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BCS models for conventional superconductors
These fit models are suited for scanning tunneling spectroscopy on superconductors. They all calculate the current by a convolution of the tip and sample density of states.
The integral for the current is calculated as follows:
- V_bias: sample bias voltage
- rho: density of states
- f: Fermi-Dirac occupation of the density of states
- M_if: tunnel matrix element (assumed to be constant).
The differential conductance is obtained from the current by calculating the numeric derivative.
If used, the BCS density of states is defined as follows:
- E: energy
- Delta: BCS gap parameter
- delta: Dynes parameter, R.C. Dynes, V. Narayanamurti, and J.P. Garno, Phys. Rev. Lett. 41, 1509 (1978)
Several different fit models suited for particular systems base on calculating this integral. There are fit functions that model a single-gap or two-gap superconductors, and some, that assume a step-like gap. The density of states of the tip is assumed in some models as a metal tip or, as a superconducting tip, described by BCS theory.
In systems with magnetic adsorbates the subgap excitations (Shiba-states) can be modeled by Lorentzian-like resonances.
Notice: this is only suitable in the weak tunneling regime
M. Ruby et al., Phys. Rev. Lett. 115, 087001 (2015)