Theory of Charge Sensing in Quantum-Dot Structures

Charge sensing in quantum-dot structures is studied by an exactly solvable reduced model and numerical density-matrix renormalization-group methods. Charge sensing is characterized by repeated cycling of the occupation of current-carrying states due to the capacitive coupling to trap states. In agreement with recent experiments, it results in characteristic asymmetric Coulomb-blockade peaks as well as sawtooth and domelike structures. Temperature introduces asymmetric smearing of these features and correlations in the conductance provide a fingerprint of charge sensing.

Figure 1

Conductance (solid line) through one connected state with ten disconnected states as function of chemical potential. (a) Intermediate coupling case: $ϵ=-1.08$, $t=0.2$, $U=0.16$, and $e_m=-1.2+0.02m$ ($m=1,\dots ,10$). (b) Strongly connected case: $ϵ=-1$, $t=0.5$, $U=0.08$, $e_m=-1.24+0.04m$. Dotted curves: Conductances for fixed occupations $n_d=0,\dots ,10$ of the disconnected states. As $n_d$ changes with $\mu$, the conductance (solid line) switches accordingly. Inset: Schematic of the connected and disconnected dots.

Figure 2

Conductance as a function of overall chemical potential $\mu$ and external gate voltage $V_g$ for the disconnected states (see inset in Fig. 1). Connected state: $ϵ=0$; disconnected states: $e_m=-0.55+0.05m$ ($m=1,\dots ,5$), $U=0.1$, and $t=0.2$.

Figure 3

(a) Temperature dependence of the conductance as function of $\mu$ (connected state: $\epsilon =-1.3$; disconnected state: $e_1=-1.26$; $U=0.4$; $t=0.3$). The different curves correspond to $\pi kT=0$, 0.1, 0.2, 0.3, 0.4. (b) Occupation of the connected state $n_{\alpha }$ (open symbols) and disconnected state $n_d$ (filled symbols) for several values of couplings as the disconnected state opens up additional non-current-carrying lead. Lines: results of the exact solution of Eq. (3); symbols: DMRG calculations for different couplings of the disconnected state (circles $t=0$, squares $t=0.1$, diamonds $t=0.2$). (c) Conductance of connected state in (b).

Figure 4

Occupation for two connected states ($t=0.5$) at ${ϵ}_1=-1.1$ (gray circles) and ${ϵ}_2=-1$ (gray squares) and two disconnected states $e_1=-1.12$ (solid line), $e_2=-1.02$ (dotted line) as function of $\mu$ obtained from DMRG ($U=0.3$). To demonstrate that right after the switch $n_{\alpha }(\mu )=n_{\alpha }(\mu -U)$, we plot $n_{\alpha }(\mu +U)$ for values of $\mu$ prior to the switch, i.e., $-1.2<\mu <-1$ and $-0.48<\mu <-0.28$ (white symbols). A clear overlap between the white and gray symbols is seen.