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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Derivation of low-energy Hamiltonians for heavy-fermion materials

Here, by utilizing a multiorbital periodic Anderson model with parameters obtained from ab initio band structure calculations, combined with degenerate perturbation theory, we derive effective Kondo-Heisenberg and spin Hamiltonians that capture the interaction among the effective magnetic moments. This derivation encompasses fluctuations via both nonmagnetic 4⁢𝑓 0 and magnetic 4⁢𝑓 2 virtual states, and its accuracy is confirmed through comparison with experimental data obtained from CeIn 3 . The significant agreement observed between experimental results and theoretical predictions underscores the potential of deriving minimal models from first-principles calculations for achieving a quantitative description of 4⁢𝑓 materials. Moreover, our microscopic derivation unveils the underlying origin of anisotropy in the exchange interaction between Kramers doublets, shedding light on the conditions under which this anisotropy may be weak compared to the isotropic contribution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

BCS-BEC crossover in a (t 2g ) 4 excitonic magnet

The condensation of spin-orbit-induced excitons in t 2 g 4 electronic systems is attracting considerable attention. At large Hubbard U , antiferromagnetism was proposed to emerge from the Bose-Einstein Condensation (BEC) of triplons ( J eff = 1 ). Furthermore, we show that even at intermediate U regimes, the spin-orbit exciton condensation is possible leading also to staggered magnetic order. The canonical electron-hole excitations (excitons) transform into local triplon excitations at large U , and this BEC strong coupling regime is smoothly connected to the intermediate U excitonic insulator region. We solved the degenerate three-orbital Hubbard model with spin-orbit coupling ( λ ) in one dimension using the density matrix renormalization group, while in two dimensions we use the Hartree-Fock approximation (HFA). Employing these techniques, we provide the full λ versus U phase diagrams for both one- and two-dimensional lattices. Our main result is that at intermediate Hubbard U , increasing λ at fixed U the system transitions from an incommensurate spin-density-wave metal to a Bardeen-Cooper-Schrieffer (BCS) excitonic insulator, with coherence length r coh of O ( a ) and O ( 10 a ) in 1 d and 2 d , respectively, with a being the lattice spacing. Further increasing λ , the system eventually crosses over to the BEC limit (with r coh ≪ a ).

1-dimensional systems↗
DOE OSTI2020

Electron transport through antiferromagnetic spin textures and skyrmions in a magnetic tunnel junction

An ideal layered $\hat{x}$-polarized antiferromagnet (AFM) between two antialigned $±\hat{z}$ polarized ferromagnetic (FM) contacts transmits no current due to a π phase difference of the matrix elements coupling the spin degenerate states to the two FM contacts. Inserting a normal-metal layer or tunnel barrier layer between one FM contact and the AFM alters this phase difference, and due to the unequal weighting of the two spins at the interface, it also breaks the spin degeneracy of the two AFM states. Further, the broken symmetry of the matrix elements combined with the broken degeneracy of the AFM states results in a Fano resonance in the transmission and a turn-on of the $T_{↑,↓}$ transmission channel. Such a magnetic tunnel junction geometry with two antialigned $±\hat{z}$ FM contacts can electrically detect an AFM skyrmion. The AFM skyrmion serves as an analog of the oblique polarizer in the triple-polarizer experiment. Resistances and resistance ratios are calculated and compared for FM and AFM skyrmions in a magnetic tunnel junction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Ferrorotational domain walls revealed by electric quadrupole second harmonic generation microscopy

