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Conducting polymers are of interest for a broad range of applications from bioelectronics to thermoelectrics. The factors that govern their complex charge transport physics include the structural disorder present in these highly doped polymer films and the Coulombic interactions between the electronic charge carriers and the dopant counterions. Previous studies have shown that at low doping levels carriers are strongly trapped in the vicinity of the counterions, while at high doping levels charge transport is not limited by Coulombic trapping, which manifests itself in the conductivity being independent of the size of the dopant counterion. Here we use a recently developed ion exchange doping method to investigate the ion size dependence of a semi-crystalline polythiophene-based model system across a wide range of conductivities. We find that the regime, in which the charge and thermoelectric transport is not or only weakly dependent on ion size, extends to surprisingly low conductivities. We explain this surprising observation by a heterogeneous doping that involves doping of the amorphous domains to high doping levels first before doping of the ordered, crystalline domains occurs. Our study provides new insights into how the thermoelectric physics of conducting polymers evolves as a function of doping level.

Organic thermoelectrics offer the potential to deliver flexible, low-cost devices that can directly convert heat to electricity. Previous studies have reported high conductivity and thermoelectric power factor in the conjugated polymer poly[2,5-bis(3-tetradecylthiophen-2-yl)thieno[3,2- b]thiophene] (PBTTT). Here we investigate the thermoelectric properties of PBTTT films, in which the polymer chains were aligned uniaxially by mechanical rubbing and the films were doped by a recently developed ion exchange technique that provides a choice over the counterions incorporated into the film, allowing for more optimized morphology and better stability than conventional charge transfer doping. To optimize the polymer alignment process we took advantage of two Design of Experiment (DOE) techniques, Regular Two-Level Factorial Design and Central Composite Design. Rubbing temperature Trub and post-alignment annealing temperature Tanneal were the two factors that were most strongly correlated with conductivity. We were able to achieve high polymer alignment with a dichroic ratio > 15 and high electrical conductivities of up to 4345 S/cm for transport parallel to the polymer chains demonstrating that the ion exchange method can achieve conductivities comparable/higher than conventional charge transfer doping. While the conductivity of aligned films increased by a factor of 4 compared to unaligned films, the Seebeck coefficient (S) remained nearly unchanged. The combination of DOE methodology, high-temperature rubbing, and ion exchange doping provide a systematic, controllable strategy to tune structure-thermoelectric property relationships in semiconducting polymers.

Heavy heteroatom substitution of the backbone is an effective strategy to improve molecular packing and charge delocalization in polymer semiconductors. Such a backbone modification also facilitates oxidative doping as a result of reduced ionization potential. Here, we explore the effect of single-atom selenium substitution on doping and charge transport properties of a class of polythiophene copolymers. The room temperature conductivities of the doped polymers are significantly enhanced by the selenium substitution for both molecular doping and ion exchange doping. The enhanced conduction is rationalized by the better crystallinity of the selenium-containing system, which can be reinforced by a chain-extended ribbon-phase morphology induced by thermal annealing, which is robust towards doping. The resulting increase in the charge delocalization of the doped selenium-containing system is evidenced by temperature-dependent conductivities. In ion exchange doped films we achieve the maximum conductivity of ~700 S/cm and a high thermoelectric power factor of 46.5 μW m-1 K-2 for the doped selenophene polymer and we observed signatures of a Metal-Insulator transition that are characteristics for heterogeneous conduction systems. Our results show that single-atom selenium substitution is an effective molecular design approach for improving the charge transport and thermoelectric properties of conjugated polymers.

The measurement of the mechanical properties of conjugated polymers can reveal highly relevant information linking optoelectronic properties to underlying microstructures and the knowledge of the glass transition temperature ( Tg ) is paramount for informing the choice of processing conditions and for interpreting the thermal stability of devices. In this work, we use dynamical mechanical analysis (DMA) to determine Tg of a range of state-of-the-art conjugated polymers with different degrees of crystallinity that are widely studied for applications in organic field-effect transistors (OFETs). We compare our measured values for Tg to the theoretical value predicted by a recent work based on the concept of effective mobility ζ. The comparison shows that for conjugated polymers with a modest length of the monomer units, the Tg values agree well with theoretical predictions. However, for the near-amorphous, indacenodithiophene–benzothiadiazole (IDT-BT) family of polymers with more extended backbone units, values for Tg appear to be significantly higher predicted by theory. We find instead that values for Tg are correlated with the sub-bandgap optical absorption suggesting the possible role of the interchain short contacts within materials’ amorphous domains.

