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

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

2009-01-22

arxiv.org/abs/0901.3420v1

Phys. Rev. B 79, 205101 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

6 pages. 2 figures

Scientific paper

10.1103/PhysRevB.79.205101

We study the stability of spinless Fermions with power law hopping $H_{ij} \propto |i - j|^{-\alpha}$. It is shown that at precisely $\alpha_c =2$, the dispersive inflection point coalesces with the band minimum and the charge carriers exhibit a transition into negative effective mass regime, $m_\alpha^* < 0$ characterized by retarded transport in the presence of an electric field. Moreover, bands with $\alpha < 2$ must be accompanied by counter-carriers with $m_\alpha^* > 0$, 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($\alpha =1$). The analysis is generalized to regular lattices in dimensions $d$ = 1, 2, and 3.

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