Understanding Doping of Quantum Materials.

Doping mobile carriers into ordinary semiconductors such as Si, GaAs, and ZnO was the enabling step in the electronic and optoelectronic revolutions. The recent emergence of a class of "quantum materials", where uniquely quantum interactions between the components produce specific behaviors such as topological insulation, unusual magnetism, superconductivity, spin-orbit-induced and magnetically induced spin splitting, polaron formation, and transparency of electrical conductors, pointed attention to a range of doping-related phenomena associated with chemical classes that differ from the traditional semiconductors. These include wide-gap oxides, compounds containing open-shell d electrons, and compounds made of heavy elements yet having significant band gaps. The atomistic electronic structure theory of doping that has been developed over the past two decades in the subfield of semiconductor physics has recently been extended and applied to quantum materials. The present review focuses on explaining the main concepts needed for a basic understanding of the doping phenomenology and indeed peculiarities in quantum materials from the perspective of condensed matter theory, with the hope of forging bridges to the chemists that have enabled the synthesis of some of the most interesting compounds in this field.

Antidoping in Insulators and Semiconductors Having Intermediate Bands with Trapped Carriers.

Ordinary doping by electrons (holes) generally means that the Fermi level shifts towards the conduction band (valence band) and that the conductivity of free carriers increases. Recently, however, some peculiar doping characteristics were sporadically recorded in different materials without noting the mechanism: electron doping was observed to cause a portion of the lowest unoccupied band to merge into the valance band, leading to a decrease in conductivity. This behavior, that we dub as "antidoping," was seen in rare-earth nickel oxides SmNiO_{3}, cobalt oxides SrCoO_{2.5}, Li-ion battery materials, and even MgO with metal vacancies. We describe the physical origin of antidoping as well as its inverse problem-the "design principles" that would enable an intelligent search of materials. We find that electron antidoping is expected in materials having preexisting trapped holes and is caused by the annihilation of such "hole polarons" via electron doping. This may offer an unconventional way of controlling conductivity.

Topological Insulators versus Topological Dirac Semimetals in Honeycomb Compounds.

Intriguing physical properties of materials stem from their chemical constituents, whereas the connection between them is often not clear. Here, we uncover a general chemical classification for the two quantum phases in the honeycomb ABX structure-topological insulator (TI) and topological Dirac semimetal (TDSM). First, we find among the 816 (existing as well as hypothetical) calculated compounds, 160 TIs (none were noted before), 96 TDSMs, 282 normal insulators (NIs), and 278 metals. Second, based on this classification, we have distilled a simple chemical regularity based on compound formulas for the selectivity between TI and TDSM: the ABX compounds that are TDSM have B atoms (part of the BX honeycomb layers) that come from the periodic table columns XI (Cu, Ag, Au) or XII (Zn, Cd, Hg), or Mg (group II), whereas the ABX compounds whose B atoms come from columns I (Li, Na, K, Rb, Cs) or II (Ca, Sr, Ba) are TIs. Third, focusing on the ABX bismide compounds that are thermodynamically stable, we find a structural motif that delivers topological insulation and stability at the same time. This study opens the way to simultaneously design new topological materials based on the compositional rules indicated here.

Electron Doping of Proposed Kagome Quantum Spin Liquid Produces Localized States in the Band Gap.

Carrier doping of quantum spin liquids is a long-proposed route to the emergence of high-temperature superconductivity. Electrochemical intercalation in kagome hydroxyl halide materials shows that samples remain insulating across a wide range of electron counts. Here we demonstrate through first-principles density-functional calculations, corrected for self-interaction, the mechanism by which electrons remain localized in various Zn-Cu hydroxyl halides, independent of the chemical identity of the dopant-the formation of polaronic states with attendant lattice displacements and a dramatic narrowing of bandwidth upon electron addition. The same theoretical method applied to electron doping in cuprate Nd_{2}CuO_{4} correctly produces a metallic state when the initially formed polaron dissolves into an extended state. Our general findings explain the insulating behavior in a wide range of "doped" quantum magnets and demonstrate that new quantum spin liquid host materials are needed to realize metallicity borne of a spin liquid.

Cu-In Halide Perovskite Solar Absorbers.

