Abstract
We clarify the mechanism for negative differential conductivity in holographic conductors. Negative differential conductivity is a phenomenon in which the electric field decreases with the increase of the current. This phenomenon is widely observed in strongly correlated insulators, and it has been known that some models of AdS/CFT correspondence (holographic conductors) reproduce this behaviour. We study the mechanism for negative differential conductivity in holographic conductors by analyzing the lifetime of the bound states of the charge carriers. We find that when the system exhibits negative differential conductivity, the lifetime of the bound states grows as the electric field increases. This suggests that the negative differential conductivity in this system is realized by the suppression of the ionization of the bound states that supplies the free carriers.
Highlights
It is known that the system has bound states of a positively charged particle and a negatively charged particle [12]
We find that when the system exhibits negative differential conductivity, the lifetime of the bound states grows as the electric field increases
We analyzed the lifetime of the bound states by using AdS/CFT correspondence to reveal the mechanism of NDC
Summary
Our goal is to study the behavior of the lifetime of the bound states of positive carrier and negative carrier when NDC is realized. A QNM is realized as a perturbation field on a background configuration. We consider a perturbation of the normalizable mode of the transverse vector field for. We analyze the behavior of the QNM of the perturbation field of A2 in detail and clarify its dependence on E in the NDC region. Where A(z, t) is the perturbation field of the transverse vector mode. In order to solve this equation properly, we should impose the ingoing wave boundary condition at z = z∗. We need to impose the vanishing condition at the boundary: A(0) = 0 at z = 0. This condition ensures that the solution is a resonance state without an external source. We solve eq (3.3) under these conditions by the shooting method. Note that the location of the pole of QNM depends on E, J, T , since eq (3.3) depends on them
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