Tunneling in low-dimensional and strongly correlated electron systems
Patton, Kelly Ray
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It is well known that the tunneling density of states has anomalies (cusps, algebraic suppressions, and pseudogaps) at the Fermi energy in a wide variety of low-dimensional and strongly correlated electron systems. We propose that the origin of these anomalies is the infrared catastrophe associated with the sudden introduction of a new electron into a conductor during a tunneling event. A nonperturbative theory of the electron propagator is developed to correctly account for this infrared catastrophe. The method uses a Hubbard-Stratonovich transformation to decouple the electron-electron interactions, subsequently representing the electron Green’s function as a weighted functional average of noninteracting Green’s functions in the presence of space- and time-dependent external potentials. The field configurations responsible for the infrared catastrophes are then treated using methods developed for the x-ray edge problem.