arXiv subjects

Christian Loppacher

Publications and source records attributed to Christian Loppacher.

4 recordsLinked to original sources

arXiv2026

Inverse heterodyne effect in bimodal Kelvin probe force microscopy

Heterodyne Kelvin probe force microscopy (He-KPFM) enables high-sensitivity electrostatic measurements by converting a bias-modulated interaction into a resonant response at a higher cantilever eigenmode. While the "direct" heterodyne actuation of the second eigenmode is well established, the dynamical back-action of this heterodyne-driven motion on the fundamental eigenmode has remained largely unexplored, particularly in open-loop operation where the second mode is excited to a finite amplitude. Here, we demonstrate an inverse heterodyne effect: a force component generated by heterodyne frequency conversion acts back on the first eigenmode and produces measurable inter-mode energy exchange. The analysis combines a bimodal virial and power-balance framework with a non-truncated description of the tip-surface capacitance-gradient dynamics developed and validated in a companion manuscript submitted concurrently to the same journal. On this basis, we derive closed-form expressions linking inverse heterodyne coupling to the experimentally accessible observables of non-contact AFM open-loop amplitude-modulated He-KPFM. The theory predicts that inverse heterodyne coupling appears predominantly in the dissipation channel, with a sharply resonant dependence on the demodulation frequency near the second-eigenmode resonance, while its conservative contribution to the frequency shift remains comparatively weaker under typical conditions. Ultrahigh-vacuum experiments validate these predictions and isolate the inverse heterodyne signature through frequency- and voltage-dependent measurements. Beyond KPFM, this work connects heterodyne force microscopy to a broader class of driven multimode systems in which nonlinear coupling and frequency conversion produce inter-mode energy transfer, back-action, and dissipation-based observables.

cond-mat.mtrl-sci↗

arXiv2026

On the capacitance gradient description in Heterodyne Kelvin Probe Force Microscopy

Kelvin probe force microscopy (KPFM) probes local surface-potential variations through the electrostatic force between a conductive tip and a surface, which depends on the potential difference and the tip-surface capacitance gradient (CG). In heterodyne KPFM, the oscillating tip is usually treated by combining a bias-modulated electric field with a first-order truncated Taylor-series expansion of the CG. Although convenient, this treatment is limited to a poorly defined small-amplitude regime and leaves the convergence of the series unresolved. Here, we establish a rigorous spectral description of the CG dynamics and of the resulting electrostatic force beyond this approximation. We formulate a non-truncated Taylor-series description of the CG and prove its convergence for a realistic Hudlet-based capacitance model in both monomodal and bimodal motion. In the monomodal case, we show the equivalence between Fourier-series and Taylor-series descriptions, derive explicit expressions for the dominant Fourier coefficients, and introduce order-truncation criteria that replace the usual qualitative notion of a small-amplitude regime. We then extend the formalism to bimodal motion and derive the effective CG coefficients governing the static, first-eigenmode, and second-eigenmode components of the electrostatic interaction. Numerical simulations confirm the convergence of the Taylor-based coefficients toward the Fourier coefficients and support the truncation-regime hierarchy in both configurations. This work establishes the formal basis for describing electrostatic force components and AFM observables in open-loop heterodyne experiments and provides a general framework for CG dynamics in multimode force microscopy involving nonlinear electromechanical coupling and frequency conversion.

cond-mat.mtrl-sci↗

arXiv2009

Understanding the atomic-scale contrast in Kelvin Probe Force Microscopy

A numerical analysis of the origin of the atomic-scale contrast in Kelvin probe force microscopy (KPFM) is presented. Atomistic simulations of the tip-sample interaction force field have been combined with a non-contact Atomic Force Microscope/KPFM simulator. The implementation mimics recent experimental results on the (001) surface of a bulk alkali halide crystal for which simultaneous atomic-scale topographical and Contact Potential Difference (CPD) contrasts were reported. The local CPD does reflect the periodicity of the ionic crystal, but not the magnitude of its Madelung surface potential. The imaging mechanism relies on the induced polarization of the ions at the tip-surface interface owing to the modulation of the applied bias voltage. Our findings are in excellent agreement with previous theoretical expectations and experimental observations.

physics.atm-clus↗

arXiv2008

Analytical Approach to the Local Contact Potential Difference on (001) Ionic Surfaces: Implications for Kelvin Probe Force Microscopy

An analytical model of the electrostatic force between the tip of a non-contact Atomic Force Microscope (nc-AFM) and the (001) surface of an ionic crystal is reported. The model is able to account for the atomic contrast of the local contact potential difference (CPD) observed while nc-AFM-based Kelvin Probe Force Microscopy (KPFM) experiments. With the goal in mind to put in evidence this short-range electrostatic force, the Madelung potential arising at the surface of the ionic crystal is primarily derived. The expression of the force which is deduced can be split into two major contributions: the first stands for the coupling between the microscopic structure of the tip apex and the capacitor formed between the tip, the ionic crystal and the counter-electrode; the second term depicts the influence of the Madelung surface potential on the mesoscopic part of the tip, independently from its microscopic structure. These short-range electrostatic forces are in the range of ten pico-Newtons. When explicitly considering the crystal polarization, an analytical expression of the bias voltage to be applied on the tip to compensate for the local CPD, i.e. to cancel the short-range electrostatic force, is derived. The compensated CPD has the lateral periodicity of the Madelung surface potential. However, the strong dependence on the tip geometry, the applied modulation voltage as well as the tip-sample distance, which can even lead to an overestimation of the real surface potential, makes quantitative KPFM measurements of the local CPD extremely difficult.

physics.atm-clus↗