The long-term chemical instability and the presence of toxic Pb in otherwise stellar solar absorber APbX3 made of organic molecules on the A site and halogens for X have hindered their large-scale commercialization. Previously explored ways to achieve Pb-free halide perovskites involved replacing Pb2+ with other similar M2+ cations in ns2 electron configuration, e.g., Sn2+ or by Bi3+ (plus Ag+), but unfortunately this showed either poor stability (M = Sn) or weakly absorbing oversized indirect gaps (M = Bi), prompting concerns that perhaps stability and good optoelectronic properties might be contraindicated. Herein, we exploit the electronic structure underpinning of classic Cu[In,Ga]Se2 (CIGS) chalcopyrite solar absorbers to design Pb-free halide perovskites by transmuting 2Pb to the pair [BIB + CIII] such as [Cu + Ga] or [Ag + In] and combinations thereof. The resulting group of double perovskites with formula A2BCX6 (A = K, Rb, Cs; B = Cu, Ag; C = Ga, In; X = Cl, Br, I) benefits from the ionic, yet narrow-gap character of halide perovskites, and at the same time borrows the advantage of the strong Cu(d)/Se(p) → Ga/In(s/p) valence-to-conduction-band absorption spectra known from CIGS. This constitutes a new group of CuIn-based Halide Perovskite (CIHP). Our first-principles calculations guided by such design principles indicate that the CIHPs class has members with clear thermodynamic stability, showing direct band gaps, and manifesting a wide-range of tunable gap values (from zero to about 2.5 eV) and combination of light electron and heavy-light hole effective masses. Materials screening of candidate CIHPs then identifies the best-of-class Rb2[CuIn]Cl6, Rb2[AgIn]Br6, and Cs2[AgIn]Br6, having direct band gaps of 1.36, 1.46, and 1.50 eV, and theoretical spectroscopic limited maximal efficiency comparable to chalcopyrites and CH3NH3PbI3. Our finding offers a new routine for designing new-type Pb-free halide perovskite solar absorbers.

Rapid Transition of the Hole Rashba Effect from Strong Field Dependence to Saturation in Semiconductor Nanowires.

The electric field manipulation of the Rashba spin-orbit coupling effects provides a route to electrically control spins, constituting the foundation of the field of semiconductor spintronics. In general, the strength of the Rashba effects depends linearly on the applied electric field and is significant only for heavy-atom materials with large intrinsic spin-orbit interaction under high electric fields. Here, we illustrate in 1D semiconductor nanowires an anomalous field dependence of the hole (but not electron) Rashba effect (HRE). (i) At low fields, the strength of the HRE exhibits a steep increase with the field so that even low fields can be used for device switching. (ii) At higher fields, the HRE undergoes a rapid transition to saturation with a giant strength even for light-atom materials such as Si (exceeding 100 meV Å). (iii) The nanowire-size dependence of the saturation HRE is rather weak for light-atom Si, so size fluctuations would have a limited effect; this is a key requirement for scalability of Rashba-field-based spintronic devices. These three features offer Si nanowires as a promising platform for the realization of scalable complementary metal-oxide-semiconductor compatible spintronic devices.

Strong Absorption Enhancement in Si Nanorods.

We report two orders of magnitude stronger absorption in silicon nanorods relative to bulk in a wide energy range. The local field enhancement and dipole matrix element contributions were disentangled experimentally by single-dot absorption measurements on differently shaped particles as a function of excitation polarization and photon energy. Both factors substantially contribute to the observed effect as supported by simulations of the light-matter interaction and atomistic calculations of the transition matrix elements. The results indicate strong shape dependence of the quasidirect transitions in silicon nanocrystals, suggesting nanostructure shape engineering as an efficient tool for overcoming limitations of indirect band gap materials in optoelectronic applications, such as solar cells.

Quasi-Direct Optical Transitions in Silicon Nanocrystals with Intensity Exceeding the Bulk.

Comparison of the measured absolute absorption cross section on a per Si atom basis of plasma-synthesized Si nanocrystals (NCs) with the absorption of bulk crystalline Si shows that while near the band edge the NC absorption is weaker than the bulk, yet above ∼ 2.2 eV the NC absorbs up to 5 times more than the bulk. Using atomistic screened pseudopotential calculations we show that this enhancement arises from interface-induced scattering that enhances the quasi-direct, zero-phonon transitions by mixing direct Γ-like wave function character into the indirect X-like conduction band states, as well as from space confinement that broadens the distribution of wave functions in k-space. The absorption enhancement factor increases exponentially with decreasing NC size and is correlated with the exponentially increasing direct Γ-like wave function character mixed into the NC conduction states. This observation and its theoretical understanding could lead to engineering of Si and other indirect band gap NC materials for optical and optoelectronic applications.

