Universal power-law exponents in differential tunneling conductance for planar insulators near Mott criticality at low temperatures

Abstract

We consider the low-temperature differential tunneling conductance G for interfaces between a planar insulating material in the Mott-class and a metal. For values of the applied potential difference V that are not very small, there is a experimentally observed universal regime in which G ∼ Vm, where m is a universal exponent. We consider the theoretical prediction of the values of m by using the method of effective field theory (EFT), which is appropriate for discussing universal phenomena. We describe the Mott material by the EFT pertaining the long-distance behavior of a spinless Hubbard-like model with nearest neighbors interactions previously considered. At the Mott transition, the EFT is known to be given by a double Abelian Chern-Simons theory. The simplest realization of this theory at the tunneling interface yields a Conformal Field Theory with central charges (c, c) = (1, 1) and Jain filling fraction ν = 2/3 describing a pair of independent counter-propagating chiral bosons (one charged and one neutral). Tunneling from the material into the metal is, therefore, described by this EFT at the Mott critical point. The resulting tunneling conductance behaves as G ∼ V(1/ν-1), yielding the prediction m = 1/2, which compares well (within a 10% deviation) with the results for this exponent in two experimental studies considered here.