Negative Differential Conductance Induced by Spin-Charge Separation

Spin-charge states of correlated electrons in a one-dimensional quantum dot attached to interacting leads are studied in the nonlinear transport regime. With nonsymmetric tunnel barriers, regions of negative differential conductance induced by spin-charge separation are found. They are due to a correlation-induced trapping of higher-spin states without magnetic field and are associated with a strong increase in the fluctuations of the electron spin.

Figure 1

The differential conductance at $k_{\mathrm{B}}T={10}^{-2}{E}_{\sigma }$ in the $(V,n_{\mathrm{g}})$ plane of a 1D quantum dot with asymmetry $A=100$, interaction strength in the leads $g_0=0.9$, charging energy $E_{\rho }=25E_{\sigma }$, and spin relaxation $w=0$ ($V$ in units of $E_{\sigma }/e$); (a) weak correlation, ${\varepsilon }_{\rho }=3.0E_{\sigma }$, ${\varepsilon }_{\sigma }=2.2E_{\sigma }$; (b) strong correlation, ${\varepsilon }_{\rho }=15E_{\sigma }$, ${\varepsilon }_{\sigma }=2.5E_{\sigma }$; (c) states involved in the transitions for $V>0$ near the linear conductance peak, and denoted by the triples of integer quantum numbers $(s,\sigma ,\rho )$; (d) noninteracting case, ${\varepsilon }_{\rho }={\varepsilon }_{\sigma }=2E_0$. Right edge: grey scale in arbitrary units, labels, and scales at axes of (a),(b),(d) are identical.

Figure 2

Differential conductance (units $e^2{\gamma }_{\mathrm{r}}/E_{\sigma }$) at positive voltages $V$, in units $E_{\sigma }/e$ (right), near $\left(100\right)\leftrightarrow \left(200\right)$, and at $-V$ (left), for $g_{\rho }=0.135$, $g_{\sigma }=1.25$, and $g_0=0.9$, at $n_{\mathrm{g}}$ in region I, with $k_{\mathrm{B}}T={10}^{-2}{E}_{\sigma }$. Top panels: $w=0$, with $A=1$ (red), 2 (green), 2.6 (blue), 5 (magenta), 50 (cyan). Middle: $A=10$ with $w/\tilde{\gamma }=0.3$ (red), 0.35 (green), 0.4 (blue), 0.45 (magenta), 0.5 (cyan). Bottom: phase diagram of the crossover between positive and negative conductance at $T=0$ for $g_0=1$ (red), 0.9 (green), 0.8 (blue), 0.7 (magenta), 0.65 (cyan) for $n_{\mathrm{g}}$ in region I [$w$ in units of the scaled intrinsic tunneling rate $\tilde{\gamma }={\gamma }_{\mathrm{l}}(E_{\sigma }/\mathrm{\hbar }{\omega }_{\mathrm{c}}{)}^{\alpha }$].

Figure 3

Differential conductance (red curve, left scale, units $e^2{\gamma }_{\mathrm{r}}/E_{\sigma }$) and spin variance (blue curve, right scale) as a function of bias voltage $V$ (unit $E_{\sigma }/e$) for $n_{\mathrm{g}}$ in region I, $A=100$, $w=0$, $k_{\mathrm{B}}T=2\times {10}^{-2}{E}_{\sigma }$, $E_{\rho }=25E_{\sigma }$, ${\varepsilon }_{\sigma }=2.5E_{\sigma }$, ${\varepsilon }_{\rho }=15E_{\sigma }$, $g_0=0.9$.