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

0.00 0.02 0.04 0.06 0.08 0.10 q (˚ A−1) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 E (eV) InSb 200 keV DM 400 keV DM

Condensed matter systems of interest (where to find them and how to characterize them)

Lucas K. Wagner University of Illinois at Urbana-Champaign With some slides from Sinead Griffin (LBNL) and Peter Abbamonte (UIUC)

lkwagner@illinois.edu

A bit about me

EiΨi(r1, r2, . . .) = ˆ HΨi(r1, r2, . . .) + Solve minimal approximations including electron correlations explicitly

H = − 1 2 ∑

i

∇2

i + ∑ i<j

1 rij − ∑

αi

Zα riα + ∑

α<β

ZαZβ rαβ

lkwagner@illinois.edu

First principles quantum Monte Carlo

⟨ΨT|e−τH𝒫e−τH|ΨT⟩ ⟨ΨT|e−τHe−τH|ΨT⟩

Obtain the ground state wave function by projection Use resolution of identity

⟨ΨT|e−τH𝒫e−τH|ΨT⟩ = ∫ ⟨ΨT|R1⟩⟨R2|e−τH|R3⟩⟨R3|𝒫|R4⟩⟨R4|e−τH|R5⟩⟨R5|ΨT⟩dR1dR2dR3dR4dR5

Each R is a many-body coordinate. This is a 15N dimensional integral. Evaluate using Monte Carlo. H = − 1 2 ∇2 + ∑

ij

1 rij + …

1 2 3 4 5

Experimental gap (eV)

1 2 3 4 5

Theoretical gap (eV)

MnO FeO ZnO VO2 (rutile) VO2 (monoclinic) La2CuO4 NiO ZnSe FN-DMC DFT(PBE)

lkwagner@illinois.edu

Some things my group does

Computing magnetic properties of materials Attempting to predict and understand unconventional superconductivity Spin-orbit coupling with explicit electronic interactions arXiv: 1809.04133

W S Γ K −10 −8 −6 −4 −2

E/eV

AÕÕ AÕ

1

Interacting effective Hamiltonians 10.3389/fphy. 2018.00043

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.

lkwagner@illinois.edu

“Materials by design”

193,000 inorganic crystals (some duplicates) Protein data bank: 42,000 distinct protein sequences 391,334 organic and inorganic 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

0.00 0.02 0.04 0.06 0.08 0.10 q (˚ A−1) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 E (eV) InSb 200 keV DM 400 keV DM

Could extend reach (except radioactive In) q dependence becomes important; many low-gap materials have light excitations -> no overlap

lkwagner@illinois.edu

Candidate materials (~90% ‘failure rate’)

Materials by design

~40,000 materials + doping & composites Simple density functional theory available online almost immediate More advanced calculations (months->year) Synthesis and properties (months->year)

‘Failure rate’ comes from the material being impossible to synthesize, or the property filter

• f DFT not being accurate enough. We usually

generate a ranked list. After this we have a pretty good handle on how the material behaves and whether it . Development to a working device can take years or decades after this, with substantial investment of capital. People are trying to make this better.

[WIMPs] ⧪ Black holes [ Axion ]

Dark matter mass range unexplored

Band gap meV Energy deposition

• n electron by

absorption 1 meV Dark matter mass 1 meV

Effect of spin-orbit coupling

• Direct detection of sub-GeV masses is within the reach of

short, small-scale experiments

• Small band gap semiconductors could be used to observe

absorption or scattering events Aim: To identify semiconductors with millielectronvolt band gaps Strategy: Search for materials with band gaps opened by spin-

• rbit coupling

Spin-orbit semiconductors for dark matter detection

Inzani, Griffin

86,412 inorganic materials Spin-orbit interactions in 4,357 compounds 3 “would-be metals” with band gaps

• pened up through spin orbit coupling

Method II: Refined electronic structures calculated by density functional theory Method I: High-throughput computational screening

Spin-orbit semiconductors for dark matter detection

1 Family of materials with meV-scale band gaps Tin pnictides ASn2Pn2 Band gap variable by composition 0 – 200 meV

Candidate materials for dark matter detection identified Synthesis pending…

Inzani, Griffin

Part 2: determining detection limits

lkwagner@illinois.edu

Scattering

Electron energy loss scattering γ γd e− e− DM DM Dark matter scattering through a dark photon γ e− e− e− e− Im 1 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

General points about the electron form factor

• P. Abbamonte, UIUC

2 3 * ( )

( ) ( )

i e k q k k q k k

F dr e ψ ψ δ ω ω ω

− ⋅ + +

= − + ⌠ ⎮ ⌡

∑

q r

r r First approximation to the electron form factor: General electron form factor is the van Hove function:

2 ,

ˆ ( , ) | | ( )

q m n m n m

S q n m P ω ρ δ ω ω ω = < > − +

∑

Bloch states (e.g., from a DFT package) Energy conservation Many-body wave functions Density

• perator

Boltzmann factor if T≠0 Still need this,

• f course

Loss functions for Si vs. GaAs

• M. K. Kundmann, Ph.D. Thesis, U.C. Berkeley, Nov. 1988

Si

• P. Abbamonte, UIUC
• 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

M-EELS facility at UIUC

Key points:

• cameras + axes to center the stages
• Δqacc ≈ 0.013 Å-1, Δqres ≈ 0.02 Å-1
• 2.2 meV energy resolution
• Measures electronic modes
• Surface probe: Works on 2D

materials, single layers

LaB6 thermionic source electrostatic lenses (aberration-corrected) Low-T sample goniometer cylindrical analyzer area detector Low-T piezo phi rotation

• S. Vig, et al., SciPost
• Phys. 3, 026 (2017)
• P. Abbamonte, UIUC

M-EELS facility at UIUC

2 2

( , , ) ( , )

z z eff i s

V k k q S q dE σ σ ω ∂ ⎡ ⎤ = ⋅ ⎣ ⎦ ∂Ω

/

1 1 1 ( , ) ( , ) ~ Im 1 ( , )

B

k T

S q q e q

ω

ω χ ω π ε ω

−

ʹʹ = − ⋅ − −

!

* S. Vig, et al., SciPost Phys. 3, 026 (2017) M-EELS measures the surface dynamic charge susceptibility:

• P. Abbamonte, UIUC

lkwagner@illinois.edu

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