Detection of a Chirality-Induced Spin Selective Quantum Capacitance in α-Helical Peptides

Advanced Kelvin probe force microscopy simultaneously detects the quantum capacitance and surface potential of an α-helical peptide monolayer. These indicators shift when either the magnetic polarization or the enantiomer is toggled. A model based on a triangular quantum well in thermal and chemical equilibrium and electron–electron interactions allows for calculating the electrical potential profile from the measured data. The combination of the model and the measurements shows that no global charge transport is required to produce effects attributed to the chirality-induced spin selectivity effect. These experimental findings support the theoretical model of Fransson et al. Nano Letters2021, 21 (7), 3026–3032. Measurements of the quantum capacitance represent a new way to test and refine theoretical models used to explain strong spin polarization due to chirality-induced spin selectivity.

RP-HPLC was performed on a Shiseido C18 (5 µm, 4.6 mm I.D. x 250 mm) column at a flow rate of 1 mL/min using the following method: 10% solvent B for 3 min, followed by a gradient of 10 to 95% solvent B over 14 min and 95% solvent B for 3 min.Preparative RP-HPLC was performed on a YMC C18 (5 µm, 20 mm I.D. x 250 mm) column at a flow rate of 10 mL/min using the following method: 20% solvent B for 5 min, followed by a two-step gradient of 20 to 40% solvent B over 10 min and 40 to 75% solvent B over 20 min.Data was acquired using EZChrom Elite (Version 3.3.2).

High-resolution mass spectrometry (HR-MS)
HR-MS spectra were obtained by the mass spectrometry service of the Laboratory of Organic Chemistry at ETH Zürich on a Bruker Daltonics MaXis ESI-QTOF spectrometer.

Sample fabrication
Substrate fabrication Heavily n-doped silicon wafers of 525 µm thickness are cleaned in O 2 plasma for 2min at 500W.A 2 nm thick Ti-adhesion layer, followed by a 10nm Ni and 5 nm of Au, is subsequently e-beam evaporated in an Evatec BAK501 LL at a rate of 0.1 nm/s and a pressure of 1.3 10 −6 mbar.
Self-assembled monolayer adsorption The substrates are cut into samples of 5x5mm.
Each piece is split in half using a diamond pen.The two half-substrates are cleaned with Acetone, IPA, and DI-water in an ultrasonic bath for 10 min each and finally dried with a stream of dry air before immersing the sample into analytical grade EtOH to sonicate for further 10min.In parallel 1 mM L-or D-Peptide in EtOH solvent is prepared and filled into 1 mL plastic Eppendorf cuvettes.Subsequently, one half substrate is transferred into each peptide solution without intermediate drying and incubated for 48 h to form a selfassembled monolayer (SAM).After SAM formation, the substrates are washed three times in analytical grade EtOH by gently shaking for 2min to wash away unbound peptides prior to drying under a stream of N 2 .
Sample mounting for AFM Immediately after drying, the two-half substrates are placed centered onto a neodymium magnet (2 mm thick, 12 mm diameter, S-12-02-N, obtained from www.supermagnete.ch,Switzerland) so that the fracture line is merged.The rough fracture line self-aligns the sample effortlessly within a sub-micron precision several times.
In this position, the substrates were fixed with silver paste.It was ensured that the silver paste G 3303B, Leitsilber-deutsches Fabrikat PLANO (Wetzlar,Germany) established direct electrical contact between the metal coatings of the sample and the magnet.The magnetic orientation is checked with a magnetic compass.The magnet is then placed onto an Asylum specimen holder (2 mm thick, 15 mm diameter) and transferred into the environmental chamber of the AFM, where the silver paste is dried under a constant stream of N 2 .After 30 min the chamber is reopened to finally position the sample, connect the grounds, to install a tip OMCL-AC160TS Olympus (Tokyo, Japan) for AFM lithography, and check the electrical connection between the sample and ground (the measured resistance is usually below 10 Ω).