Air-stable semiconducting inks suitable for complementary logic are key to create low-power printed integrated circuits (ICs). High-performance printable electronic inks with two-dimensional materials have the potential to enable the next generation of high performance, low-cost printed digital electronics. Here we demonstrate air-stable, low voltage (< 5 V) operation of inkjet-printed n-type molybdenum disulfide (MoS2) and p-type indacenodithiophene-co-benzothiadiazole (IDT-BT) field-effect transistors (FETs), estimating a switching time of {\tau} ~ 3.3 {\mu}s for the MoS2 FETs. We achieve this by engineering high-quality MoS2 and air-stable IDT-BT inks suitable for inkjet-printing complementary pairs of n-type MoS2 and p-type IDT-BT FETs. We then integrate MoS2 and IDT-BT FETs to realise inkjet-printed complementary logic inverters with a voltage gain |Av| ~ 4 when in resistive load configuration and |Av| ~ 1.36 in complementary configuration. These results represent a key enabling step towards ubiquitous long-term stable, low-cost printed digital ICs.

The thermoelectric effect is a physical phenomenon which intricately relates the thermal energy of charge carriers to their charge transport. Understanding the mechanism of this interaction in different systems lies at the heart of inventing novel materials which can revolutionize thermoelectric power gener- ation technology. Despite a recent surge of interest in organic thermoelectric materials, the community has had difficulties in formulating the charge trans- port mechanism in the presence of a significant degree of disorder. Here, we analyze the thermoelectric properties of various conducting polymers doped by a solid-state diffusion of dopant molecules based on a transport model with a power-law energy-dependence of transport function. A fine control of the degree of doping via post-doping annealing provides an accurate empirical evidence of a strong energy dependence of the carrier mobility in the conducting polymers. A superior thermoelectric power factor of conducting polymers doped by solid-state diffusion to that of other doping methods can be attributed to a resulting higher intrinsic mobility and higher free carrier concentration.

Vezie, Michelle S. et al., The specific optical absorption of an organic semiconductor is critical to the performance of organic optoelectronic devices. For example, higher light-harvesting efficiency can lead to higher photocurrent in solar cells that are limited by sub-optimal electrical transport. Here, we compared over 40 conjugated polymers, and found that many different chemical structures share an apparent maximum in their extinction coefficients. However, a diketopyrrolopyrrole-thienothiophene copolymer shows remarkably high optical absorption at relatively low photon energies. By investigating its backbone structure and conformation with measurements and quantum chemical calculations, we find that the high optical absorption can be explained by the high persistence length of the polymer. Accordingly, we demonstrate high absorption in other polymers with high theoretical persistence length. Visible light harvesting may be enhanced in other conjugated polymers through judicious design of the structure., M.S.V. and S. F. are grateful to the Engineering and Physical Sciences Research Council (EPSRC) for a doctoral training award and a CDT studentship (EP/G037515/1) respectively. G.P. and S.C.H. acknowledge the University of Cyprus for funding through the internal grant "ORGANIC". B.D., A.G. and M.C.Q. acknowledge financial support from the Ministerio de Economía y Competitividad of Spain through projects CSD2010–00044 (Consolider NANOTHERM), SEV-2015_0496 and MAT2012–37776 and the European Research Council through project ERC CoG648901. I.M., R.S.A. and I.McC. acknowledge support from the European Commission FP7 Project ArtESun (604397). J.N. is grateful to the Royal Society for a Wolfson Merit Award, and acknowledges financial support from EPSRC grants EP/K030671/1, EP/K029843/1 and EP/J017361/1. The authors thank Dr. Isabel Alonso for performing supplementary ellipsometric measurements; we thank Prof. Thomas Kirchartz, Dr. Jarvist Moore Frost, Dr. Christian Müller and Dr. Isabel Alonso for helpful discussions.

