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In this comprehensive study, we conduct a theoretical investigation into the Stark shift of topological states (TSs) in finite armchair graphene nanoribbons (AGNRs) and heterostructures under transverse electric fields. Our focus centers on the multiple end zigzag edge states of AGNRs and the interface states of $9-7-9$ AGNR heterostructures. For the formal TSs, we observe a distinctive blue Stark shift in energy levels relative to the electric field within a range where the energy levels of TSs do not merge into the energy levels of bulk states. Conversely, for the latter TSs, we identify an oscillatory Stark shift in energy levels around the Fermi level. Simultaneously, we reveal the impact of the Stark effect on the transmission coefficients for both types of TSs. Notably, we uncover intriguing spectra in the multiple end zigzag edge states. In the case of finite $9-7-9$ AGNR heterostructures, the spectra of transmission coefficient reveal that the coupling strength between the topological interface states can be well controlled by the transverse electric fields. The outcomes of this research not only contribute to a deeper understanding of the electronic property in graphene-based materials but also pave the way for innovations in next-generation electronic devices and quantum technologies., Comment: 7 pages and 10 figures

We theoretically investigate charge transport through serial double quantum dots (SDQDs) with strong electron correlations using nonequilibrium Green's function techniques. In the linear response regime, we compute the charge stability diagram and analyze the Coulomb oscillatory tunneling current, revealing both thermal and nonthermal broadening effects on the current spectra in relation to two gate voltages. In the nonlinear response regime, we focus on tunneling currents in SDQDs under the Pauli spin blockade (PSB) scenario. We find that current rectification with negative differential conductance is significantly degraded as temperature increases, making it challenging to distinguish between the inter-site spin triplet and singlet states. Notably, we observe a robust reversed tunneling current that remains stable against temperature variations, provided the resonant channel in the PSB scenario is coupled to the states of the right (left) electrode, which is fully occupied by particles (depleted). This characteristic provides valuable insights for designing transistors capable of operating over a wide temperature range., Comment: 10 pages and 5 Figures

This study investigates the band inversion of flat bands in zigzag graphene nanoribbons (ZGNRs) using a tight-binding model. The band inversion results from symmetry breaking in the transverse direction, achievable through deposition on specific substrates such as separated silicon carbide or hexagonal boron nitride sheets. Upon band inversion, ZGNRs exhibit electronic structures characterized by valley degeneracy and band gap properties, which can be modulated by transverse electric fields. To explore the impact of this level degeneracy on thermoelectric properties, we employ Green's function techniques to calculate thermoelectric quantities in ZGNR segments with staggered sublattice potentials and transverse electric fields. Two carrier transport scenarios are considered: the chemical potential is positioned above and below the highest occupied molecular orbital. We analyze thermionic-assisted transport (TAT) and direct ballistic transport (DBT). Level degeneracy enhances the electric power factors of ZGNRs by increasing electrical conductance, while the Seebeck coefficient remains robust in the TAT scenario. Conversely, in DBT, the enhancement of the power factor primarily stems from improvements in the Seebeck coefficient at elevated temperatures., Comment: 10 pages and 12 figures

This comprehensive study investigates charge transport through the multiple end zigzag edge states of finite-size armchair graphene nanoribbons/boron nitride nanoribbons (n-AGNR/w-BNNR) junctions under a longitudinal electric field, where n and w denote the widths of the AGNRs and the BNNRs, respectively. In 13-atom wide AGNR segments, the edge states exhibit a blue Stark shift in response to the electric field, with only the long decay length zigzag edge states showing significant interaction with the red Stark shift subband states. Charge tunneling through such edge states assisted by the subband states is elucidated in the spectra of the transmission coefficient. In the 13-AGNR/6-BNNR heterojunction, notable influences on the energy levels of the end zigzag edge states of 13-AGNRs induced by BNNR segments are observed. We demonstrate the modulation of these energy levels in resonant tunneling situations, as depicted by bias-dependent transmission coefficient spectra. Intriguing nonthermal broadening of tunneling current shows a significant peak-to-valley ratio. Our findings highlight the promising potential of n-AGNR/w-BNNR heterojunctions with long decay length edge states in the realm of GNR-based single electron transistors at room temperature., Comment: In the revised manuscript, we have added new references

The thermoelectric properties of armchair graphene nanoribbons (AGNRs) with array characteristics are investigated theoretically using the tight-binding model and Green's function technique. The AGNR structures with array characteristics are created by embedding a narrow boron nitride nanoribbon (BNNR) into a wider AGNR, resulting in two narrow AGNRs. This system is denoted as w-AGNR/n-BNNR, where 'w' and 'n' represent the widths of the wider AGNR and narrow BNNR, respectively. We elucidate the coupling effect between two narrow symmetrical AGNRs on the electronic structure of w-AGNR/n-BNNR. A notable discovery is that the power factor of the 15-AGNR/5-BNNR with the minimum width surpasses the quantum limitation of power factor for 1D ideal systems. The energy level degeneracy observed in the first subbands of w-AGNR/n-BNNR structures proves to be highly advantageous in enhancing the electrical power outputs of graphene nanoribbon devices., Comment: 6 pages and 5 figures, revised manuscript