AFM lithography Clean metal reference areas are established with AFM lithography
on each enantiomer half-sample.For this purpose, the tip is placed within 300 µm of the fracture line so that the tip position can be switched to the opposite side of the fracture (to the opposite enantiomer SAM) without opening the gas chamber.The tip is then fully calibrated (usually k = 22nN/nm, ω 0 =296 kHz, Q = 150), and an overview scan in noncontact Amplitude Modulated (AM) AFM mode over 20x20 µm is performed to ensure a flawless monolayer.If successful, the tip is brought into hard contact, and subsequent scans are performed in contact mode at an applied force of 1.3 µN to shear off adsorbed molecules.
The 500x500 nm wide area was scanned three times at scanning angles of 0 • , 90 • , and finally again at 0 • to remove all molecules.A control experiment on a sample with no adsorbed monolayer showed no signs of destruction of the scratched gold surface.After the lithography, the result is checked with the same tip in non-contact AM-AFM mode.Finally, the precise location of the scratched area is documented to locate the position for subsequent KPFM measurements.On each half sample, three reference areas were cleaned.The thickness of the monolayer is t = 1.07 ± 0.13 nm.The length of a 10-mer α-helix is around 1.5 nm, translating to a tilt-angle of 46 ±8 • (see Fig. S6).Tilting is consistent with angles given in literature. 1 After lithography, the sample is kept under N 2 and only exposed to ambient air when exchanging the AFM tip or flipping the magnetic orientation.Comparison between the blank substrate and scratched substrate The surface potential difference is sensitive to any adsorbed contaminants.To check whether AFM lithography reliably removes all peptides from the surface.The U CPD of a scratched reference area and the U CPD of the blank sample (only immersed in analytical grade EtOH for 48 h) were compared.No significant difference is found, confirming that the AFM lithography process removed the peptides to create a reliable reference.

AFM measurements
General instrument preparation A fresh Pt coated tip Pt OMCL-AC240TS Olympus (Tokyo, Japan) is mounted, and the magnetization direction is adjusted into the desired direction (see Sample preparation for KPFM).Prior to any measurements, the sample is kept at least 1h under N 2 in the AFM to stabilize the measurement system and minimize humidity.The temperature control is kept active to regulate a temperature of 31 • C.After relocating the reference areas with AM-AFM, the instrument is calibrated.The used tip was calibrated with getReal TM calibration to find ω 0 = 75.821kHz, k = 2.32 nN/nm, Q = 131 and the optical lever sensitivity respectively the amplitude A = 9.5 nm for the published data set.
Measurement Scheme First, a FM-KPFM FM-AFM scan is performed at each 2.5x2.5 µm reference area.Then a time-domain domain measurement is recorded first on the reference area, then on the SAM at 1 µm away from the reference area.Finally, a second FM-KPFM FM-AFM scan is performed to ensure that the tip did not pick up debris and no damage happened to the sample or the tip during time-domain measurements.This is repeated for all the reference areas prior to switching the magnetic orientation.The magnet is switched at least twice -so that one magnetic configuration has been measured twice to ensure the stability of the system over time.Only data from the identical reference area are compared.

FM-AFM Kelvin probe force microscopy
The FM-AFM measurements are based on a single-pass method described elsewhere in detail. 2 In essence, the mechanical oscillation is kept at resonance with a phase-locked loop having a bandwidth of 400 Hz and a range of

Time-domain Kelvin distance curve measurements
The time-domain measurements 3 are recorded open-loop with the lock-in amplifier recording phase, amplitude of the mechanical oscillation, the applied tip voltage and the stage position z at a rate of 3.6 kHz.The lock-in bandwidth is 5 kHz.The mechanical oscillation is modulated with an electrical signal of ω m =10 Hz at an amplitude of 2 V.A static potential U DC is added to the modulation to compensate for contact potential difference.The applied voltage corresponds to the U CPD measured in the FM-KPFM scan.The free, mechanical amplitude is adjusted to 9nm.The z-stage is moved up and down to acquire height-dependent data in a triangular waveform with an amplitude of 60 nm and a velocity of 0.5 nm/s.The return is triggered at a phase shift of 35 • -corresponding to a tip-sample spacing of circa 10 nm.After an approach and retract curve are completed, the x-y position is stepped on a 4x4 raster covering an area of 100x100nm to average out local variations of the film.

Temperature induced effects
Reversible temperature-induced effects would further support an intrinsic mechanism.5][6] The experimental setup allows for the gathering of temperature-dependent measurements in a limited range between 31 • C to 60 • C.However, the measurements were not reproducible in the sense that after a heating-cooling cycle, the surface potential changed irreversibly.Heating the sample also leads to a reversible entropic conformation change of the polypeptides, 4 changes in the magnetization(direction) inside the nickel layer by affecting the chemical potential.It also partially demagnetizes the used magnets since the applied temperature is close to the Curie temp of the magnets.The experimental disentanglement of those effects would exceed the scope of this publication.Figure S7: FM-KPFM measurement setup.The measurement system can be described as a force-coupled system consisting of a mechanical, driven oscillator (a) and an electrical equivalent circuit (b).In time-domain KPFM the frequency shift of the mechanical oscillator is recorded while it is mechanically excited (c).An applied voltage between the tip and the sample modulates the electronic states of the sample and generates modulated fields which can be deduced as the phase shift of the mechanical oscillator.The higher the magnitude of the electric field, the lower the oscillator phase.A simple capacitive coupling between the sample and tip is expected for a metallic sample and leads to a Kelvin parabola (c).

