Metal-insulator transition of isotopically enriched neutron-transmutation-doped ^{70}Ge:Ga in magnetic fields

TL;DR

This study investigates how magnetic fields influence the metal-insulator transition in isotopically enriched ^{70}Ge:Ga, revealing a change in critical exponent and establishing a scaling law for conductivity near the transition.

Contribution

It demonstrates that magnetic fields alter the critical exponent of the MIT in ^{70}Ge:Ga and establishes a universal scaling rule relating conductivity, doping concentration, and magnetic field.

Findings

Magnetic fields change the critical exponent from 0.5 to 1.1.

Conductivity obeys a scaling law on the (N,B) plane.

Critical exponents mu and mu' are equal, confirming the scaling hypothesis.

Abstract

We have investigated the temperature dependence of the electrical conductivity sigma(N,B,T) of nominally uncompensated, neutron-transmutation-doped ^{70}Ge:Ga samples in magnetic fields up to B=8 T at low temperatures (T=0.05-0.5 K). In our earlier studies at B=0, the critical exponent mu=0.5 defined by sigma(N,0,0) \propto (N-N_c)^{mu} has been determined for the same series of ^{70}Ge:Ga samples with the doping concentration N ranging from 1.861 \times 10^{17} cm^{-3} to 2.434 \times 10^{17} cm^{-3}. In magnetic fields, the motion of carriers loses time-reversal symmetry, the universality class may change and with it the value of mu. In this work, we show that magnetic fields indeed affect the value of mu (mu changes from 0.5 at B=0 to 1.1 at B \geq 4 T). The same exponent mu'=1.1 is also found in the magnetic-field-induced MIT for three different ^{70}Ge:Ga samples, i.e., sigma(N,B,0) \propto [B_c(N)-B]^{mu'} where B_c(N) is the concentration-dependent critical magnetic induction. We show that sigma(N,B,0) obeys a simple scaling rule on the (N,B) plane. Based on this finding, we derive from a simple mathematical argument that mu=mu' as has been observed in our experiment.