In this comprehensive study, we undertake a thorough theoretical examination of the electronic subband structures within cove-edged zigzag graphene nanoribbons (CZGNRs) using the tight-binding model. These unique nanostructures arise from the systematic removal of carbon atoms along the zigzag edges of conventional zigzag graphene nanoribbons (ZGNRs). Notably, CZGNRs that exhibit intriguing band gaps can be conceptualized as interconnected graphene quantum dots (GQDs). An essential finding of our investigation is the inverse relationship between the size of GQDs and the band gaps of CZGNRs, a relationship that remains consistent regardless of the number of GQDs present. Additionally, we delve into the examination of electron effective masses in proximity to the edges of the first conduction subband of CZGNRs as GQD sizes expand. We observe a significant increase in electron effective masses as GQDs become larger, which is attributed to the increasing similarity between larger GQDs and ZGNRs. To further understand the practical implications, we explore the transport properties of finite CZGNRs when connected to electrodes through line contacts. The presence of edge defects introduces intriguing asymmetries in the tunneling current, leading to a significant reduction in its magnitude. Notably, we observe that the saturation current magnitude is less influenced by the length of CZGNRs and is instead more sensitive to the choice of materials used for the contacted electrodes. Lastly, we investigate the tunneling currents through GQDs featuring boron nitride textures within the Coulomb blockade region, unveiling an irregular staircase-like pattern in the tunneling current behavior., Comment: 10 pages and 11 figures

We present a theoretical investigation of electron heat current in asymmetrical length armchair graphene nanoribbon (AGNR) heterostructures with vacancies, focusing on the topological states (TSs). In particular, we examine the 9-7-9 AGNR heterostructures where the TSs are well-isolated from the conduction and valence subbands. This isolation effectively mitigates thermal noise of subbands arising from temperature fluctuations during charge transport. Moreover, when the TSs exhibit an orbital off-set, intriguing electron heat rectification phenomena are observed, primarily attributed to inter-TS electron Coulomb interactions. To enhance the heat rectification ratio ($\eta_Q$), we manipulate the coupling strengths between the heat sources and the TSs by introducing asymmetrical lengths in the 9-AGNRs. This approach offers control over the rectification properties, enabling significant enhancements. Additionally, we introduce vacancies strategically positioned between the heat sources and the TSs to suppress phonon heat current. This arrangement effectively reduces the overall phonon heat current, while leaving the TSs unaffected. Our findings provide valuable insights into the behavior of electron heat current in AGNR heterostructures, highlighting the role of topological states, inter-TS electron Coulomb interactions, and the impact of structural modifications such as asymmetrical lengths and vacancy positioning. These results pave the way for the design and optimization of graphene-based devices with improved thermal management and efficient control of electron heat transport., Comment: 13 pages and 13 figures

In this study, we investigate the charge transport properties of semiconducting armchair graphene nanoribbons (AGNRs) and heterostructures through their topological states (TSs), with a specific focus on the Coulomb blockade region. Our approach employs a two-site Hubbard model that takes into account both intra- and inter-site Coulomb interactions. Using this model, we calculate the electron thermoelectric coefficients and tunneling currents of serially coupled TSs (SCTSs). In the linear response regime, we analyze the electrical conductance ($G_e$), Seebeck coefficient ($S$), and electron thermal conductance ($\kappa_e$) of finite AGNRs. Our results reveal that at low temperatures, the Seebeck coefficient is more sensitive to many-body spectra than the electrical conductance. Furthermore, we observe that the optimized $S$ at high temperature is less sensitive to electron Coulomb interactions than $G_e$ and $\kappa_e$. In the nonlinear response regime, we observe a tunneling current with negative differential conductance through the SCTSs of finite AGNRs. This current is generated by electron inter-site Coulomb interactions rather than intra-site Coulomb interactions. Additionally, we observe current rectification behavior in asymmetrical junction systems of SCTSs of AGNRs. Notably, we also uncover the remarkable current rectification behavior of SCTSs of 9-7-9 AGNR heterostructure in the Pauli spin blockade configuration. Overall, our study provides valuable insights into the charge transport properties of TSs in finite AGNRs and heterostructures. We emphasize the importance of considering electron-electron interactions in understanding the behavior of these materials., Comment: corrected some typos

