STM images

CP2K can generate volumetric data for simulated scanning tunneling microscopy (STM) images with the &DFT%PRINT%STM section. The implementation is a post-SCF analysis based on the Tersoff–Hamann approximation: it sums the densities of the Kohn–Sham states in an energy window set by the requested sample bias. The result is written as a cube file and is proportional to the tunneling-current signal within this approximation.

CP2K writes a three-dimensional field, not a finished two-dimensional topograph. A visualization or post-processing program can obtain

  • a constant-height image by sampling the cube on a plane parallel to the surface, or

  • a constant-current image by finding, for every lateral position, the height at which the cube field reaches a chosen isovalue.

The older STM how-to and STM exercise provide additional worked examples.

Energy windows and occupations

Let \(E_\mathrm{ref}\) be the reference energy and \(V\) the value supplied with BIAS. By default, \(E_\mathrm{ref}\) is the Fermi energy from the SCF calculation. CP2K includes states in the following intervals:

  • for \(V < 0\), \(E_\mathrm{ref} + V < \varepsilon_n \le E_\mathrm{ref}\) (occupied states),

  • for \(V > 0\), \(E_\mathrm{ref} < \varepsilon_n \le E_\mathrm{ref} + V\) (unoccupied states).

The orbital-density contribution is weighted by the occupied part for negative bias and by the unoccupied part for positive bias. This also accounts for fractional occupations when smearing is used. Multiple bias values can be specified in one section.

REF_ENERGY replaces the default reference energy. This is useful when comparing energy windows between calculations, but the user must first align the chosen reference consistently, for example through a common vacuum or electrostatic potential reference.

Positive-bias images require enough unoccupied eigenstates to span the requested window. Set NLUMO to request additional unoccupied states during the STM post-processing. CP2K reports how many states enter every bias window and warns when the requested window extends beyond the available eigenvalues. Increase NLUMO until that warning disappears and the image is converged.

Minimal input

The STM section belongs under &FORCE_EVAL / &DFT / &PRINT. For example,

&FORCE_EVAL
  ...
  &DFT
    ...
    &PRINT
      &STM
        BIAS [eV] -1.0 1.0
        NLUMO 50
        TH_TORB S
        STRIDE 1 1 1
      &END STM
    &END PRINT
  &END DFT
&END FORCE_EVAL

This requests occupied- and unoccupied-state cubes over 1 eV windows around the Fermi energy. NLUMO 50 is only an example; the required number depends on the density of states and must be checked in the output.

The most relevant keywords are:

  • BIAS: one or more bias energies in eV;

  • NLUMO: number of additional unoccupied states;

  • TH_TORB: tip-orbital symmetry; the default and conventional Tersoff–Hamann choice is S; repeated keywords request multiple symmetries;

  • STRIDE: subsampling of the real-space grid; use 1 1 1 for the full grid and larger values to reduce file size;

  • REF_ENERGY: optional reference energy instead of the SCF Fermi energy;

  • APPEND: append to existing cube files.

The cube filenames contain STM_d, a numeric code for the selected tip-orbital symmetry, and the bias index. The cube header records the actual bias value. When several biases or tip symmetries are requested, inspect the output and cube headers rather than assigning a physical bias from the filename alone.

Current limitations

Important

The STM print section is currently implemented only for Gamma-point calculations. If an explicit k-point mesh is present, CP2K prints a warning and does not generate the STM cubes. A large surface supercell evaluated at Gamma may be suitable, but the electronic structure and simulated image must be checked with respect to lateral cell size or against k-point-converged reference calculations.

For a spin-polarized calculation, the current implementation adds the alpha- and beta-spin contributions to the same cube. It does not produce separate spin-resolved STM images. Likewise, the output is an independent-particle, Tersoff–Hamann-type signal; it does not include a microscopic tip, tip–sample relaxation, a tunneling-current prefactor, or a self-consistent finite-bias transport calculation.

TH_TORB S is the usual spherical-tip approximation. The other supported values apply spatial derivatives corresponding to the selected tip-orbital symmetry. They remain idealized tip models; an arbitrary hybrid tip orbital is not constructed by the STM section.