Evolution of electronic structure as a function of layer thickness in group-VIB transition metal dichalcogenides: emergence of localization prototypes.

Layered group-VIB transition metal dichalcogenides (with the formula of MX2) are known to show a transition from an indirect band gap in the thick n-monolayer stack (MX2)n to a direct band gap at the n = 1 monolayer limit, thus converting the system into an optically active material suitable for a variety of optoelectronic applications. The origin of this transition has been attributed predominantly to quantum confinement effect at reduced n. Our analysis of the evolution of band-edge energies and wave functions as a function of n using ab initio density functional calculations including the long-range dispersion interaction reveals (i) the indirect-to-direct band gap transformation is triggered not only by (kinetic-energy controlled) quantum confinement but also by (potential-energy controlled) band repulsion and localization. On its own, neither of the two effects can explain by itself the energy evolution of the band-edge states relevant to the transformation; (ii) when n decreased, there emerge distinct regimes with characteristic localization prototypes of band-edge states deciding the optical response of the system. They are distinguished by the real-space direct/indirect in combination with momentum-space direct/indirect nature of electron and hole states and give rise to distinct types of charge distribution of the photoexcited carriers that control excitonic behaviors; (iii) the various regimes associated with different localization prototypes are predicted to change with modification of cations and anions in the complete MX2 (M = Cr, Mo, W and X = S, Se, Te) series. These results offer new insight into understanding the excitonic properties (e.g., binding energy, lifetime etc.) of multiple layered MX2 and their heterostructures.

Reinterpretation of the expected electronic density of states of semiconductor nanowires.

One-dimensional semiconductor nanowires hold the promise for various optoelectronic applications since they combine the advantages of quantized in-plane energy levels (as in zero-dimensional quantum dots) with a continuous energy spectrum along the growth direction (as in three-dimensional bulk materials). This dual characteristic is reflected in the density of states (DOS), which is thus the key quantity describing the electronic structures of nanowires, central to the analysis of electronic transport and spectroscopy. By comparing the DOS derived from the widely used "standard model", the effective mass approximation (EMA) in single parabolic band mode, with that from direct atomistic pseudopotential theory calculations for GaAs and InAs nanowires, we uncover significant qualitative and quantitative shortcomings of the standard description. In the EMA description the nanowire DOS is rendered as a series of sharply rising peaks having slowly decaying tails, with characteristic peak height and spacing, all being classifiable in the language of atomic orbital momenta 1S, 1P, 1D, etc. Herein we find in the thinner nanowires that the picture changes significantly in that not only does the profile of each DOS peak lose its pronounced asymmetry, with significant changes in peak width, height, and spacing, but also the origin of the high-energy peaks changes fundamentally: below some critical diameter, the region of atomic orbital momentum classified states is occupied by a new set of DOS peaks folded-in from other non-Γ-valleys. We describe explicitly how distinct physical effects beyond the conventional EMA model contribute to these realistic DOS features. These results represent a significant step toward understanding the intriguing electronic structure of nanowires reflecting the coexistence of discrete and continuum states. Experimental examinations of the predicted novel DOS features are called for.

Switching a normal insulator into a topological insulator via electric field with application to phosphorene.

The study of topological insulators has generally involved search of materials that have this property as an innate quality, distinct from normal insulators. Here we focus on the possibility of converting a normal insulator into a topological one by application of an external electric field that shifts different bands by different energies and induces a specific band inversion, which leads to a topological state. Phosphorene is a two-dimensional (2D) material that can be isolated through mechanical exfoliation from layered black phosphorus, but unlike graphene and silicene, single-layer phosphorene has a large band gap (1.5-2.2 eV). Thus, it was unsuspected to exhibit band inversion and the ensuing topological insulator behavior. Using first-principles calculations with applied perpendicular electric field F⊥ on few-layer phosphorene we predict a continuous transition from the normal insulator to a topological insulator and eventually to a metal as a function of F⊥. The tuning of topological behavior with electric field would lead to spin-separated, gapless edge states, that is, quantum spin Hall effect. This finding opens the possibility of converting normal insulating materials into topological ones via electric field and making a multifunctional "field effect topological transistor" that could manipulate simultaneously both spin and charge carrier. We use our results to formulate some design principles for looking for other 2D materials that could have such an electrical-induced topological transition.