We theoretically analyze the thermoelectric properties of graphene quantum dot arrays (GQDAs) with line- or surface-contacted metal electrodes. Such GQDAs are realized as zigzag graphene nanoribbons (ZGNRs) with periodic vacancies. Gaps and minibands are formed in these GQDAs, which can have metallic and semiconducting phases. The electronic states of the first conduction (valence) miniband with nonlinear dispersion may have long coherent lengths along the zigzag edge direction. With line-contacted metal electrodes, the GQDAs have the characteristics of serially coupled quantum dots (SCQDs) if the armchair edge atoms of the ZGNRs are coupled to the electrodes. By contrast, the GQDAs have the characteristics of parallel QDs if the zigzag edge atoms are coupled to the electrodes. The maximum thermoelectric power factors of SCQDs with line-contacted electrodes of Cu, Au, Pt, Pd, or Ti at room temperature were similar or greater than $0.186~nW/K$; their figures of merit were greater than three. GQDAs with line-contacted metal electrodes have much better thermoelectric performance than surface contacted metal electrodes., Comment: 9 pages, 12 figures and improve Fig. 2

Transport and thermoelectric properties of finite textured graphene nanoribbons (t-GNRs) connected to electrodes with various coupling strengths are theoretically studied in the framework of the tight-binding model and Green's function approach. Due to quantum constriction induced by the indented edges, such t-GNRs behave like serially-coupled graphene quantum dots (SGQDs). These types of SGQDs can be formed by tailoring zigzag GNRs (ZGNRs) or armchair GNRs (AGNRs). Their bandwidths and gaps can be engineered by varying the size of the quantum dot and the neck width at indented edges. Effects of defects and contact junction on electrical conductance, Seebeck coefficient and electron thermal conductance of t-GNRs are calculated. When a defect occurs in the interior site of textured ZGNRs (t-ZGNRs), the maximum power factor within the central gap or near the band edges is found to be insensitive to the defect scattering. Furthermore, we found that SGQDs formed by t-ZGNRs have significantly better electrical power outputs than those of textured ANGRs due to the improved functional shape of the transmission coefficient in t-ZGNRs. With a proper design of contact the maximum power factor ( figure of merit) of t-ZGNRs could reach $90\%$ ($95\%$) of the theoretical limit., Comment: 12 pages, 14 figures, typos and new references

How to design silicon-based quantum wires with figure of merit ($ZT$) larger than three is under hot pursuit due to the advantage of low cost and the availability of matured fabrication technique. Quantum wires consisting of finite three dimensional quantum dot (QD) arrays coupled to electrodes are proposed to realize high efficient thermoelectric devices with optimized power factors. The transmission coefficient of 3D QD arrays can exhibit 3D, 2D, 1D and 0D topological distribution functions by tailoring the interdot coupling strengths. Such topological effects on the thermoelectric properties are revealed. The 1D topological distribution function shows the maximum power factor and the best $ZT$ value. We have demonstrated that 3D silicon QD array nanowires with diameters below $20~nm$ and length $250~nm$ show high potential to achieve $ZT\ge 3$ near room temperature., Comment: 5 pages, 6 figures

Novel intrinsic two-dimensional materials have attracted many researchers' attention. The unusual transport and optical properties of these materials originate mainly from triangular lattices (TLs). Therefore, the application of energy harvesting calls for a study of the thermoelectric properties of 2D TLs coupled to electrodes. The transmission coefficient of 2D TLs is calculated by using the Green's function technique to treat ballistic transports. Especially important among our findings is the electron-hole asymmetric behavior of the power factor ($PF$). Specifically, the maximum $PF$ of electrons is significantly larger than that of holes. At room temperature, the maximum $PF$ of electrons is dictated by the position of the chemical potential of electrodes near the band edge of TLs. The enhancement of $PF$ with increasing electronic states results from the enhancement of electrical conductance and constant Seebeck coefficient. When the band gap is ten times larger than the thermal energy, it is appropriate to make one-band model predictions for thermoelectric optimization., Comment: 6 pages, 7 figures

The thermal power ($PF=S^2G_e$) depends on the Seebeck coefficient ($S$) and electron conductance ($G_e$). The enhancement of $G_e$ will unavoidably suppress $S$ because they are closely related. As a consequence, the optimization of $PF$ is extremely difficult. Here, we theoretically investigated the thermoelectric properties of two-dimensional quantum dot (QD) arrays with carriers injected from electrodes. The Lorenz number of 2D QD arrays in the resonant tunneling procedure satisfies the Wiedemann-Franz law, which confirms the formation of minibands. When the miniband center is far away from the Fermi level of the electrodes, the electron transport is in the thermionic-assisted tunneling procedure (TATP). In this regime, $G_e$ in band-like situation and $S$ in atom-like situation can happen simultaneously. We have demonstrated that the enhancement of $G_e$ with an increasing number of electronic states will not suppress $S$ in the TATP., Comment: 5 pages, 6 figures

