Current-voltage asymmetries and negative differential conductance due to strong electron correlations in double quantum dots

A theory for asymmetric current-voltage characteristics, in particular negative differential conductance, for double quantum dots with strongly correlated electron states is formulated. By expressing the double quantum dot in terms of its many-body eigenstates, a diagrammatic technique for Hubbard operator nonequilibrium Green’s functions is employed. The Green’s function for the double quantum dot is calculated beyond mean field theory, and it is found that the spectral weights of the conductive transitions in the double quantum dot redistribute dynamically (bias voltage dependent). The resulting asymmetric current-voltage characteristics and negative differential conductance is discussed in terms of the relative level spacing in the two quantum dots and the hopping rate between the quantum dots. Numerical results of the current-voltage characteristics are presented and compared to experiments.

Figure 1

A typical $J\text{−}V$ characteristics calculated within the theory developed in this paper, further discussed in Sec. 4. The upper inset shows a typical experimental $J\text{−}V$ result on the DQD reported in Ref. 10. The lower inset shows the geometry of the DQD system.

Figure 2

Sketch of the double quantum dot system. The QDs interact via the interdot Coulomb repulsion $U_{AB}$ and hopping $t$. The coupling strength between the DQD and the left/right contact is denoted by ${\Gamma }^{L∕R}$.

Figure 3

(a) Sketch of the energy parameters of the serial DQD coupled to external contacts. In ${\text{QD}}_{A∕B}$ the bare single-particle energy is ${\epsilon }_{A\sigma ∕B\sigma }$ (for other parameters we refer to the text). (b) Schematic picture of the energies of the DQD system in the diagonal representation, where ${\mu }_{L∕R}$ is the (quasi-) chemical potential of the left/right contact. The energy for a transition between the empty state and one-particle state $\mid {\gamma }_{n\sigma }⟩,n=1,2$, is denoted by ${\Delta }_{n\sigma }$. The arrows illustrate the strengths of the transition probabilities between the one-particle states in the DQD and the contacts. In this configuration, the higher transitions, e.g., $\mid N+1⟩⟨N\mid$ etc., lie outside the range of conduction.

Figure 4

The transition matrix elements ${\mid {\left(d_{A\sigma }\right)}^{0{\gamma }_{1\sigma }}\mid }^2={\mid {\left(d_{B\sigma }\right)}^{0{\gamma }_{2\sigma }}\mid }^2$ (solid) and ${\mid {\left(d_{A\sigma }\right)}^{0{\gamma }_{2\sigma }}\mid }^2={\mid {\left(d_{B\sigma }\right)}^{0{\gamma }_{1\sigma }}\mid }^2$ (dashed) as functions of the relative level spacing $({\epsilon }_A-{\epsilon }_B)∕\Gamma$ for various hopping strengths $t∕\Gamma$.

Figure 5

Dressed transition energies as functions of the bias voltage for case (A) in Table with ${\Gamma }^{L∕R}=0.375\mathrm{meV}$ at $T=5\mathrm{K}$.

Figure 6

Dressed population numbers $N_n={\sum }_{\sigma }{N}_{n\sigma },n=1,2$, as functions of the bias voltage for case (A) in Table .

Figure 7

$J\text{−}V$ characteristics (upper panel) and $dJ∕dV$ (lower panel) for the DQD calculated in the full loop approximation (solid), with the loop correction (dashed) and within the HIA (dotted). Parameters are taken from case (A) in Table .

Figure 8

Symmetry of the $J\text{−}V$ characteristics and $dJ∕dV$ with respect to the relative positions of the levels in the QDs. The plots are calculated for $t∕\Gamma =1$.

Figure 9

$J\text{−}V$ characteristics and $dJ∕dV$ for different relative level spacing $({\epsilon }_A-{\epsilon }_B)∕\Gamma <0$ in the two QDs and fixed hopping strength $\left(t∕\Gamma =1\right)$ between the QDs.

Figure 10

$J\text{−}V$ characteristics and $dJ∕dV$ for different hopping strengths $t∕\Gamma$ and fixed level spacing $({\epsilon }_A-{\epsilon }_B)∕\Gamma =-2$.

Figure 11

$J\text{−}V$ characteristics and $dJ∕dV$ for various left and right couplings ${\Gamma }^L∕{\Gamma }^R$ given the hopping strength $t∕\Gamma =1$ and level spacing $({\epsilon }_A-{\epsilon }_B)∕\Gamma =-2$.

Figure 12

$J\text{−}V$ characteristics and $dJ∕dV$ for increasing relative level spacing $({\epsilon }_A-{\epsilon }_B)∕\Gamma$ given a fixed hopping rate $t∕\Gamma =1$. Note that the solid $J\text{−}V$ curve is the same as one given in Fig. 1.

Figure 13

$J\text{−}V$ characteristics and $dJ∕dV$ for increasing hopping rate $t∕\Gamma$ given a fixed relative level spacing $({\epsilon }_A-{\epsilon }_B)∕\Gamma =-8∕3$.