Prediction and Synthesis of Strain Tolerant RbCuTe Crystals Based on Rotation of One-Dimensional Nano Ribbons within a Three-Dimensional Inorganic Network.

A unique possibility for a simple strain tolerant inorganic solid is envisioned whereby a set of isolated, one-dimensional (1D) nano objects are embedded in an elastically soft three-dimensional (3D) atomic matrix thus forming an interdimensional hybrid structure (IDHS). We predict theoretically that the concerted rotation of 1D nano objects could allow such IDHSs to tolerate large strain values with impunity. Searching theoretically among the 1:1:1 ABX compounds of I-I-VI composition, we identified, via first-principles thermodynamic theory, RbCuTe, which is a previously unreported but now predicted-to-be-stable compound in the MgSrSi-type structure, in space group Pnma. The predicted structure of RbCuTe consists of ribbons of copper and telluride atoms placed antipolar to one another throughout the lattice with rubidium atoms acting as a matrix. A novel synthetic adaptation utilizing liquid rubidium and vacuum annealing of the mixed elemental reagents in fused silica tubes as well as in situ (performed at the Advanced Photon Source) and ex situ structure determination confirmed the stability and predicted structure of RbCuTe. First-principles calculations then showed that the application of up to ∼30% uniaxial strain on the ground-state structure result in a buildup of internal stress not exceeding 0.5 GPa. The increase in total energy is 15-fold smaller than what is obtained for the same RbCuTe material but in structures having a contiguous set of 3D chemical bonds spanning the entire crystal. Furthermore, electronic structure calculations revealed that the HOMO is a 1D energy band localized on the CuTe ribbons and that the 1D insulating band structure is also resilient to such large strains. This combined theory and experiment study reveals a new type of strain tolerant inorganic material.

Intrinsic circular polarization in centrosymmetric stacks of transition-metal dichalcogenide compounds.

The circular polarization (CP) that the photoluminescence inherits from the excitation source in n monolayers of transition-metal dichalcogenides (MX_{2})_{n} has been previously explained as a special feature of odd values of n, where the inversion symmetry is absent. This "valley polarization" effect results from the fact that, in the absence of inversion symmetry, charge carriers in different band valleys could be selectively excited by different circular polarized light. Although several experiments observed CP in centrosymmetric MX_{2} systems, e.g., for bilayer MX_{2}, they were dismissed as being due to some extrinsic sample irregularities. Here we show that also for n=even, where inversion symmetry is present and valley polarization physics is strictly absent, such intrinsic selectivity in CP is to be expected on the basis of fundamental spin-orbit physics. First-principles calculations of CP predict significant polarization for n=2 bilayers: from 69% in MoS_{2} to 93% in WS_{2}. This realization could broaden the range of materials to be considered as CP sources.

Intrinsic Transparent Conductors without Doping.

Transparent conductors (TCs) combine the usually contraindicated properties of electrical conductivity with optical transparency and are generally made by starting with a transparent insulator and making it conductive via heavy doping, an approach that generally faces severe "doping bottlenecks." We propose a different idea for TC design-starting with a metallic conductor and designing transparency by control of intrinsic interband transitions and intraband plasmonic frequency. We identify the specific design principles for three such prototypical intrinsic TC classes and then search computationally for materials that satisfy them. Remarkably, one of the intrinsic TC, Ag(3)Al(22)O(34), is predicted also to be a prototype 3D compounds that manifest natural 2D electron gas regions with very high electron density and conductivity.

Assessing capability of semiconductors to split water using ionization potentials and electron affinities only.

We show in this article that the position of semiconductor band edges relative to the water reduction and oxidation levels can be reliably predicted from the ionization potentials (IP) and electron affinities (AE) only. Using a set of 17 materials, including transition metal compounds, we show that accurate surface dependent IPs and EAs of semiconductors can be computed by combining density functional theory and many-body GW calculations. From the extensive comparison of calculated IPs and EAs with available experimental data, both from photoemission and electrochemical measurements, we show that it is possible to sort candidate materials solely from IPs and EAs thereby eliminating explicit treatment of semiconductor/water interfaces. We find that at pH values corresponding to the point of zero charge there is on average a 0.5 eV shift of IPs and EAs closer to the vacuum due to the dipoles formed at material/water interfaces.

