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Fingerprints of Intrinsic Phase Separation:
Magnetically-doped 2D Electron Gas

 
Published in  Phys. Rev. Lett. 106, 186402 (2011)

 INTRODUCTION
"Direct or Indirect routes towards the metal-insulator transition: existence of an intermediate phase near the MIT"

In addition to Anderson and Mott localization, intrinsic phase separation (IPS) has long been advocated as the third fundamental mechanism controlling the doping-driven metal-insulator transitions. In electronic system, where charge neutrality precludes global phase separation, it may lead to various inhomogeneous states and dramatically affect transport.

The relevance of such a nano-scale PS in its many proposed forms (bubbles, stripes, checkerboard patterns), has been advocated for the bad metal regimes of cupratesmanganites , and even low density  2D electron gases.

Still, in most of these cases, no clear and conclusive evidence has been presented that intrinsic (not disorder driven) phase separation - as driving force for the metal-insulator crossover - dominates the bad metal regime.
fig1
Fig. 1:  In presence of IPS, carriers are trapped in FM clusters from which they can escape only by thermal activation. Such activation-limited transport results in resistivity which is a strong function of temperature and magnetic field, but of a very weak density dependence-the smoking gun for IPS.
 
 MODEL

 "Example of a physical system where  IPS can be precisely and clearly identified"

To make progress in understanding the relevance of IPS, we focus on the model where the microscopic origin of IPS is understood, and transport signatures can be identified that makes it possible to distinguish IPS from spurious disorder effects.

Recent experimental work  on Mn-doped 2DEG  seem to be an ideal setting for such an IPS. Here sufficient doping induces FM correlations between the Mn-spins, which can prevail over the usual Mn-Mn  AFM superexchange that exists even in absence of carriers.

Corresponding minimal Hamiltonian describing such system is of the form:

formula

At very low doping levels the situation is rather subtle. Here the average kinetic energy gain obtained by FM ordering is not sufficient to balance the energy cost of AFM superexchange that opposes it. A compromise is reached through phase separation (Fig. 1) with  FM carrier-rich regions being formed inside carrier-poor PM (AFM) system.

fig-2-phase diagram
Fig. 2:  DMFT phase diagram. Shaded areas show the IPS regions at three different values of Jex. As Jex increases, the critical density nc increases, while the critical-end-point temperature Tc decreases, until IPS is suppressed.

MAIN RESULTS

"How to recognize IPS: specific and concrete transport features of IPS that makes it diffrent from extrinsic (disorder) PS"

To establish quantitatively IPS we first constructed  phase diagram shown in Fig. 2.
Here for carrier densities below critical value nc=f(Jex) system phase separates (shaded area) with carries being trapped inside FM clusters.

To study  an effect of such IPS on transport, we calculated resistivity in such coexistence region.  As a results, we find an anomalous behavior in transport in an intermediate regime around the transition: resistivity curves display  strong temperature dependence (Fig. 3-a)-b)), but are very weak function of  carrier densities n (Fig. 3-c)-d)). This behavior also reflects the fact that within this region activation energy as well as the size of the PS regions is density independent.

Such transport behavior with a sharp upturn in resistivity in the low temperature regime, and its weak n-dependence  are direct consequences of IPS.

Our theoretical predictions (right panel of Fig. 3)  are in striking agreement with recent experiments (left panel) on Mn-doped CdTe quantum wells, a system where we identify the microscopic origin for intrinsic phase separation.
transport
Fig. 3: a)--experiment and b)--theory shows  resistivity as function of  temperature T at different carrier densities n. (c) and (d) show the same data as function of n at fixed T to emphasize weak n-dependence of resistivity below the percolation threshold.