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arXiv · 0901.3420

Negative effective mass transition and anomalous transport in power-law hopping bands

Shimul Akhanjee
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Abstract

We study the stability of spinless Fermions with power law hopping $H_{ij} \propto |i - j|^{-α}$. It is shown that at precisely $α_c =2$, the dispersive inflection point coalesces with the band minimum and the charge carriers exhibit a transition into negative effective mass regime, $m_α^* < 0$ characterized by retarded transport in the presence of an electric field. Moreover, bands with $α< 2$ must be accompanied by counter-carriers with $m_α^* > 0$, having a positive band curvature, thus stabilizing the system in order to maintain equilibrium conditions and a proper electrical response. We further examine the semi-classical transport and response properties, finding an infrared divergent conductivity for 1/r hopping($α=1$). The analysis is generalized to regular lattices in dimensions $d$ = 1, 2, and 3.

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Shimul Akhanjee. 2009-01-22. Negative effective mass transition and anomalous transport in power-law hopping bands. https://doi.org/10.1103/physrevb.79.205101

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