A quantum particle can pass through a narrow potential barrier. Thanks to the Heisenberg uncertainty principle, there is a small probability that an electron, for example, can be existing inside a finite-potential wall. The shorter "the tunnel," the more probable the electron passes through the wall. This tunnelling phenomenon is contrary to classical mechanics because no way a particle can move through a finite potential wall without the particle energy overcomes the height (magnitude) of potential.
Suppose one configures an open-loop circuit connected to a voltage (bias) but with a narrow separation made of vacuum (say, a few angstroms). Electrons may tunnel the vacuum barrier to flow as a tunnelling current. This configuration is similar to that of inside STM. The electric circuit in STM consists of a conducting substrate (metal or highly-doped semiconductor) and an angstrom-width needle/tip equipped on a piezoelectric motor.
One can scan over the substrate by controlling the piezoelectric device to move the STM tip horizontally. STM can probe the topography of substrate with a so-called constant-current technique. The magnitude of tunnelling current is set unchanged (so the tip-to-substrate distance). The vertical position of the tip acts as the variable recorded as the surface roughness in topographic mapping. One can also place the needle above a feature of interest on the map and ramp up the voltage bias to take spectroscopy.
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Given that two electrons with opposite momentum bind into a pair due to an attractive force. We can disrupt the interaction in two ways: overcoming the attractive force or disrupting the net of momentum. If there is a magnetic impurity, its field directs both momenta to cause the net to be nonzero to break the pairing. This pair-breaking interaction may resonate to produce the so-called Yu-Shiba-Rusinov excitation state (YSR state).