Domain walls are ubiquitous in materials that undergo phase transitions driven by spontaneous symmetry breaking. Domain walls in ferroics and multiferroics have received tremendous attention recently due to their emergent properties distinct from their domain counterparts—for example, their high mobility and controllability, as well as their potential applications in nanoelectronics. However, it is extremely challenging to detect, visualize, and study the ferrorotational (FR) domain walls because the FR order, in contrast to ferromagnetism and ferroelectricity, is invariant under both the spatial-inversion and the time-reversal operations and, thus, hardly couple with conventional experimental probes. Here, a FR candidate NiTi⁢O 3 is investigated by ultrasensitive electric quadrupole (EQ) second-harmonic generation rotational anisotropy (SHG RA) to probe the point symmetries of the two degenerate FR domain states, showing their relation by the vertical mirror operations that are broken below the FR critical temperature. We then visualize the real-space FR domains by scanning EQ SHG microscopy, and further, resolve the FR domain walls by revealing a suppressed SHG intensity at the domain walls. By taking local EQ SHG RA measurements, we show the restoration of the mirror symmetry at FR domain walls and prove their unconventional nonpolar nature. In conclusion, our findings not only provide a comprehensive insight into FR domain walls, but also demonstrate a unique and powerful tool for future studies on domain walls of unconventional ferroics both of which pave the way towards future manipulations and applications of FR domain walls.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Emergent disorder and mechanical memory in periodic metamaterials

Ordered mechanical systems typically have one or only a few stable rest configurations, and hence are not considered useful for encoding memory. Multistable and history-dependent responses usually emerge from quenched disorder, for example in amorphous solids or crumpled sheets. In contrast, due to geometric frustration, periodic magnetic systems can create their own disorder and espouse an extensive manifold of quasi-degenerate configurations. Inspired by the topological structure of frustrated artificial spin ices, we introduce an approach to design ordered, periodic mechanical metamaterials that exhibit an extensive set of spatially disordered states. While our design exploits the correspondence between frustration in magnetism and incompatibility in meta-mechanics, our mechanical systems encompass continuous degrees of freedom, and thus generalize their magnetic counterparts. We show how such systems exhibit non-Abelian and history-dependent responses, as their state can depend on the order in which external manipulations were applied. We demonstrate how this richness of the dynamics enables to recognize, from a static measurement of the final state, the sequence of operations that an extended system underwent. Thus, multistability and potential to perform computation emerge from geometric frustration in ordered mechanical lattices that create their own disorder.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Twisted bilayer graphene. IV. Exact insulator ground states and phase diagram

Here, we derive the exact insulator ground states of the projected Hamiltonian of magic-angle twisted bilayer graphene (TBG) flat bands with Coulomb interactions in various limits, and study the perturbations away from these limits. We define the (first) chiral limit where the AA stacking hopping is zero, and a flat limit with exactly flat bands. In the chiral-flat limit, the TBG Hamiltonian has a U(4) × U(4) symmetry, and we find that the exact ground states at integer filling – 4 ≤ $\textit{ν}$ ≤ 4 relative to charge neutrality are Chern insulators of Chern numbers $ν_C$ = 4 – |$\textit{ν}$ |, 2 – |$\textit{ν}$ |, $\cdots$, |$\textit{ν}$ | – 4, all of which are degenerate. This confirms recent experiments where Chern insulators are found to be competitive low-energy states of TBG. When the chiral-flat limit is reduced to the nonchiral-flat limit which has a U(4) symmetry, we find $\textit{ν}$ = 0 , ± 2 has exact ground states of Chern number 0, while $\textit{ν}$ = ±1, ± 3 has perturbative ground states of Chern number $ν_C$ = ± 1, which are U(4) ferromagnetic. In the chiral-nonflat limit with a different U(4) symmetry, different Chern number states are degenerate up to second-order perturbations. In the realistic nonchiral-nonflat case, we find that the perturbative insulator states with Chern number $ν_C$ = 0 (0 < |$ν_C$| < 4 – |$\textit{ν}$ |) at integer fillings $\textit{ν}$ are fully (partially) intervalley coherent, while the insulator states with Chern number |$ν_C$| = 4 – |$\textit{ν}$ | are valley polarized. However, for 0 < |$ν_C$| ≤ 4 – |$\textit{ν}$ |, the fully intervalley coherent states are highly competitive (0.005 meV/electron higher). At nonzero magnetic field |$\textit{B}$ | > 0, a first-order phase transition for $\textit{ν}$ = ± 1, ± 2 from Chern number $ν_C$ = sgn ($\textit{νB}$)(2 – |$\textit{ν}$ |) to $ν_C$ = sgn ($\textit{νB}$)(4 – |$\textit{ν}$ |) is expected, which agrees with recent experimental observations. Lastly, the TBG Hamiltonian reduces into an extended Hubbard model in the stabilizer code limit.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