Heat engines made of quantum-dot (QD) superlattice nanowires (SLNWs) offer promising applications in energy harvesting due to the reduction of phonon thermal conductivity. In solid state electrical generators (refrigerators), one needs to generate (remove) large amount of charge current (heat current). Consequently, a high QD SLNW density is required for realistic applications. This study theoretically investigated the properties of power factor and electron heat rectification for an SLNW array under the transition from a one dimensional system to a two dimensional system. The SLNW arrays show the functionality of heat diodes, which is mainly attributed to a transmission coefficient with a temperature-bias direction dependent characteristic., Comment: 8 pages, 11 figures

Heat engines (HEs) made of low dimensional structures offer promising applications in energy harvesting due to their reduced phonon thermal conductance. Many efforts have been devoted to the design of HEs made of quantum-dot (QD) superlattice nanowire (SLNW), but only SLNWs with uniform energy levels in QDs were considered. Here we propose a HE made of SLNW with staircase-like QD energy levels. It is demonstrated that the nonlinear Seebeck effect can lead to significant electron transports for such a nanowire with staircase-like energy levels. The asymmetrical alignment of energy levels of quantum dots embedded in nanowires can be controlled to allow resonant electron transport under forward temperature bias, while they are in off-resonant regime under backward bias. Under such a mechanism,the power output and efficiency of such a SLNW are better than SLNWs with uniform QD energy levels. The SLNW HE has direction-dependent power output and heat current. In addition, the HE has the functionality of a heat diode with impressive negative differential thermal conductance under open circuit condition., Comment: 6 pages and 5 figures

It is known that the figure of merit ($ZT$) of thin nanowires can be significantly enhanced at room temperature due to the reduction of phonon thermal conductance arising from the increase of boundary scattering of phonons. It is expected that the phonon thermal conductance of nanowires filled with quantum dots (QDs) will be further reduced. Here we consider a superlattice nanowire (SLNW) modeled by a linear chain of strongly coupled QDs connected to electrodes. We study the dependence of $ZT$ on the QD energy level ($E_0$) (relative to the Fermi level $E_F$ in the electrodes), inter-dot coupling strength ($t_c$), tunneling rate ($\Gamma$), and temperature $T$ in order to optimize the design. It is found that at room temperature the maximum power factor occurs when $(E_0-E_F)/k_BT \approx 2.4$ and $\Gamma=t_c$, a result almost independent of the number of QDs in SLNW as long as $t_c/k_BT <0.5$. By using reasonable physical parameters we show that thin SLNW with cross-sectional width near $3~nm$ has a potential to achieve $ZT\ge3$., Comment: 6 pages, 6 figures and correct title of article

The quantum dot arrays (QDAs) embedded into inhomogeneous nanowires connected to metallic electrodes show an electron heat rectification effect, which is attributed to the thermal voltage arising from a temperature bias and the QDA with a broken spatial inversion symmetry. The staircase energy levels of QDAs can be controlled to the resonant and off resonant transports for electrons in the forward and backward temperature biases, respectively. The effect of electron Coulomb interactions on the rectification efficiency of heat diode is clarified by the case of double QDs. We find that it is important to reduce phonon heat currents for implementing a high efficient electron heat diode at high temperature., Comment: 5 pages and 6 figures

It is theoretically demonstrated that the figure of merit ($ZT$) of quantum dot (QD) junctions can be significantly enhanced when the degree of degeneracy of the energy levels involved in electron transport is increased. The theory is based on the the Green-function approach in the Coulomb blockade regime by including all correlation functions resulting from electron-electron interactions associated with the degenerate levels ($L$). We found that electrical conductance ($G_e$) as well as electron thermal conductance ($\kappa_e$) are highly dependent on the level degeneracy ($L$), whereas the Seebeck coefficient ($S$) is not. Therefore, the large enhancement of $ZT$ is mainly attributed to the increase of $G_e$ when the phonon thermal conductance ($\kappa_{ph}$) dominates the heat transport of QD junction system. In the serially coupled double-QD case, we also obtain a large enhancement of $ZT$ arising from higher $L$. Unlike $G_e$ and $\kappa_e$, $S$ is found almost independent on electron inter-dot hopping strength., Comment: typos corrections

The nonlinear electron and heat currents of quantum dot molecules (QDMs) under a temperature bias are theoretically investigated, including all correlation functions arising from electron Coulomb interactions in QDMs. Unlike the case of double QDs, the maximum efficiency of serially coupled triple QDs (SCTQD) occurs in the orbital depletion regime owing to the interdot Coulomb blockade. The electron current in SCTQD shows a bipolar oscillatory behavior with respect to the variation of QD energy levels, whereas the heat current does not show such a behavior. This is mainly attributed to thermal-induced bias. In addition, we illustrate how the efficiency of SCTQD is influenced by the external load resistance, and phonon heat flow. Finally, a direction-dependent electron current driven by a temperature bias has been demonstrated for a SCTQD with staircase-like energy levels., Comment: 8 pages and 9 figures. arXiv admin note: substantial text overlap with arXiv:1601.00812

