Extreme Fermi Surface Smearing in a Maximally Disordered Concentrated Solid Solution

Abstract

We show that the Fermi surface can survive the presence of extreme compositional disorder in the equiatomic alloy Ni0.25Fe0.25Co0.25Cr0.25. Our high-resolution Compton scattering experiments reveal a Fermi surface which is smeared across a significant fraction of the Brillouin zone (up to 40% of 2π a ). The extent of this smearing and its variation on and between different sheets of the Fermi surface has been determined, and estimates of the electron mean-free-path and residual resistivity have been made by connecting this smearing with the coherence length of the quasiparticle states.The emergence of the Fermi surface (FS) from the theory of the electronic structure of metals, together with the pioneering experimental determinations of its shape, stand proudly among the greatest achievements of twentieth century physics [1]. The FS, defined by the discontinuity in the momentum distribution, exists even for interacting electrons [2,3], and here we demonstrate its remarkable ability to survive maximal compositional disorder in which the electron mean-free-path (which we can also extract from our measurements) is comparable to the lattice spacing. In disordered systems, the Mott-Ioffe-Regel (MIR) limit describes the semiclassical upper bound for coherent transport in a metal, occuring when the electron mean-free-path becomes comparable with the interatomic spacing [4]. The modern description of the electronic structure of crystalline solidsthe band theory of electrons -depends on the notion of perfect crystals exhibiting long-range order. The Bloch wavefunctions which emerge are a direct consequence of the discrete translational invariance of the potential experienced by the electrons traveling through the ionic lattice. This premise is strongly challenged in substitutionally disordered random alloys (concentrated solid solutions) where there is no such periodicity. Abandoning the familiar concepts associated with a well-defined reciprocal lattice, such as the Brillouin zone (BZ) and indeed the FS, seems inevitable. However, there is considerable theoretical and experimental evidence (e.g. [5, 6]) that by considering an ordered system comprising suitably chosen effective scatterers to restore periodicity, the BZ and FS can be resurrected. The resulting electron states, however, have finite lifetimes due to the presence of disorder, and the "bands" are smeared in both energy, E (resulting in a finite electron lifetime) and crystal mo-mentum, k (finite mean-free-path). This also means that the discontinuity in the momentum distribution associated with the FS is also smeared out in both E and k, with correspondingly reduced Fermi energy electron lifetimes and short mean-free-paths. A sharp FS in an ultrapure metal at cryogenic temperatures is associated with electron mean-free-paths of more than a centimeter [7]. While bulk resistivities of metals are rather well known, comparatively little direct information exists about electron mean-free-paths [8].A new class of metallic alloys, referred to as "high entropy alloys"...

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