The ellipticity parameterization for an NFW profile: An overlooked angular structure in strong lens modeling

Galaxy-scale gravitational lenses are often modeled with two-component mass profiles where one component represents the stellar mass and the second is a Navarro Frenk White (NFW) profile representing the dark matter. Outside of the spherical case, the NFW profile is costly to implement, and so it is approximated via two different methods; ellipticity can be introduced via the lensing potential (NFWp) or via the mass by approximating the NFW profile as a sum of analytical profiles (NFWm). While the NFWp method has been the default for lensing applications, it gives a different prescription of the azimuthal structure, which we show introduces ubiquitous gradients in ellipticity and boxiness in the mass distribution rather than having a constant elliptical shape. Because an unmodeled azimuthal structure has been shown to be able to bias lens model results, we explored the degree to which this azimuthal structure that was introduced can affect the model accuracy. We constructed input profiles using composite models using both the NFWp and NFWm methods and fit these mocks with a power-law elliptical mass distribution (PEMD) model with external shear. As a measure of the accuracy of the recovered lensing potential, we calculated the value of the Hubble parameter H 0 one would determine from the lensing fit. We found that the fits to the NFWp input return H 0 values that are systematically biased by about 3% lower than the NFWm counterparts. We explored whether such an effect is attributable to the mass sheet transformation (MST) by using an MST-independent quantity, ξ 2 . We show that, as expected, the NFWm mocks are degenerate with PEMD through an MST. For the NFWp, an additional bias was found beyond the MST due to the azimuthal structure exterior to the Einstein radius. We recommend modelers use an NFWm prescription in the future, such that the azimuthal structure can be introduced explicitly rather than implicitly.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2015

Evidence Report: Risk of Cardiovascular Disease and Other Degenerative Tissue Effects from Radiation Exposure

Occupational radiation exposure from the space environment may result in non-cancer or non-CNS degenerative tissue diseases, such as cardiovascular disease, cataracts, and respiratory or digestive diseases. However, the magnitude of influence and mechanisms of action of radiation leading to these diseases are not well characterized. Radiation and synergistic effects of radiation cause DNA damage, persistent oxidative stress, chronic inflammation, and accelerated tissue aging and degeneration, which may lead to acute or chronic disease of susceptible organ tissues. In particular, cardiovascular pathologies such as atherosclerosis are of major concern following gamma-ray exposure. This provides evidence for possible degenerative tissue effects following exposures to ionizing radiation in the form of the GCR or SPEs expected during long-duration spaceflight. However, the existence of low dose thresholds and dose-rate and radiation quality effects, as well as mechanisms and major risk pathways, are not well-characterized. Degenerative disease risks are difficult to assess because multiple factors, including radiation, are believed to play a role in the etiology of the diseases. As additional evidence is pointing to lower, space-relevant thresholds for these degenerative effects, particularly for cardiovascular disease, additional research with cell and animal studies is required to quantify the magnitude of this risk, understand mechanisms, and determine if additional protection strategies are required.The NASA PEL (Permissive Exposure Limit)s for cataract and cardiovascular risks are based on existing human epidemiology data. Although animal and clinical astronaut data show a significant increase in cataracts following exposure and a reassessment of atomic bomb (A-bomb) data suggests an increase in cardiovascular disease from radiation exposure, additional research is required to fully understand and quantify these adverse outcomes at lower doses (less than 0.5 gray (SI unit for ionizing radiation dosage, i.e. one joule of radiation energy per one kilogram of matter)) to facilitate risk prediction. This risk has considerable uncertainty associated with it, and no acceptable model for projecting degenerative tissue risk is currently available. In particular, risk factors such as obesity, alcohol, and tobacco use can act as confounding factors that contribute to the large uncertainties. The PELs could be violated under certain scenarios, including following a large SPE (solar proton event) or long-term GCR (galactic cosmic ray) exposure. Specifically, for a Mars mission, the accumulated dose is sufficiently high that epidemiology data and preliminary risk estimates suggest a significant risk for cardiovascular disease. Ongoing research in this area is intended to provide the evidence base for accurate risk quantification to determine criticality for extended duration missions. Data specific to the space radiation environment must be compiled to quantify the magnitude of this risk to decrease the uncertainty in current PELs and to determine if additional protection strategies are required. New research results could lead to estimates of cumulative radiation risk from CNS and degenerative tissue diseases that, when combined with the cancer risk, may have major negative impacts on mission design, costs, schedule, and crew selection. The current report amends an earlier report (Human Research Program Requirements Document, HRP-47052, Rev. C, dated Jan 2009) in order to provide an update of evidence since 2009.

