calc_V_gate

qdflow.physics.simulation.calc_V_gate(gate_params, x, y, z, effective_peak=None)

Calculates the potential due to a single gate.

This model assumes the gate behaves like a infinite cylindrical conductor of radius rho, centered at x = mean, z = -h, with axis parallel to the y-axis, and a screening length of screen. See fig. 2 of arXiv:2509.13298.

The potential is calculated using the following formula:

\(V_\text{gate}(r)=V_\text{peak} \frac{\mathcal{K}_0(r/\lambda_\text{screen})}{\mathcal{K}_0(h/\lambda_\text{screen})}\),

where \(r\) is the distance from the central axis of the cylindrical gate, and \(\mathcal{K}_0(x)\) is the modified Bessel function of the second kind.

Parameters:

  • gate_params (thomas_fermi.GateParameters) – The set of parameters defining the gate

  • x (float or ndarray[float]) – The x-values (in nm) of the point(s) for which to calculate the potential. x refers to the direction parallel to the nanowire.

  • y (float or ndarray[float]) – The y-values (in nm) of the point(s) for which to calculate the potential. y refers to the direction parallel to the central axis of the cylindrical gates.

  • z (float or ndarray[float]) – The z-values (in nm) of the point(s) for which to calculate the potential. z refers to the direction normal to the plane that contains the 2DEG.

  • effective_peak (float | None) – If given, this value will be used instead of gate_params.peak.

Returns:

The potential (in meV) at each of the input points due to the gate.

Return type:

float or ndarray[float]