Organic semiconductors can be employed as the active layer in accumulation mode organic electrochemical transistors (OECTs), where redox stability in aqueous electrolytes is important for long‐term recordings of biological events. It is observed that alkoxy‐benzo[1,2‐b:4,5‐b′]dithiophene (BDT) copolymers can be extremely unstable when they are oxidized in aqueous solutions. The redox stability of these copolymers can be improved by molecular design of the copolymer where it is observed that the electron rich comonomer 3,3′‐dimethoxy‐2,2′‐bithiophene (MeOT2) lowers the oxidation potential and also stabilizes positive charges through delocalization and resonance effects. For copolymers where the comonomers do not have the same ability to stabilize positive charges, irreversible redox reactions are observed with the formation of quinone structures, being detrimental to performance of the materials in OECTs. Charge distribution along the copolymer from density functional theory calculations is seen to be an important factor in the stability of the charged copolymer. As a result of the stabilizing effect of the comonomer, a highly stable OECT performance is observed with transconductances in the mS range. The analysis of the decomposition pathway also raises questions about the general stability of the alkoxy‐BDT unit, which is heavily used in donor–acceptor copolymers in the field of photovoltaics.

We report a neutral salt water based battery which uses p-type and n-type solution processed polymer films as the cathode and the anode of the cell. The specific capacity of the electrodes (approximately 30 mAh cm-3) is achieved via formation of bipolarons in both the p-type and n-type polymers. By engineering ethylene glycol and zwitterion based side chains attached to the polymer backbone we facilitate rapid ion transport through the non-porous polymer films. This, combined with efficient transport of electronic charge via the conjugated polymer backbones, allowed the films to maintain constant capacity at high charge and discharge rates (>1000 C-rate). The electrodes also show good stability during electrochemical cycling (less than 30% decrease in capacity over >1000 cycles) and an output voltage up to 1.4 V. The performance of these semiconducting polymers with polar side-chains demonstrates the potential of this material class for fast-charging, water based electrochemical energy storage devices.

Conventional semiconducting polymer synthesis typically involves transition metal mediated coupling reactions that link aromatic units with single bonds along the backbone. Rotation around these bonds contributes to conformational and energetic disorder and therefore potentially limits charge delocalization, whereas the use of transition metals present difficulties for sustainability and application in biological environments. We show that a simple aldol condensation reaction can prepare polymers where double bonds lock-in a rigid backbone conformation, thus eliminating free rotation along the conjugated backbone. This polymerization route requires neither organometallic monomers nor transition metal catalysts and offers a reliable design strategy to facilitate delocalization of frontier molecular orbitals, elimination of energetic disorder arising from rotational torsion and allowing closer interchain electronic coupling. These characteristics are desirable for high charge carrier mobilities. Our polymers with a high electron affinity display long wavelength NIR absorption with air stable electron transport in solution processed organic thin film transistors.

The control of spins and spin to charge conversion in organics requires understanding the molecular spin-orbit coupling (SOC), and a means to tune its strength. However, quantifying SOC strengths indirectly through spin relaxation effects has proven diffi- cult due to competing relaxation mechanisms. Here we present a systematic study of the g-tensor shift in molecular semiconductors and link it directly to the SOC strength in a series of high mobility molecular semiconductors with strong potential for future devices. The results demonstrate a rich variability of the molecular g-shifts with the effective SOC, depending on subtle aspects of molecular composition and structure. We correlate the above g -shifts to spin-lattice relaxation times over four orders of magnitude, from 200 {\mu}s to 0.15 {\mu}s, for isolated molecules in solution and relate our findings for isolated molecules in solution to the spin relaxation mechanisms that are likely to be relevant in solid state systems., Comment: Accepted for publication in Nature Communications

Diketopyrrolopyrrole (DPP) - based polymers have been consistently used for the fabrication of solar cell devi ces and transistors, due to the existence of intermolecular short contacts, resulting in high electron and hole mobilities. However, they also often show limit ed external quantum efficiencies (EQEs). In this contribution we analyze the limitations on EQE by a combined study of exciton dissociation efficiency, charge separation and recombination kinetics in thin films and solar devices of a DPP - based donor polyme r, DPPTT - T ( thieno[3,2 - b]thiophene - diketopyrrolopyrrole copolymer ) blended with varying weight fractions of the fullerene acceptor PC 70 BM. From the correlations between photoluminescence quenching (PLQ), transient absorption studies an d EQE measurements, w e conclude that the main limitation of photon - to - charge conversion in DPPTT - T/PC 70 BM devices is poor exciton dissociation. This exciton quenching limit is related to the low affinity/miscibility of the materials, as confirmed by WAXD diffraction and t ransmission electron microscopy data, but also to the relatively short DPPTT - T singlet exciton lifetime , possibly associated with high non - radiative losses . A further strategy to improve EQE in this class of polymers without sacrificing the good extraction properties in optimized blends is therefore to limit those non - radiative decay processes.

