Wednesday, September 2, 2015

There is no metal-insulator transition in extremely large magnetoresistance materials

There is currently a lot of interest in layered materials with extremely large magnetoresistance [XMR], partly stimulated by a Nature paper last year.
The figure below shows the data from that paper, which is my main focus in this post.

A recent PRL contains the following paragraph

A striking feature of the XMR in WTe2 is the turn-on temperature behavior: in a fixed magnetic field above a certain critical value Hc, a turn-on temperature T is observed in the R(T) curve, where it exhibits a minimum at a field-dependent temperature T. At T<T, the resistance increases rapidly with decreasing temperature while at T>T, it decreases with temperature [2]. This turn-on temperature behavior, which is also observed in many other XMR materials such as graphite [19,20], bismuth [20]PtSn4 [21]PdCoO2 [22]NbSb2 [23], and NbP [24], is commonly attributed to a magnetic-field-driven metal-insulator transition and believed to be associated with the origin of the XMR [10,19,20,23,25].

My main point is that this temperature dependence and the "turn-on" has a very simple physical explanation: it is purely a result of the strong temperature dependence of the charge carrier mobility (scattering rate), which is reflected in the temperature dependence of the zero field resistance.
It is completely unnecessary to invoke a metal-insulator transition.
The "turn on" is really a smooth crossover.
I made this exact same point in a post last year about PdCoO2  and in this old paper.

Following the discussion [especially equation (1)] in the Nature paper, consider a semi-metal that has equal density of electrons and holes (n=p). For simplicity assume they have the same temperature dependent mobility mu(T). Then the total resistivity in a magnetic field B is given by
Differentiating this expression with respect to temperature T, for fixed B, one finds that the resistance is a minimum, at a temperature T* given by
Further justification for this point of view should come from a Kohler plot:
A plot of the ratio of the rho(T,B)/rho(T,B=0) versus B/rho(T,B=0) should be independent of temperature.

In the specific materials there will be further complications associated with spatial anisotropy, unequal and temperature dependent election and hole densities, tilted Weyl cones, chiral anomalies, .... However, the essential physics should be the same.

XMR is due to simple (boring old) physics: extremely large mobilities at low temperatures are due to very clean samples and in some cases, near perfect compensation of electron and hole densities.

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