Patel, Zarana↗
DOE OSTI2023

Constraints on a split superconducting transition under uniaxial strain in Sr 2 RuO 4 from scanning SQUID microscopy

More than two decades after the discovery of superconductivity in Sr 2 RuO 4 , it is still unclear whether the order parameter has a single component or two degenerate components. For any two-component scenario, application of uniaxial strain is expected to lift the degeneracy, generating two distinct phase transitions. The presence of a second (lower-temperature) transition may be observable by probes that are sensitive to changes in the London penetration depth, λ, as a function of temperature, T. Furthermore, we use scanning SQUID microscopy combined with a uniaxial strain device to test for a second transition under strain. We only observe a single transition. Within the temperature range where a second transition has been suggested by μSR measurements, we further place a tight upper bound of less than 1% on the change in the zero temperature superfluid density n s ∝ λ –2 (0) due to a second transition, suggesting that such a transition does not occur. These results constrain theories of the order parameter in Sr 2 RuO 4 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Pressure control of magnetic order and excitations in the pyrochlore antiferromagnet MgCr 2 ⁢O 4

MgCr 2 O 4 is one of the best-known realizations of the pyrochlore-lattice Heisenberg antiferromagnet. The strong antiferromagnetic exchange interactions are perturbed by small further-neighbor exchanges such that this compound may in principle realize a spiral spin liquid (SSL) phase in the zero-temperature limit. However, a spin Jahn-Teller transition below T N ≈ 13 K yields a complicated long-range magnetic order with multiple coexisting propagation vectors. We present neutron scattering and thermomagnetic measurements of MgCr 2 O 4 samples under applied hydrostatic pressure up to P = 1.7 GPa demonstrating the existence of multiple close-lying nearly degenerate magnetic ground states. We show that the application of hydrostatic pressure increases the ordering temperature by around 0.8 K per GPa and increases the bandwidth of the magnetic excitations by around 0.5 meV per GPa. We also evidence a strong tendency for the preferential occupation of a subset of magnetic domains under pressure. In particular, we show that the $k$ = (0,0,1) magnetic phase, which is almost negligible at ambient pressure, dramatically increases in spectral weight under pressure. This modifies the spectrum of magnetic excitations, which we interpret unambiguously as spin waves from multiple magnetic domains. Moreover, we report that the application of pressure reveals a feature in the magnetic susceptibility above the magnetostructural transition. We interpret this as the onset of a short-range ordered phase associated with $k$ = (0,0,1), previously not observed in magnetometry measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Orthorhombic distortion drives orbital ordering in the antiferromagnetic 3$d$ 1 Mott insulator PrTiO 3

The orbital, which represents the shape of the electron cloud, very often strongly influences the manifestation of various exotic phenomena, e.g., magnetism, metal-insulator transition, colossal magnetoresistance, unconventional superconductivity, etc. in solid-state systems. The observation of the antiferromagnetism in $RE$TiO 3 ($RE$ = rare-earth) series has been puzzling since the celebrated Kugel-Khomskii model of spin-orbital superexchange predicts ferromagnetism in an orbitally degenerate $d$ 1 system. Further, the existence of the orbitally ordered vs. orbital liquid phase in both antiferromagnetic and paramagnetic phase have been unsettled issues thus far. To address these longstanding questions, we investigate single crystalline film of PrTiO 3 . Our synchrotron x-ray diffraction measurements confirm the retention of bulklike orthorhombic ($D_{2h}$) symmetry in the thin film geometry. We observe similar x-ray linear dichroism signal in both paramagnetic and antiferromagnetic phase, which can be accounted by ferro-orbital ordering (FOO). While the presence of $D_{2h}$ crystal field does not guarantee lifting of orbital degeneracy always, we find it to be strong enough in these rare-earth titanates, leading to the FOO state. Thus, our work demonstrates the orthorhombic distortion is the driving force for the orbital ordering of antiferromagnetic $RE$TiO 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Quantum dynamics in strongly driven random dipolar magnets