In this paper, we compare the photophysics and photovoltaic device performance of two indenofluorene based polymers: poly[2,8-(6,6,12,12-tetraoctylindenofluorene)-co-4,7-(2,1,3-benzothiodiazole] (IF8BT) and poly[2,8-(6,6,12,12-tetraoctylindenofluorene)-co-5,5-(40,70-di-2-thienyl-20,10,30-benzothiodiazole] (IF8TBTT) blended with [6,6]-phenyl C61 butyric acid methyl ester (PCBM). Photovoltaic devices made with IF8TBTT exhibit greatly superior photocurrent generation and photovoltaic efficiency compared to those made with IF8BT. The poor device efficiency of IF8BT/PCBM devices is shown to result from efficient, ultrafast singlet F€orster energy transfer from IF8BT to PCBM, with the resultant PCBM singlet exciton lacking sufficient energy to drive charge photogeneration. The higher photocurrent generation observed for IF8TBTT/PCBM devices is shown to result from IF8TBTT’s relatively weak, red-shifted photoluminescence characteristics, which switches off the polymer to fullerene singlet energy transfer pathway. As a consequence, IF8TBTT singlet excitons are able to drive charge separation at the polymer/fullerene interface, resulting in efficient photocurrent generation. These results are discussed in terms of the impact of donor/acceptor energy transfer upon photophysics and energetics of charge photogeneration in organic photovoltaic devices. The relevance of these results to the design of polymers for organic photovoltaic applications is also discussed, particularly with regard to explaining why highly luminescent polymers developed for organic light emitting diode applications often give relatively poor performance in organic photovoltaic devices.

Using density-matrix renormalization-group calculations for infinite cylinders, we elucidate the properties of the spin-liquid phase of the spin-$\frac{1}{2}$ $J_1$-$J_2$ Heisenberg model on the triangular lattice. We find four distinct ground-states characteristic of a non-chiral, $Z_2$ topologically ordered state with vison and spinon excitations. We shed light on the interplay of topological ordering and global symmetries in the model by detecting fractionalization of time-reversal and space-group dihedral symmetries in the anyonic sectors, which leads to coexistence of symmetry protected and intrinsic topological order. The anyonic sectors, and information on the particle statistics, can be characterized by degeneracy patterns and symmetries of the entanglement spectrum. We demonstrate the ground-states on finite-width cylinders are short-range correlated and gapped; however some features in the entanglement spectrum suggest that the system develops gapless spinon-like edge excitations in the large-width limit., Comment: 6 pages, 4 figures, 1 table, and 10 pages of supplemental materials. v3: equivalent to the published version

Resonance Raman Spectroscopy (RRS) is employed in this study to examine the influence of molecular weight on the optical response of a diketopyrrolopyrrole polymer (DPP-TT-T) in solution. The vibronic structure observed for the ground state absorption of this polymer is found to vary with molecular weight and solvent. Resonance Raman Intensity Analysis (RRIA) revealed that the absorption spectra can be described by at least two dipole-allowed transitions and the vibronic structure variation is due to differing contributions from linear and curved segments of the polymer. © 2016 SPIE. 9923 Sponsors: The Society of Photo-Optical Instrumentation Engineers (SPIE) Conference code: 125526

We study the phase diagram of the frustrated Heisenberg model on the triangular lattice with nearest and next-nearest neighbor spin exchange coupling, on 3-leg ladders. Using the density-matrix renormalization-group method, we obtain the complete phase diagram of the model, which includes quasi-long-range $120^\circ$ and columnar order, and a Majumdar-Ghosh phase with short-ranged correlations. All these phases are non-chiral and planar. We also identify the nature of phase transitions., Comment: 12 pages, 15 figures, 1 table, and no supplemental materials. v3: equivalent to the published version