The transport of electrons through serially coupled quantum dot molecules (SCQDM) is investigated theoretically for application as an energy harvesting engine (EHE), which converts thermal heat to electrical power. We demonstrate that the charge current driven by a temperature bias shows bipolar oscillatory behavior with respect to gate voltage due to the unbalance between electrons and holes, which is different from the charge current driven by an applied bias. In addition, we reveal a Lenz's law between the charge current and the thermal induced voltage. The efficiency of EHE is higher for SCQDM in the orbital depletion situation rather than the orbital filling situation, owing to the many-body effect. The EHE efficiency is enhanced with increasing temperature bias, but suppressed as the electron hopping strength reduces. The fluctuation of QD energy levels at different sites also leads to a reduction of EHE efficiency. Finally, we demonstrate direction-dependent charge currents driven by the temperature bias for application as a novel charge diode., Comment: 6 pages and 8 figures

The quantum interference and orbital filling effects on the thermoelectric (TE) properties of quantum dot molecules with high figure of merit are illustrated via the full solution to the Hubbard- Anderson model in the Coulomb blockade regime. It is found that under certain condition in the triangular QD molecule (TQDM), destructive quantum interference (QI) can occur, which leads to vanishing small electrical conductance, while the Seebeck coefficient is modified dramatically. When TQDM is in the charge localization state due to QI, the Seebeck coefficient is seriously suppressed at low temperature, but highly enhanced at high temperature. Meanwhile, the behavior of Lorenz number reveals that it is easier to block charge transport via destructive QI than the electron heat transport at high temperatures. The maximum power factor (PF) in TQDM occurs at full-filling condition. Nevertheless, low-filling condition is preferred for getting maximum PF in serially coupled triple QDs in general. In double QDs, the maximum PF can be achieved either with orbital-depletion or orbital-filling as a result of electron-hole symmetry. Our theoretical work provides a useful guideline for advancing the nanoscale TE technology., Comment: 7 pages, 8 figures and errors correction

The thermoelectric properties of quantum dot arrays (QDAs) embedded in nanowires connected to electrodes are studied theoretically in the Coulomb blockade regime. A Hurbbard-Anderson model is used to simulate the electronic contribution to thermoelectric proper- ties of a QDA junction system. The electrical conductance, Seebeck coefficient, and electron thermal conductance are calculated by both the Keldysh Green function method and the mean-field approach. The phonon thermal conductivities are calculated by using the equation of phonon radiative transfer method. In the Coulomb blockade regime the electron thermal conductance is much smaller than the phonon thermal conductance. Therefore, the optimal figure of merit (ZT) can be enhanced by increasing thermal power and decreasing phonon thermal conductance simultaneously. We found that it is possible to obtain ZT value of InGaAs/GaAs QDAs embedded in nanowires larger than one at room temperature., Comment: 6 pages, 6 figures and some corrections

We study the charge transport properties of triangular quantum dot molecule (TQDM) connected to metallic electrodes, taking into account all correlation functions and relevant charging states. The quantum interference (QI) effect of TQDM resulting from electron coherent tunneling between quantum dots is revealed and well interpreted by the long distance coherent tunneling mechanism. The spectra of electrical conductance of TQDM with charge filling from one to six electrons clearly depict the many-body and topological effects. The calculated charge stability diagram for conductance and total occupation numbers match well with the recent experimental measurements. We also demonstrate that the destructive QI effect on the tunneling current of TQDM is robust with respect to temperature variation, making the single electron QI transistor feasible at higher temperatures.

The effect of long distance coherent tunneling (LDCT) on the charge and heat currents in serially coupled triple quantum dots (TQDs) connected to electrodes is illustrated by using a combination of the extended Hurbbard model and Anderson model. The charge and heat currents are calculated with a closed-form Landauer expression for the transmission coefficient suitable for the Coulomb blockade regime. The physical parameters including bias-dependent quantum dot energy levels, electron Coulomb interactions, and electron hopping strengths are calculated in the framework of effective mass theory for semiconductor TQDs. We demonstrate that the effect of LDCT on the charge and heat currents can be robust. In addition, it is shown that prominent heat rectification behavior can exist in the TQD system with asymmetrical energy levels., Comment: 15 pages, 5 figures

The nonlinear thermoelectric properties of serially coupled quantum dots (SCQDs) embedded in a nanowire connected to metallic electrodes are theoretically studied in the Coulomb blockade regime. We demonstrate that the electron heat current of SCQDs exhibit a direction-dependent behavior (heat rectification) in an asymmetrical structure in which the electron Coulomb interactions are significant. The phonon thermal conductivity of the nanowire is also calculated, which is used to estimate the phonon heat current. Finally, we discuss how to reduce phonon heat current to allow observation of electron heat rectification behavior in the SCQD junction system in low temperature regime ($\approx 3 K$)., Comment: 9 pages and 6 figures

