Possible experimental manifestations of the many-body localization

Recently, it was predicted that if all one-electron states in a noninteracting disordered system are localized, the interaction between electrons in the absence of coupling to phonons leads to a finite-temperature metal-insulator transition. Here, we show that even in the presence of a weak coupling to phonons the transition manifests itself (i) in the nonlinear conduction, leading to a bistable $I\text{−}V$ curve, and (ii) by a dramatic enhancement of the nonequilibrium current noise near the transition.

Figure 1

Schematic temperature dependence of the dc conductivity $\sigma \left(T\right)$ for electrons subject to a disorder potential localizing all single-particle eigenstates, in the presence of weak short-range electron-electron $\lambda {\delta }_{\zeta }$, $\lambda ⪡1$, established in Ref. 5. Below the point of the many-body metal-insulator transition, $T<T_c\sim {\delta }_{\zeta }∕\mid \lambda \ln \lambda \mid$, no inelastic relaxation occurs and $\sigma \left(T\right)=0$. At $T⪢{\delta }_{\zeta }∕{\lambda }^2$, the high-temperature metallic perturbation theory (Ref. 10) is valid, and corrections to the Drude conductivity ${\sigma }_{\infty }$ are small. In the interval ${\delta }_{\zeta }∕\lambda ⪡T⪡{\delta }_{\zeta }∕{\lambda }^2$, electron-electron interaction leads to electron transitions between localized states, and the conductivity depends on temperature as a power law.

Figure 2

(a) Sketch of the bistable $I\text{−}V$ curve for a fixed value of $T_{\mathit{ph}}$; (b) $(\mathcal{E},T_{\mathit{ph}})$ plane with the bistable region schematically shown by shading. The dashed line represents the crossover between the metallic state at high electric field $\mathcal{E}$ or high phonon temperature $T_{\mathit{ph}}$ and the insulating state at low $\mathcal{E}$ and low $T_{\mathit{ph}}$.

Figure 3

Sketch of the dependences $(T_{\mathit{el}}-T_{\mathit{ph}})∕\left(e\mathcal{E}\right)$ (dashed line) and $L_{\mathit{ph}}\left(T_{\mathit{el}}\right)$ (solid lines, electron-phonon coupling strength being weaker for higher curves). The actual value of $T_{\mathit{el}}$ is determined by their crossing.