Derivation of KPFM mesurands
Dynamic AFM is sensitive to changes in the oscillator properties determined by the phase, resonance frequency, and amplitude.A change in the spring constant k at fixed excitation frequency ω induces a difference in the phase and amplitude.
Modulating an electrical signal enhances the specificity of the sensor to electrostatic interaction forces between the sample and the tip.The system is a driven mechanical oscillator and an electrical circuit coupled via (electric) force field F ts .Fig. S7 illustrates the equivalent circuit of the electrical system.In the low-frequency range and far away from the surface, the circuit is dominated by parasitic capacitance and resistances and is practically independent of the atomic tip position d.Since the time constant is much shorter than the applied electrical modulation signal, the tip voltage is equivalent to the applied signal.
A harmonic oscillator differential equation models the cantilever dynamics 2,7,8 where Q is the quality factor of the cantilever resonance, q the deflection of the cantilever, and a(t) the external excitation signal.The force field F ts is evaluated at the tip-sample distance z ts .
For the analysis shown here, only the non-contact case is considered with z ts > 0. Under these circumstances, a periodic excitation a(t) = a 0 cos(ωt+φ e ) produces a periodic response of the resonator which is driven at a constant frequency very close to the resonance, implying This motivates to write F ts and q as a Fourier series, where The strong resonance enhancement of the fundamental harmonic reduces the influence of higher harmonics, such that further analysis can be restricted to the fundamental mode.
Inserting the harmonic ansatz into Eq.( 1) and solving for static deflection, amplitude, and frequency leads to ) with ) The time-odd contribution f o,1 affects the quality factor of the resonator due to dissipation.Away from the surface, a constant damping can be assumed in good approximation.
The time-even contribution f e,1 influences the cantilever resonance frequency.The shift in resonance frequency is and translates immediately in a change in phase assuming constant Q and a constant ω not to far away from ω 0 can be linearized to and can be calculated for any force-distance law, provided that the first (even) Fourier component exists and the harmonic approximation applies.
In KPFM the interaction force is modulated with an electric force. 9The electrostatic energy 10 stored in the tip-sample capacitance is E = − 1 2 C∆U 2 , the force is thus assuming that the electrical potential difference is independent of the tip-sample distance.
This assumption is only valid at tip-sample distances when there is no significant overlap between the quantum mechanical wave functions of the charges of the tip and sample.The potential modulation is of the form U (t) = U DC + U AC cos(ω m t) with the modulation frequency ω m ≪ ω 0 .The Fourier coefficients will thus have time-modulated components as well.Using Eq. ( 8) the component is In the harmonic approximation, the tip position during a (fast) oscillation is x = A cos(ωt) by integration by parts to obtain the cycle-averaged force gradient.
Close to the surface d/R ≤ 1, the electric tip interactions are limited to the appex. 2 The interaction at the tip with an effective radius R is modeled with a sphere at a distance h from a metallic plate with the approximation found in Hudlet et al. 11 and and can be used to evaluate the cycle-averaged capacitance.Usual approximations 8 used in contact mechanic AFM are not possible since all length scales are similar.Thus, the gradient is numerically evaluated as a function of minimal tip-sample distance d t Evaluating the above equation and using Eq. 12, the Kelvin parabola for a slow modulation is obtained: Modulating with a signal of the form with compensating the average electrostatic force setting U DC = U CPD , the signal at ω m is minimized and the final signal becomes If a force on the cantilever changes instantaneously, this will affect the dynamics instantaneously, but transients slow the change in amplitude, phase (or resonance frequency) 7 and add an additional phase delay ∆ϕ.Writing the transfer-function for phase detection using the Laplace transform L and ignoring the electronic phase-detecting system and assuming a small phase change close to resonance ∆ϕ yields where Θ(t) is the unit step function.It results in a low pass filter with a cut-off at the critical frequency ω c = ω 0 /2Q ≈ 320 Hz.For slow harmonic phase modulations (s ≪ ω m /ω c ) the detected signal is low pass filtered which introduces a phase delay into the Kelvin parabola of Since ω m /ω c ≪ 1, the phase delays are small, and the observed hysteresis of the phase signal is ∆φ(t) = φ(t)−φ(t+π/ω m ) due to the phase delays expanding φ(0+ϕ) = φ(0)+ϕ∂φ/∂ϕ| ϕ=0 around null phase delay All parameters in this expression are obtained independently from time-resolved measurements and be used as a calibration.
In case of dynamic contact potential difference through spin-moment locking ∆U ↑↓ , the Kelvin parabola shifts by ∆U ↑↓ depending upon the voltage sweep direction (see Fig. S8).
Simple electronic circuit analysis yields that an additional phase adds to Eq. 29 due to the