The transport properties of a metal core/semiconductor shell quantum dot molecule (QDM) embedded in a matrix connected to metallic electrodes are theoretically studied in the framework of Keldysh Green function technique. The effects of the electron plasmon interactions (EPIs) on the tunneling current spectra of QDM are examined. The energy levels of the QDs, intradot and interdot Coulomb interactions, electron interdot hopping strengths, and tunneling rates of QDs are renormalized by the EPIs. The differential conductance spectra show peaks arising from the plasmon assisted tunneling process, intradot and interdot Coulomb interactions, and coherent tunneling between the QDs., Comment: 4 pages, 4 figures

The transport properties of serially coupled quantum dots (SCQDs) embedded in a matrix connected to metallic electrodes are theoretically studied in the linear and nonlinear regimes. The current rectification and negative differential conductance of SCQDs under the Pauli spin blockade condition are attributed to the combination of bias-direction dependent probability weight and off-resonant energy levels yielded by the applied bias across the junctions. We observe the spin-polarization current rectification under the Zeeman effect. The maximum spin-polarization current occurs in the forward bias regime. Such behavior is different from the charge current rectification. Finally, the Seebeck coefficient ($S$)of SCQDs is calculated and analyzed in the cases without and with electron phonon interactions. The application of SCQDs as a temperature detector is discussed on the basis of the nonlinear behavior of $S$ with respect to temperature difference across the junction., Comment: 7 pages, 7 figures

The thermoelectric properties of a semiconduct quantum dot chain (SQDC) connected to metallic electrodes are theoretically investigated in the Coulomb blockade regime. An extended Hubbard model is employed to simulate the SQDC system consisted of {\color{blue}N=2,3,4, and 5} quantum dots (QDs). The charge and heat currents are calculated in the framework of Keldysh Green's function technique. We obtained a closed-form Landauer expression for the transmission coefficient of the SQDC system with arbitrary number of QDs by using the method beyond mean-field theory. The electrical conductance ($G_e$), Seebeck coefficient (S), thermal conductance, and figure of merit (ZT) are numerically calculated and analyzed in the linear response regime. When thermal conductance is dominated by phonon carriers, the optimization of ZT is determined by the power factor ($pF=S^2G_e$). We find that the optimization of ZT value favors the following conditions:(1) QDs with low energy level fluctuations, (2) QD energy levels lie above the Fermi level of electrodes, (3) $\Gamma < t_c \ll U_0$, where $t_c$, $U_0$, and $\Gamma$ are electron interdot hopping strength, on-site electron Coulomb interaction, and tunneling rate, respectively, and (4) $\Gamma_L=\Gamma_R$ with $\Gamma_L+\Gamma_R$ kept constant, where $\Gamma_L (\Gamma_R)$ is the left (right) tunneling rate. It is predicted that high ZT values can be achieved by tailoring above conditions., Comment: 23 pages and 10 figures

We study bistability in the electron transport through a ring of N coupled quantum dots with two orbitals in each dot. One orbital is localized (called b orbital) and coupling of the b orbitals in any two dots is negligible; the other is delocalized in the plane of the ring (called d orbital), due to coupling of the d orbitals in the neighboring dots, as described by a tight-binding model. The d orbitals thereby form a band with finite width. The b and d orbitals are connected to the source and drain electrodes with a voltage bias V, allowing the electron tunnelling. Tunnelling current is calculated by using a nonequilibrium Green function method recently developed to treat nanostructures with multiple energy levels. We find a bistable effect in the tunnelling current as a function of bias V, when the size N>50; this effect scales with the size N and becomes sizable at N~100. The temperature effect on bistability is also discussed. In comparison, mean-field treatment tends to overestimate the bistable effect., Comment: Published in JPSJ; minor typos corrected

We have theoretically studied the thermoelectric properties of serially coupled quantum dots (SCQD) embedded in an insulator matrix connected to metallic electrodes. In the framework of Keldysh Green's function technique, the Landauer formula of transmission factor is obtained by using the equation of motion method. Based on such analytical expressions of charge and heat currents, we calculate the electrical conductance, Seebeck coefficient, electron thermal conductance and figure of merit (ZT) of SCQD in the linear response regime. The effects of electron Coulomb interactions on the reduction and enhancement of ZT are analyzed. We demonstrate that ZT is not a monotonic increasing function of interdot electron hopping strength ($t_c$). We also show that in the absence of phonon thermal conductance, SCQD can reach the Carnot efficiency as $t_c$ approaches zero., Comment: corrected some argumenets

