotic unperturbed FRW space? Using Cartan's formalism with local orthonormal bases we cast the laws of linear cosmological gravitomagnetism into a form showing the close correspondence with the laws of ordinary magnetism. Our results, valid for any equation of state for cosmological matter, are: 1) The dragging of a gyroscope axis by rotational perturbations of matter beyond the Hubble-dot radius from the gyroscope is exponentially suppressed, where dot is the derivative with respect to cosmic time. 2) If the perturbation of matter is a homogeneous rotation inside some radius around a gyroscope, then exact dragging of the gyroscope axis by the rotational perturbation is reached exponentially fast as the rotation radius grows beyond the H-dot radius. 3) For the most general linear cosmological perturbations the time-evolution of all gyroscope spin axes exactly follow a weighted average of the energy currents of cosmological matter. The weight function is the same as in Ampere's law except that the inverse square law is replaced by the Yukawa force with the Hubble-dot cutoff. Our results demonstrate (in first order perturbation theory for FRW cosmologies with k = 0) the validity of Mach's hypothesis that axes of local non-rotating frames precisely follow an average of the motion of cosmic matter.

gr-qc↗
arXiv2004

The Cosmological Origin of Inertia: Mach's Principle

The axes of gyroscopes experimentally define local non-rotating frames, i.e. the time-evolution of axes of inertial frames. But what physical cause governs the time-evolution of gyroscope axes? Starting from an unperturbed FRW cosmology with k=0 we consider linear cosmological vorticity perturbations and ask: Will cosmological vorticity perturbations exactly drag the axes of gyroscopes relative to the directions of geodesics to galaxies in the asymptotic FRW space? Using Cartan's formalism with local orthonormal bases we cast the laws of gravitomagnetism into a form showing the close correspondence with the laws of ordinary magnetism. Our results, valid for any equation of state, are: 1) The dragging of a gyroscope axis by rotational perturbations beyond the H-dot radius (H=Hubble constant) is exponentially suppressed. 2) If the perturbation is a homogeneous rotation inside a perturbation radius, then exact dragging of the gyroscope axis by the rotational perturbation is reached exponentially fast, as the perturbation radius gets larger than the H-dot radius. 3) The time-evolution of a gyroscope axis exactly follows a specific average of the matter inside the H-dot radius. In this sense Mach's Principle is a consequence of cosmology with Einstein gravity.

gr-qc↗
arXiv2002

Cosmological Vorticity Perturbations, Gravitomagnetism, and Mach's Principle

The axes of gyroscopes experimentally define non-rotating frames. But what physical cause governs the time-evolution of gyroscope axes? Starting from an unperturbed, spatially flat FRW cosmology, we consider cosmological vorticity perturbations (i.e. vector perturbations, rotational perturbations) at the linear level. We ask: Will cosmological rotational perturbations drag the axis of a gyroscope relative to the directions (geodesics) to galaxies beyond the rotational perturbation? We cast the laws of Gravitomagnetism into a form showing clearly the close correspondence with the laws of ordinary magnetism. Our results are: 1) The dragging of a gyroscope axis by rotational perturbations beyond the $\dot{H}$ radius (H = Hubble constant) is exponentially suppressed. 2) If the perturbation is a homogeneous rotation inside a radius significantly larger than the $\dot{H}$ radius, then the dragging of the gyroscope axis by the rotational perturbation is exact for any equation of state for cosmological matter. 3) The time-evolution of a gyroscope axis exactly follows a specific average of the matter inside the $\dot{H}$ radius for any equation of state. In this precise sense Mach's Principle follows from cosmology with Einstein Gravity.

gr-qc↗