The random dipolar magnet LiHo x Y 1– x F 4 enters a strongly frustrated regime for small Ho 3+ concentrations with x < 0.05. In this regime, the magnetic moments of the Ho 3+ ions experience small quantum corrections to the common Ising approximation of LiHo x Y 1– x F 4 , which lead to a $\mathbb{Z}_2$-symmetry breaking and small, degeneracy breaking energy shifts between different eigenstates. Here we show that destructive interference between two almost degenerate excitation pathways burns spectral holes in the magnetic susceptibility of strongly driven magnetic moments in LiHo x Y 1– x F 4 . Such spectral holes in the susceptibility, microscopically described in terms of Fano resonances, can already occur in setups of only two or three frustrated moments, for which the driven level scheme has the paradigmatic Λ shape. For larger clusters of magnetic moments, the corresponding level schemes separate into almost isolated many-body Λ schemes, in the sense that either the transition matrix elements between them are negligibly small or the energy difference of the transitions is strongly off-resonant to the drive. This enables the observation of Fano resonances, caused by many-body quantum corrections to the common Ising approximation also in the thermodynamic limit. Finally, we discuss its dependence on the driving strength and frequency as well as the crucial role that is played by lattice dissipation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Orbital Selectivity in Electron Correlations and Superconducting Pairing of Iron-Based Superconductors

Electron correlations play a central role in iron-based superconductors. In these systems, multiple Fe 3 d -orbitals are active in the low-energy physics, and they are not all degenerate. For these reasons, the role of orbital-selective correlations has been an active topic in the study of the iron-based systems. In this article, we survey the recent developments on the subject. For the normal state, we emphasize the orbital-selective Mott physics that has been extensively studied, especially in the iron chalcogenides, in the case of electron filling n ∼ 6 . In addition, the interplay between orbital selectivity and electronic nematicity is addressed. For the superconducting state, we summarize the initial ideas for orbital-selective pairing and discuss the recent explosive activities along this direction. We close with some perspectives on several emerging topics. These include the evolution of the orbital-selective correlations, magnetic and nematic orders, and superconductivity as the electron filling factor is reduced from 6 to 5, as well as the interplay between electron correlations and topological band structure in iron-based superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Symmetry-breaking polymorphous descriptions for correlated materials without interelectronic U

Correlated materials with open-shell d- and f-ions having degenerate band edge states show a rich variety of interesting properties ranging from metal-insulator transition to unconventional superconductivity. The textbook view for the electronic structure of these materials is that mean-field approaches are inappropriate, as the interelectronic interaction U is required to open a band gap between the occupied and unoccupied degenerate states while retaining symmetry. We show that the latter scenario often defining what Mott insulators are, is in fact not needed for the 3d binary oxides MnO, FeO, CoO, and NiO. The mean-field-like band theory can indeed lift such degeneracies in the binaries when nontrivial unit cell representations (polymorphous networks) are allowed to break symmetries, in conjunction with a recently developed non-empirical exchange and correlation density-functional without an on-site interelectronic interaction U. We explain how density-functional theory (DFT) in the polymorphous representation achieves band gap opening in correlated materials through a separate mechanism to the Mott-Hubbard approach. Here, we show the method predicts magnetic moments and gaps for the four binary monoxides in both the antiferromagnetic and paramagnetic phases, offering an effective alternative to symmetry-conserving approaches for studying a range of functionalities in open d- and f-shell complex materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Disentangling electronic, lattice, and spin dynamics in the chiral helimagnet Cr 1/3 NbS 2