The Seebeck coefficient (S) of a serially coupled quantum dot (SCQD) junction system is theoretically studied via a two-level Anderson model. A change of sign in S with respect to temperature is found, which arises from the competition between tunneling currents due to electrons and holes (i.e, bipolar tunneling effect). The change of sign in S implies that one can vary the equilibrium temperature to produce thermoelectric current in either the forward or reverse direction, leading to a bipolar thermoelectric effect. For the case of two parallel SCQDs, we also observe the oscillatory behavior of S with respect to temperature., Comment: revised argument and corrected some typos

The charge transport of a serially coupled quantum dots (SCQD) connected to the metallic electrodes is theoretically investigated in the Coulomb blockade regime. A closed-form expression for the tunneling current of SCQD in the {\color{red} weak interdot hopping} limit is obtained by solving an extended two-site Hubbard model via the Green's function method. We use this expression to investigate spin current rectification, negative differential conductance, and coherent tunneling in the nonlinear response regime. The current rectification arising from the space symmetry breaking of SCQD is suppressed by increasing temperature. The calculation of SCQD is extended to the case of multiple parallel SCQDs for studying the charge ratchet effect and SCQD with multiple levels. In the linear response regime, the functionalities of spin filter and low-temperature current filter are demonstrated to coexist in this system. It is further demonstrated that two-electron spin singlet and triplet states can be readily resolved from the measurement of Seebeck coefficient rather than that of electrical conductance., Comment: 11 pages, 9 figures. Revised argument, results unchanged, added references

Based on the multiple energy level Anderson model, this study theoretically examines the thermoelectric effects of semiconductor quantum dots (QDs) in the nonlinear response regime. The charge and heat currents in the sequential tunneling process are calculated by using the Keldysh Green's function technique. Results show that the thermal rectification effect can be observed in a multiple QD junction system, whereas the tunneling rate, size fluctuation, and location distribution of QD significantly influence the rectification efficiency., Comment: 5 pages, 8figures

The electrical conductance, thermal conductance, thermal power and figure of merit (ZT) of semiconductor quantum dots (QDs) embedded into an insulator matrix connected with metallic electrodes are theoretically investigated in the Coulomb blockade regime. The multilevel Anderson model is used to simulate the multiple QDs junction system. The charge and heat currents in the sequential tunneling process are calculated by the Keldysh Green function technique. In the linear response regime the ZT values are still very impressive in the small tunneling rates case, although the effect of electron Coulomb interaction on ZT is significant. In the nonlinear response regime, we have demonstrated that the thermal rectification behavior can be observed for the coupled QDs system, where the very strong asymmetrical coupling between the dots and electrodes, large energy level separation between dots and strong interdot Coulomb interactions are required., Comment: 8 page and 14 figures

It is illustrated that semiconductor quantum dots (QDs) embedded into an insulating matrix connected with metallic electrodes and some vacuum space can lead to significant thermal rectification effect. A multilevel Anderson model is used to investigate the thermal rectification properties of the multiple-QD junction. The charge and heat currents in the tunneling process are calculated via the Keldysh Green's function technique. We show that pronounced thermal rectification and negative differential thermal conductance (NDTC) behaviors can be observed for the multiple-QD junction with asymmetrical tunneling rates and strong interdot Coulomb interactions., Comment: 3 pages, 4 figures

We demonstrate that two-dimensional (2D) arrays of coupled quantum dots (QDs) with six-fold degenerate p orbitals can display bistable states, suitable for application in high-density memory device with low power consumption. Due to the inter-dot coupling of $p_x$ and $p_y$ orbitals in these QD arrays, two dimensional conduction bands can be formed in the x-y plane, while the $p_z$ orbitals remain localized in the x-y plane such that the inter-dot coupling between them can be neglected. We model such systems by taking into account the on-site repulsive interactions between electrons in $p_z$ orbitals and the coupling of the localized $p_z$ orbitals with the 2D conduction bands formed by $p_x$ and $p_y$ orbitals. The Green's function method within an extended Anderson model is used to calculate the tunneling current through the QDs. We find that bistable tunneling current can exist for such systems due to the interplay of the on-site Coulomb interactions (U) between the $p_z$ orbitals and the delocalized nature of conduction band states derived from the hybridization of $p_x$ / $p_y$ orbitals. This bistable current is not sensitive to the detailed band structure of the two dimensional band, but depends critically on the strength of $U$ and the ratio of the left and right tunneling rates. The behavior of the electrical bistability can be sustained when the 2D QD array reduces to a one-dimensional QD array, indicating the feasibility for high-density packing of these bistable nanoscale structures.

