Graduate Scanning Tunneling Microscope I-V curve

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The I-V curve for a scanning tunneling microscope (STM) is exponential for conducting samples, while the characteristics differ for semiconductors and non-conductors. STM relies on electrical current flow, making it unsuitable for directly imaging electrically insulating materials. For metals and semiconductors, the current-voltage relationship is influenced by the density of electron states in both the tip and the sample material. Understanding these differences is crucial for interpreting STM data accurately. Further technical details can be found at the provided link.
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I know that scanning tunneling microscopy (STM) I-V curve is exponential for a conducting sample.
How would it look like if I had a semiconductor and a non-conductor sample?
 
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Scanning tunneling microscopy is based on the flow of an electrical current. Thus, this method isn’t suited to directly image electrically insulating material. Regarding metals and semiconductors, the current-voltage characteristics depends on the density of electron states of the tip and sample material. Have a look at http://hoffman.physics.harvard.edu/research/STMtechnical.php
 
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Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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