We report the discovery of a correlated insulator with a bulk gap at two-thirds filling in a geometrically frustrated Hubbard model that describes the low-energy physics of Mo$_3$S$_7$(dmit)$_3$. This is very different from the Mott insulator expected at half-filling. We show that the insulating phase, which persists even for very weak electron-electron interactions ($U$), is adiabatically connected to the Haldane phase and is consistent with experiments on Mo$_3$S$_7$(dmit)$_3$, Comment: 4+epsilon pages; accepted by PRL

A series of low bandgap indacenodithiophene polymers is purified by recycling SEC in order to isolate narrow polydispersity fractions. This additional purification step is found to have a significant beneficial influence on the solar cell performance and the reasons for this performance increase are investigated.

Electromechanical systems currently offer a path to engineering quantum states of microwave and micromechanical modes that are of both fundamental and applied interest. Particularly desirable, but not yet observed, are mechanical states that exhibit entanglement, wherein non-classical correlations exist between distinct modes; squeezing, wherein the quantum uncertainty of an observable quantity is reduced below the standard quantum limit; and Schr\"odinger cats, wherein a single mode is cast in a quantum superposition of macroscopically distinct classical states. Also, while most investigations of electromechanical systems have focussed on single- or few-body scenarios, the many-body regime remains virtually unexplored. In such a regime quantum phase transitions naturally present themselves as a resource for quantum state generation, thereby providing a route toward entangling a large number of electromechanical systems in highly non-classical states. Here we show how to use existing superconducting circuit technology to implement a (quasi) quantum phase transition in an array of electromechanical systems such that entanglement, squeezing, and Schr\"odinger cats become simultaneously observable across multiple microwave and micromechanical oscillators., Comment: main: 19 pages, 6 figures. suppl. info.: 8 pages, 4 figures. v3: new and expanded numerical results with damping, slightly different system parameters, supplementary information added, changed title and abstract. Comments welcome. Note: some characters missing in figures due to arXiv latex compiler error

Organic field-effect transistors exhibit operational instabilities when a gate bias is applied. For a constant gate bias the threshold voltage shifts towards the applied gate bias voltage, an effect known as the bias-stress effect. We have performed a detailed experimental and theoretical study of operational instabilities in p-type transistors with silicon-dioxide gate dielectric. We propose a mechanism in which holes in the semiconductor are converted into protons in the presence of water and a reversible migration of these protons into the gate dielectric to explain the instabilities in organic transistors. We show how redistribution of charge between holes in the semiconductor and protons in the gate dielectric can consistently explain the experimental observations. Furthermore, we explain in detail the recovery of a pres-stressed transistor on applying zero gate bias. We show that recovery dynamics depends strongly on the extent of stressing. Our mechanism is consistent with the known aspects of bias-stress effect like acceleration due to humidity, constant activation energy and reversibility.

Matrix Product State (MPS) wavefunctions have many applications in quantum information and condensed matter physics. One application is to represent states in the thermodynamic limit directly, using a small set of position independent matrices. For this infinite MPS ansatz to be useful it is necessary to be able to calculate expectation values, and we show here that a large class of observables, including operators transforming under lattice translations as eigenstates of arbitrary momentum $k$, can be represented in the Schur form of a lower or upper triangular matrix and we present an algorithm for evaluating such expectation values in the asymptotic limit. The sum or the product of two such Schur operators is also a Schur operator, and is easily constructed to give a simple method of constructing arbitrary polynomial combinations of operators. Some simple examples are the variance $\langle (H-E)^2\rangle$ of an infinite MPS, which gives a simple method of evaluating the accuracy of a numerical approximation to a eigenstate, or a vertex operator $\langle c^\dagger_{k_1} c^\dagger_{k_2} c_{k_4} c_{k_3}\rangle$. This approach is a step towards improved algorithms for the calculation of dynamical properties and excited states.