Derivation of electrostatic potential
The Hamiltonian of the electronic system is where m * is the reduced electron mass, ϕ(⃗ r i ) the potential of the i-th electron position and G(⃗ r i , ⃗ r j ) the Coulomb interaction inside the molecule electron gas.
We will look at the electron envelope function of a molecule, omitting 12 chemical bonding details assuming a triangular quantum well.The triangular quantum well will account for the polar nature of chiral molecules and the charge reorganization of adsorbed molecules. 13e molecular layer is assumed to be homogeneous in in-plane directions.
Assuming that the wave function does not penetrate the metal layer simplifies calculations; therefore, the potential is infinite in the left half space.It is thus sufficient to consider z > 0. The electron-electron interactions are treated within the self-consistent Hartree approximation.The approach is inspired by the treatment of a 2D electron gas 14 and is reduced to 1D.The single particle-envelope wave function ψ n fulfills the Hartree equation A good approximation for the ground state of the Fang-Howard variational wave function is The variational parameter b s defines the penetration depth of the wavefunction such that the system is in thermodynamic equilibrium with the metal.It can also be expressed in terms of the expected charge position ⟨z⟩ = 3/b s .Within the approach, an upper bound for the system's ground energy per unit area is The energy is composed of a single particle kinetic term ⟨ T ⟩ and an electron-electron inter- .
In order to find the Hartree interaction energy, the electron density distribution is and applying Poisson's equation and after integrating the Coulomb interaction energy is where n s corresponds to the area-related electron density trapped in the potential.The expected energy per area of the bound electrons is The system is in thermal equilibrium with the substrate at a chemical potential µ and can exchange electrons with the gold-nickel stack.The grand-canonical partition function of

Figure S6 :
Figure S6: Topography images of the L-peptide-monolayer under north (red) and south (grey) magnetic polarizations cross-section.Solid lines show the mean value, dashed lines the confidence intervals of the height measurements.

5
kHz controlling the topography feedback.The feedback parameters for the phase-locked loop are optimized based on the transfer function of the actual tip.The amplitude of the mechanical oscillation is kept constant at around 9 nm with an amplitude feedback loop adjusting the optothermal drive power.The mechanical oscillation at around ω 0 =75 kHz is modulated with a voltage signal at ω m = 1.4 kHz and an amplitude of 2 V.The side-bands at ω 0 ± ω m and ω 0 ± 2ω m are demodulated at a bandwidth of 100 Hz each.The Kalman filter optimizes the phase of the demodulation signals such that all the signal is in the xcomponent and adjusts the U DC = U CPD to minimize the first side-band.All the feedback loops are run on the lock-in amplifier except for the topography feedback loop.All feedback loops are monitored to operate correctly during scanning.The scans are performed at a speed of 500 nm/s and at a setpoint of 16.5 Hz, which approximately corresponds to an average tip-sample distance of 17 nm.For each scan, the channels for the topography, the frequency-shift (topography error signal), the amplitude drive power, the U CPD , and ∂ 2 C/∂z 2 signal are recorded in trace and retrace.

Figure S8 :
Figure S8: Hypothetical KFPM equivalent circuit for chiral materials.The hand and magnet symbols indicate the configurations (a) L-peptide with magnet pointing to south (b) L-peptide with magnet pointing to north (c) D-peptide with magnet pointing south, and (d) D-peptidewith magnet pointing north.Switching the enantiomer leads to an exchange of the on-set voltages of the reversed diodes, whereas switching the magnetic polarisation of the substrate switches the probed I-V characteristic (dark red) and unprobed one (light red).

e 2 n s ϵ 1 2b s 6 −
imposing that the field at the interface corresponds to the field of the dipole moment of the molecule ∂V H setting V H (0) = 0 with no loss of generality.Solving the equation leads toV H (z) = ((b s z) 2 + 4b s z + 6)e −bsz ,