Condensed matter systems of interest (where to find them and how to - PowerPoint PPT Presentation

0 . 6 0 . 5 Condensed matter systems of interest (where to find them and how to 0 . 4 characterize them) E (eV) 0 . 3 Lucas K. Wagner 0 . 2 University of Illinois at Urbana-Champaign 0 . 1 InSb With some slides from Sinead Griffin (LBNL) and Peter Abbamonte (UIUC) 200 keV DM 400 keV DM 0 . 0 0 . 00 0 . 02 0 . 04 0 . 06 0 . 08 0 . 10 A − 1 ) q (˚

A bit about me Z α Z β i + ∑ − ∑ + ∑ Z α H = − 1 1 2 ∑ + ∇ 2 r ij r i α r αβ i i < j α i α < β E i Ψ i ( r 1 , r 2 , . . . ) = ˆ Solve H Ψ i ( r 1 , r 2 , . . . ) minimal approximations including electron correlations explicitly lkwagner@illinois.edu

First principles quantum Monte Carlo 5 NiO FN-DMC ⟨ Ψ T | e − τ H 𝒫 e − τ H | Ψ T ⟩ MnO DFT(PBE) 4 Theoretical gap (eV) ZnO VO 2 (monoclinic) 3 Obtain the ground state wave ZnSe La 2 CuO 4 FeO 2 VO 2 (rutile) ⟨ Ψ T | e − τ H e − τ H | Ψ T ⟩ function by projection 1 0 0 1 2 3 4 5 Experimental gap (eV) 2 ∇ 2 + ∑ H = − 1 1 + … r ij ij Use resolution of identity ⟨ Ψ T | e − τ H 𝒫 e − τ H | Ψ T ⟩ = ∫ ⟨Ψ T | R 1 ⟩⟨ R 2 | e − τ H | R 3 ⟩⟨ R 3 | 𝒫 | R 4 ⟩⟨ R 4 | e − τ H | R 5 ⟩⟨ R 5 | Ψ T ⟩ dR 1 dR 2 dR 3 dR 4 dR 5 Each R is a many-body coordinate. This is a 15N dimensional integral. Evaluate using Monte Carlo. lkwagner@illinois.edu

Some things my group does − 2 A Õ 1 − 4 E /eV − 6 A ÕÕ − 8 − 10 W S Γ K Interacting effective Spin-orbit Attempting to Hamiltonians coupling with predict and Computing magnetic explicit electronic understand properties of materials 10.3389/fphy. interactions unconventional 2018.00043 arXiv: 1809.04133 superconductivity lkwagner@illinois.edu

Part 1: New (old) materials that could be useful for dark matter detection Part 2: Condensed matter experiment and computation to understand detection limits better for a known material.

“Materials by design” 193,000 inorganic crystals Protein data bank: 391,334 organic and inorganic (some duplicates) 42,000 distinct protein sequences crystals (some duplicates) lkwagner@illinois.edu

Many known materials that could (in principle) detect very light DM Gap(eV) lkwagner@illinois.edu

InSb: kinematic constraints for very light DM 0 . 6 Could extend reach (except radioactive In) 0 . 5 q dependence becomes important; many low-gap materials have light excitations -> 0 . 4 no overlap E (eV) 0 . 3 0 . 2 0 . 1 InSb 200 keV DM 400 keV DM 0 . 0 0 . 00 0 . 02 0 . 04 0 . 06 0 . 08 0 . 10 A − 1 ) q (˚ lkwagner@illinois.edu

Materials by design ~40,000 materials + doping & composites ‘Failure rate’ comes from the material being impossible to synthesize, or the property filter of DFT not being accurate enough. We usually generate a ranked list. Simple density functional theory After this we have a pretty good handle on how available online the material behaves and whether it . almost immediate Development to a working device can take Candidate materials years or decades after this, with substantial (~90% ‘failure rate’) investment of capital. More advanced Synthesis and People are trying to make this better. calculations properties (months->year) (months->year) lkwagner@illinois.edu