We investigate the static and ultrafast magneto-optical response of the hexagonal chiral helimagnet Cr 1/3 NbS 2 above and below the helimagnetic ordering temperature. The presence of a magnetic easy plane contained within the crystallographic $ab$-plane is confirmed, while degenerate optical pump-probe experiments reveal significant differences in the dynamic between the parent, NbS 2 , and Cr-intercalated compounds. Time-resolved magneto-optical Kerr effect measurements show a two-step demagnetization process, where an initial, subpicosecond relaxation and subsequent buildup (τ > 50ps) in the demagnetization dynamic scale similarly with increasing pump fluence. Despite theoretical evidence for partial gapping of the minority spin channel, suggestive of possible half-metallicity in Cr 1/3 NbS 2 , such a long demagnetization dynamic likely results from spin-lattice relaxation as opposed to minority state blocking. However, comparison of the two-step demagnetization process in Cr 1/3 NbS 2 with other 3d intercalated transition metal dichalcogenides reveals a behavior that is unexpected from conventional spin-lattice relaxation, and may be attributed to the complicated interaction of local moments with itinerant electrons in this material system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Spatially inhomogeneous superconductivity in UTe 2

The newly discovered superconductor UTe 2 is a strong contender for a topological spin-triplet state wherein a multicomponent order parameter arises from two nearly degenerate superconducting states. A key issue is whether both of these states intrinsically exist at ambient pressure. Through thermal expansion and calorimetry, we show that UTe 2 at ambient conditions exhibits two detectable transitions only in some samples, and the size of the thermal expansion jump at each transition varies when the measurement is performed in different regions of the sample. This result indicates that the two transitions arise from two spatially separated regions that are inhomogeneously mixed throughout the volume of the sample, each with a discrete superconducting transition temperature (T c ). Notably, samples with higher T c only show a single transition at ambient pressure. Above 0.3 GPa, however, two transitions are invariably observed in ac calorimetry. Our results not only point to a nearly vertical line (constant pressure) in the pressure-temperature phase diagram but also provide a consistent scenario for the sample dependence of UTe 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Microscopic scattering approach to in-gap states: Cr adatoms on superconducting 𝛽−Bi 2 ⁢Pd

We develop a microscopic scattering formalism to describe Yu-Shiba-Rusinov (YSR) states due to a single Cr adatom on the Bi-terminated surface of 𝛽−Bi 2 ⁢Pd, by combining ab initio Wannier functions with a real-space Green's function approach in the Bogoliubov–de Gennes formalism. Our framework reproduces key scanning tunneling spectroscopy features, including a single particle-hole asymmetric YSR peak and isotropic 𝑑⁢𝐼/𝑑⁢𝑉 maps around the impurity. Decomposing the YSR states reveals contributions from four nearly degenerate 𝐶 4⁢𝑣 representations, with energy broadening masking their individual signatures. Spin-orbit coupling induces partial spin polarization, while the spatial asymmetry between particle and hole components arises from Cr 𝑑−Bi 𝑝 hybridization. These results highlight the importance of realistic band structures and microscopic modeling for interpreting STM data and provide a foundation for studying impurity chains hosting topological excitations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Quadrupolar interactions between acceptor pairs in $\mathcal{p}$-doped semiconductors

Here, we consider the interaction between acceptor pairs in doped semiconductors in the limit of large interacceptor separation relevant for low doping densities. Modeling individual acceptors via the spherical model of Baldereschi and Lipari, we calculate matrix elements of the quadrupole tensor between the four degenerate ground states and show that the acceptor has a nonzero quadrupole moment. As a result, the dominant contribution to the large-separation acceptor-acceptor interaction comes from direct (charge-density) terms rather than exchange terms. The quadrupole is the leading nonzero moment, so the electric quadrupole-quadrupole interaction dominates for large separation. We calculate the matrix elements of the quadrupole-quadrupole interaction Hamiltonian in a product-state basis and diagonalize, obtaining a closed-form expression for the energies and degeneracies of the sixteen-state energy spectrum. All dependence on material parameters enters via an overall prefactor, resulting in surprisingly simple and universal results. This simplicity is due, in part, to a mathematical happenstance, the nontrivial vanishing of a particular Wigner 6-$\mathcal{j}$ symbol, $^\{\frac{^2_3}{\small2} \frac{^2_3}{\small2} \frac{^2_3}{\small2}$$^\}$ = 0. Results are relevant to the control of two-qubit interactions in quantum computing implementations based on acceptor spins, as well as calculations of the thermodynamic properties of insulating $\mathcal{p}$-type semiconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