What the study found
The study proposes that disorder-induced changes in the electronic local density of states can be described using Fisher information and Cramér-Rao bounds. It treats either energy or position as the random variable to build information measures that quantify spatial variation in disordered solids.
Why the authors say this matters
The authors conclude that this framework brings the idea of information geometry into scanning tunneling microscopy measurements. They also say the corresponding Cramér-Rao bounds set limits on the energy variance and position variance of electrons in disordered solids.
What the researchers tested
The researchers developed a formalism based on the normalized electronic local density of states, which they describe as a probability density when properly normalized. They constructed a real-space Fisher information matrix by treating energy as a random variable and position as an external parameter, and an energy-space Fisher information by reversing those roles.
What worked and what didn't
The abstract states that both information measures quantify variation in the local density of states caused by disorder. It also says the formalism was demonstrated explicitly with lattice models of metals and topological insulators. No failures or negative results are described in the abstract.
What to keep in mind
The available summary does not describe detailed limitations, experimental conditions, or the range of systems tested beyond the lattice models mentioned. The abstract also does not provide numerical results or compare this approach with other methods.
Key points
- The paper proposes using Fisher information to describe disorder-induced changes in local density of states.
- It defines two versions of Fisher information: one in real space and one in energy space.
- The authors say the associated Cramér-Rao bounds limit electron energy variance and position variance in disordered solids.
- The framework is presented as a way to bring information geometry into scanning tunneling microscopy measurements.
- The approach is demonstrated with lattice models of metals and topological insulators.
Disclosure
- Research title:
- Disorder alters local density of states through information measures
- Image credit:
- Photo by tonywuphotography on Pixabay
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