Spin-orbit semiconductors for dark matter detection Inzani, Griffin Direct detection of sub-GeV masses is within the reach of • short, small-scale experiments ⧪ [WIMPs] [ Axion ] Small band gap semiconductors could be used to observe • Black Dark matter mass range absorption or scattering events holes unexplored Aim: To identify semiconductors with millielectronvolt band gaps Energy deposition Dark matter mass 1 meV on electron by Strategy: Search for absorption materials with band Band gap 1 meV gaps opened by spin- meV orbit coupling Effect of spin-orbit coupling

Spin-orbit semiconductors for dark matter detection Inzani, Griffin Method I: High-throughput computational screening 1 Family of materials with meV-scale band gaps 86,412 inorganic materials Tin pnictides A Sn 2 Pn 2 Band gap variable by composition Spin-orbit interactions in 4,357 compounds 0 – 200 meV 3 “would-be metals” with band gaps opened up through spin orbit coupling Candidate materials for dark matter Method II: Refined electronic structures detection identified calculated by density functional theory Synthesis pending…

Part 2: determining detection limits

Scattering DM e − Dark matter scattering through a dark photon γ γ d DM e − e − e − Electron energy loss scattering γ e − e − 1 Im ϵ ( q , ω ) lkwagner@illinois.edu

Computation of properties The band structure is a lie Materials are collections of many particles and all excitations are many- particle excitations. pictures from materialsproject.org lkwagner@illinois.edu

General points about the electron form factor First approximation to the electron form factor: 2 * ( ) ⌠ 3 i q r F dr r ( ) r e ( ) − ⋅ ∑ = ψ ψ δ ω − ω + ω ⎮ e k q k k q k + + ⌡ k Bloch states Energy (e.g., from a conservation DFT package) General electron form factor is the van Hove function: 2 ˆ S q ( , ) n | | m P ( ) ∑ ω = < ρ > δ ω − ω + ω q m n m n m , Many-body Still need this, wave functions Boltzmann of course Density factor if T ≠ 0 operator P. Abbamonte, UIUC

Loss functions for Si vs. GaAs • Interactions shift spectral weight to the plasma frequency • S(q, ω ) for Si and GaAs are nearly the same and peaked at 15 eV • Choosing DM target requires accounting for RPA-like effects Si M. K. Kundmann, Ph.D. Thesis, U.C. Berkeley, Nov. 1988 P. Abbamonte, UIUC

M-EELS facility at UIUC Low-T sample LaB 6 cylindrical goniometer thermionic analyzer source electrostatic lenses (aberration-corrected) area detector S. Vig, et al., SciPost Phys. 3 , 026 (2017) Key points: • cameras + axes to center the stages • Δ q acc ≈ 0.013 Å -1 , Δ q res ≈ 0.02 Å -1 • 2.2 meV energy resolution • Measures electronic modes • Surface probe: Works on 2D materials, single layers Low-T piezo phi rotation P. Abbamonte, UIUC

M-EELS facility at UIUC 2 ∂ σ 2 z z V ( k , k , ) q S q ( , ) ⎡ ⎤ = σ ⋅ ω M-EELS measures ⎣ ⎦ 0 eff i s dE ∂Ω the surface dynamic 1 1 1 charge S q ( , ) ( , ) ~ q Im ʹʹ ω = − ⋅ χ ω − susceptibility: ! / k T 1 e ( , ) q − ω π − ε ω B * S. Vig, et al., SciPost Phys. 3 , 026 (2017) P. Abbamonte, UIUC

Summary There are lots of materials. Materials Genome is about sifting through them. Materials are many-body objects. All excitations are collective. All effective models are approximate and the ‘cutoff’ can be very small. Computing properties and response accurately can be challenging but progress can be made with work lkwagner@illinois.edu