Tunneling of Bloch electrons through a small-size contact

• A tunneling of Bloch waves through a contact of small diameter is studied.
• We use an inhomogeneous tunnel barrier of low transparency to describe the contact.
• The electron tunneling from the bulk-mode states into the surface states is studied.
• An asymptotically exact expression is derived for the conductance of the system.
• Prospects for the application of the results to the theory of STM are discussed.

For the first time the tunneling of Bloch waves through a contact of small diameter is studied in the framework of a model of an inhomogeneous tunnel δ-barrier of low transparency. The electron tunneling from bulk-mode states into the surface states localized near the contact interface is considered. An asymptotically exact expression (in the inverse height of the barrier) is derived for the conductance of the system. Prospects for the application of the obtained results to the theory of scanning tunneling microscopy are discussed.