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

TL;DR

This paper investigates the transition to negative effective mass in power-law hopping bands of spinless fermions, revealing a critical exponent at $ ext{alpha} = 2$ and analyzing transport properties across different dimensions.

Contribution

It identifies a critical power-law exponent where the effective mass becomes negative and explores the resulting anomalous transport phenomena in various lattice dimensions.

Findings

Negative effective mass appears at $ ext{alpha} = 2$

Infrared divergent conductivity at $ ext{alpha} = 1$

System stability requires counter-carriers with positive effective mass

Abstract

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.