Using density matrix renormalization group calculations, ground state properties of the spin-1 Heisenberg chain with exchange and single-ion anisotropies in an external field are studied. Our findings confirm and refine recent results by Sengupta and Batista, Physical Review Letters 99, 217205 (2007) (2007), on the same model applying Monte Carlo techniques. In particular, we present evidence for two types of biconical (or supersolid) and for two types of spin-flop (or superfluid) structures. Basic features of the quantum phase diagram may be interpreted qualitatively in the framework of classical spin models., Comment: Ref. 1 corrected (also in the abstract)

I revisit the infinite-size variant of the Density Matrix Renormalization Group (iDMRG) algorithm for obtaining a fixed-point translationally invariant matrix product wavefunction in the context of one-dimensional quantum systems. A crucial ingredient of this algorithm is an efficient transformation for obtaining the matrix elements of the wavefunction as the lattice size is increased, and I introduce here a versatile transformation that is demonstrated to be much more effective than previous versions. The resulting algorithm has a surprisingly close relationship to Vidal's Time Evolving Block Decimation for infinite systems, but allows much faster convergence. Access to a translationally invariant matrix product state allows the calculation of correlation functions based on the transfer matrix, which directly gives the spectrum of all correlation lengths. I also show some advantages of the Matrix Product Operator (MPO) technique for constructing expectation values of higher moments, such as the exact variance $$., Comment: 12 pages, 3 figures

By Cu NMR we studied the spin and charge structure in Nd_{2-x}Ce_{x}CuO_{4-delta}. For x=0.15, starting from a superconducting sample, the low temperature magnetic order in the sample reoxygenated under 1 bar oxygen at 900^0 C, reveals a peculiar modulation of the internal field, indicative for a phase characterized by large charge droplets ('Blob'-phase). By prolonged reoxygenation at 4 bar the blobs brake up and the spin structure changes to that of an ordered antiferromagnet (AF). We conclude that the superconductivity in the n-type systems competes with a genuine type I Mott-insulating state.

We demonstrate that the notion of spin-charge separation as follows from the Tomonaga-Luttinger theory of relativistic fermions does not suffice to completely specify the Luttinger liquid state associated with the fermions of condensed matter physics. The latter carries in addition a form of topological order which can be made visible using non-local correlation functions familiar from lattice gauge theory., Comment: 4 pages, 2 figures

We determine the boundary of the fully polarized ferromagnetic ground state in the one dimensional Kondo lattice model at partial conduction electron band filling by using a newly developed infinite size DMRG method which conserves the total spin quantum number. The obtained paramagnetic to ferromagnetic phase boundary is below $J \approx 3.5$ for the whole range of band filling. By this we solve the controversy in the phase diagram over the extent of the ferromagnetic region close to half filling., Comment: 6 pages, 4 EPS figures. Presented at MOS99

The thermoelectric effect is a physical phenomenon which intricately relates the thermal energy of charge carriers to their charge transport. Understanding the mechanism of this interaction in different systems lies at the heart of inventing novel materials which can revolutionize thermoelectric power gener- ation technology. Despite a recent surge of interest in organic thermoelectric materials, the community has had difficulties in formulating the charge trans- port mechanism in the presence of a significant degree of disorder. Here, we analyze the thermoelectric properties of various conducting polymers doped by a solid-state diffusion of dopant molecules based on a transport model with a power-law energy-dependence of transport function. A fine control of the degree of doping via post-doping annealing provides an accurate empirical evidence of a strong energy dependence of the carrier mobility in the conducting polymers. A superior thermoelectric power factor of conducting polymers doped by solid-state diffusion to that of other doping methods can be attributed to a resulting higher intrinsic mobility and higher free carrier concentration.

We present the synthesis of a novel diphenylanthracene (DPA) based semiconducting polymer. The polymer is solubilised by alkoxy groups attached directly to a DPA monomer, meaning the choice of co-monomer is not limited to exclusively highly solubilising moieties. Interestingly, the polymer shows a red-shifted elecroluminescence maximum (510 nm) when compared to its photoluminescence maximum (450 nm) which we attribute to excimer formation. The novel polymer was utilised as a host for a covalently-linked platinum(ii) complexed porphyrin dopant. Emission from these polymers was observed in the NIR and again showed almost a 100 nm red shift from photoluminescence to electroluminescence. This work demonstrates that utilising highly aggregating host materials is an effective tool for inducing red-shifted emission in OLEDs.