Charge self-regulation upon changing the oxidation state of transition metals in insulators.

Transition-metal atoms embedded in an ionic or semiconducting crystal can exist in various oxidation states that have distinct signatures in X-ray photoemission spectroscopy and 'ionic radii' which vary with the oxidation state of the atom. These oxidation states are often tacitly associated with a physical ionization of the transition-metal atoms--that is, a literal transfer of charge to or from the atoms. Physical models have been founded on this charge-transfer paradigm, but first-principles quantum mechanical calculations show only negligible changes in the local transition-metal charge as the oxidation state is altered. Here we explain this peculiar tendency of transition-metal atoms to maintain a constant local charge under external perturbations in terms of an inherent, homeostasis-like negative feedback. We show that signatures of oxidation states and multivalence--such as X-ray photoemission core-level shifts, ionic radii and variations in local magnetization--that have often been interpreted as literal charge transfer are instead a consequence of the negative-feedback charge regulation.

Theoretical prediction and experimental realization of new stable inorganic materials using the inverse design approach.

Discovery of new materials is important for all fields of chemistry. Yet, existing compilations of all known ternary inorganic solids still miss many possible combinations. Here, we present an example of accelerated discovery of the missing materials using the inverse design approach, which couples predictive first-principles theoretical calculations with combinatorial and traditional experimental synthesis and characterization. The compounds in focus belong to the equiatomic (1:1:1) ABX family of ternary materials with 18 valence electrons per formula unit. Of the 45 possible V-IX-IV compounds, 29 are missing. Theoretical screening of their thermodynamic stability revealed eight new stable 1:1:1 compounds, including TaCoSn. Experimental synthesis of TaCoSn, the first ternary in the Ta-Co-Sn system, confirmed its predicted zincblende-derived crystal structure. These results demonstrate how discovery of new materials can be accelerated by the combination of high-throughput theoretical and experimental methods. Despite being made of three metallic elements, TaCoSn is predicted and explained to be a semiconductor. The band gap of this material is difficult to measure experimentally, probably due to a high concentration of interstitial cobalt defects.

Genomic design of strong direct-gap optical transition in Si/Ge core/multishell nanowires.

Finding a Si-based material with strong optical activity at the band-edge remains a challenge despite decades of research. The interest lies in combining optical and electronic functions on the same wafer, while retaining the extraordinary know-how developed for Si. However, Si is an indirect-gap material. The conservation of crystal momentum mandates that optical activity at the band-edge includes a phonon, on top of an electron-hole pair, and hence photon absorption and emission remain fairly unlikely events requiring optically rather thick samples. A promising avenue to convert Si-based materials to a strong light-absorber/emitter is to combine the effects on the band-structure of both nanostructuring and alloying. The number of possible configurations, however, shows a combinatorial explosion. Furthermore, whereas it is possible to readily identify the configurations that are formally direct in the momentum space (due to band-folding) yet do not have a dipole-allowed transition at threshold, the problem becomes not just calculation of band structure but also calculation of absorption strength. Using a combination of a genetic algorithm and a semiempirical pseudopotential Hamiltonian for describing the electronic structures, we have explored hundreds of thousands of possible coaxial core/multishell Si/Ge nanowires with the orientation of [001], [110], and [111], discovering some "magic sequences" of core followed by specific Si/Ge multishells, which can offer both a direct bandgap and a strong oscillator strength. The search has revealed a few simple design principles: (i) the Ge core is superior to the Si core in producing strong bandgap transition; (ii) [001] and [110] orientations have direct bandgap, whereas the [111] orientation does not; (iii) multishell nanowires can allow for greater optical activity by as much as an order of magnitude over plain nanowires; (iv) the main motif of the winning configurations giving direct allowed transitions involves rather thin Si shell embedded within wide Ge shells. We discuss the physical origin of the enhanced optical activity, as well as the effect of possible experimental structural imperfections on optical activity in our candidate core/multishell nanowires.