A multi-level Anderson model is employed to simulate the system of a nanostructure tunnel junction with any number of one-particle energy levels. The tunneling current, including both shell-tunneling and shell-filling cases, is theoretically investigated via the nonequilibrium Green's function method. We obtain a closed form for the spectral function, which is used to analyze the complicated tunneling current spectra of a quantum dot or molecule embedded in a double-barrier junction. We also show that negative differential conductance can be observed in a quantum dot tunnel junction when the Coulomb interactions with neighboring quantum dots are taken into account., Comment: 4 pages and 4 figures

The dynamic properties of light-emitting single-electron transistors (LESETs) made from quantum dots are theoretically studied by using nonequilibrium Green's function method. Holes residing at QD created by small ac signals added in the base electrode of valence band lead to the exciton assisted tunnelling level for the electron tunnelling from emitter to collector, it is therefore such small signals can be amplified. LESETs can be employed as efficient single-photon detectors., Comment: 10 pages, 8 figures

The time-dependent tunnelling current arising from the electron-hole recombination of exciton state is theoretically studied using the nonequilibrium Green's function technique and the Anderson model with two energy levels. The charge conservation and gauge invariance are satisfied in the tunnelling current. Apart from the classical capacitive charging and discharging behavior, interesting oscillations superimpose on the tunnelling current for the applied rectangular pulse voltage., Comment: 14 pages, 5 figures

The transient tunneling current of single electron transistors (SETs) is theoretically investigated. The time-dependent current formula given by Jauho, Wingreen and Meir [Phys. Rev. B 50, 5528 (1994)] is applied to study the temperature effect on the transient current through a single quantum dot embedded into asymmetry barrier. It is found that the tunneling rate ratio significantly influences the feature of transient current. Finally, the oscillation structures on the exponential growth transient current of single hole transistors composed of germanium quantum dots is analyzed., Comment: 4 pages and 9 figures

We theoretically study the intraband transition spectrum of single electron transistors (SETs) composed of individual self-assembled quantum dots. The polarization of SETs is obtained by using the nonequilibrium Green's function technique and the Anderson model with three energy levels. Owing to nonradiative coupling between two excited states through the continuum of electrodes, the Fano interference effect significantly influences the peak position and intensity of infrared wavelength single-photon spectrum., Comment: 4 pages, 5 figures

The emission spectrum of exciton complexes formed in individual self-assembled quantum dots (QDs) embedded into a p-n junction is theoretically studied using an effective mass model. We calculate the particle Coulomb interactions, eletron-hole overlaps and transition energies of exciton complexes for the different strength and direction of electric field. Both redshifts and blueshifts are observed in exciton, trions and biexciton. The Stark effect may be applied to manipulate the spontaneous emission rate of individual QDs embedded in microcavities., Comment: 13pages and 7 figures

Theoretical studies of the tunnelling current and emission spectrum of a single electron transistor (SET) under optical pumping are presented. The calculation is performed via Keldysh Green's function method within the Anderson model with two energy levels. It is found that holes in the quantum dot (QD) created by optical pumping lead to new channels for the electron tunnelling from emitter to collector. As a consequence, an electron can tunnel through the QD via additional channels, characterized by the exciton, trion and biexciton states. It is found that the tunnelling current as a function of the gate voltage displays a series of sharp peaks and the spacing between these peaks can be used to determine the exciton binding energy as well as the electron-electron Coulomb repulsion energy. In addition, we show that the single-photon emission associated with the electron-hole recombination in the exciton complexes formed in the QD can be controlled both electrically and optically., Comment: 24 pages, 10 figures

The charge transport behaviors of parallel double single electron transistors (SETs) are investigated by the Anderson model with two impurity levels. The nonequilibrium Keldysh Green's technique is used to calculate the current-voltage characteristics of system. For SETs implemented by quantum dots (QDs) embedded into a thin $SiO_2$ layer, the interdot Coulomb repulsion is more important than the interdot electron hopping as a result of high potential barrier height between QDs and $SiO_2$. We found that the interdot Coulomb repulsion not onlyleads to new resonant levels, but also creates negative differential conductances., Comment: 12 pages, 7 figures

We theoretically study the tunnelling current of a single electron transistor (SET) under optical pumping. It found that holes in the quantum dot(QD) created by optical pumping lead to new channels for the electrons tunnelling from emitter to collector. As a consequence, an electron can tunnel through the QD via additional channels, characterized by the exciton, trion and biexciton states. The binding energy of exciton complexes can be determined by the Coulomb oscillatory tunnelling current., Comment: 9 pages, 2 figures

The effect of electron correlation on the photocurrent of self-assembled InAs/InGaAs quantum dot infrared photo-detector (QDIPs) is studied. It is found that Coulomb interaction and level mixing in the many-body open system lead to double peaks associated with the intra-band transitions involving two lowest levels of the quantum dot. Furthermore, the photocurrent is a nonlinear function of the steady-state carrier density and it displays a plateau due to Coulomb blockade., Comment: 7 pages, 3 figures