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06/15/2026

Israel Hernández | RISQ Workshop

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Israel Hernandez

Illinois Institute of Technology, Physics Department

Rakshya Khatiwada, Ryan Linehan, Kester Anyang

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June 15, 2026

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Extending G4CMP for Charge and Energy Transport in Sapphire

_{Sapphire For QIS and Dark Matter}

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Sapphire (α-Al₂O₃) — a high-purity single crystal with exceptional cryogenic properties — has become a key material in quantum devices and dark matter searches.

Why are we interested in Sapphire for QIS and Dark Matter?

Background radiation can produce electron-hole pairs in sapphire, which generate charge jumps that disrupt the qubits.

Qubit Based Detector For DM

Qubit Substrate & Physics Applications

• Substrate: polar material (e.g., Sapphire)
• Dark Matter detection: look for daily modulation signature
• Neutrino physics: high N target for coherent elastic neutrino-nucleus scattering (CEνNS)

Applications in QIS

Low Dielectric losses

• Preferred substrate for superconducting qubits (transmon, fluxonium) → T₁ > 100–300 µs
• Enables high-Q microwave resonators (Q > 10⁶) for quantum memories & readout
• Record-quality factor 3D cavities in circuit QED

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Low-Frequency Correlated Charge-Noise Measurements Across Multiple Energy Transitions in a Tantalum Transmon

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_{Review of G4CMP}

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Successful incorporation of phonon transport in Sapphire (and other materials) into G4CMP

Al₂O₃

_{Review of G4CMP}

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Successful incorporation of phonon transport in Sapphire (and other materials) into G4CMP

We are now interested in expanding charge transport into G4CMP for Sapphire

Al₂O₃

_{Charge Transport into G4CMP}

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G4CMP does not currently have the capability to model charge transport in Sapphire

Impact Ionization (e-h pair creation)

• Band gap energy (E_g)
• Pair energy
• Fano Factor

Ballistic Transport (before scattering)

• Electron/hole effective mass
• Valley directions (band structure)

Scattering Mechanisms (energy loss)

• Luke scattering (acoustic phonon emission)
• Optical scattering
• Impurity scattering

_{Charge Transport into G4CMP}

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G4CMP does not currently have the capability to model charge transport in Sapphire

Impact Ionization (e-h pair creation)

• Band gap energy (E_g)
• Pair energy
• Fano Factor

Ballistic Transport (before scattering)

• Electron/hole effective mass
• Valley directions (band structure)

Scattering Mechanisms (energy loss)

• Luke scattering (acoustic phonon emission)
• Optical scattering
• Impurity scattering

Can we model Sapphire charge transport into G4CMP?

_{Sapphire Parameters For Charge Transport}

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k-space energy bands of Sapphire

_{Sapphire Parameters For Charge Transport}

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m_e ≈ 0.24 m₀ (isotropic)

k-space energy bands of Sapphire

_{Sapphire Parameters For Charge Transport}

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m_e ≈ 0.24 m₀ (isotropic)

Direct band Gap, 8.7 eV (One Valley)

k-space energy bands of Sapphire

_{Sapphire Parameters For Charge Transport}

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m_e ≈ 0.24 m₀ (isotropic)

Direct band Gap, 8.7 eV (One Valley)

Hole Mass Anisotropy in Sapphire �m_h⊥ ≈ 6.3 m₀� m_h‖ ≈ 0.36 m₀ �

Fano Factor ~ 0.38

k-space energy bands of Sapphire

_{Sapphire Parameters For Charge Transport}

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m_e ≈ 0.24 m₀ (isotropic)

Direct band Gap, 8.7 eV (One Valley)

Hole Mass Anisotropy in Sapphire �m_h⊥ ≈ 6.3 m₀� m_h‖ ≈ 0.36 m₀ �

Fano Factor ~ 0.38

Findings

• Sapphire mass tensor: nearly isotropic
• Sapphire Hole tensor Anisotropic
• Band extrema: CBM & VBM at Γ
• Intervalley Scattering is not needed

Big Finding�“In Al₂O₃, electron charges are spatially localized, and optical excitation across the band gap drives charge transfer from O to Al. The resulting carrier distorts the surrounding ionic lattice, inducing a polarization field — a phenomenon known as a polaron”[Electronic Band Structure of Al₂O₃, with Comparison to AlON and AlN].���

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k-space energy bands of Sapphire

_{Sapphire Parameters For Charge Transport}

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m_e ≈ 0.24 m₀ (isotropic)

Direct band Gap, 8.7 eV (One Valley)

Hole Mass Anisotropy in Sapphire �m_h⊥ ≈ 6.3 m₀� m_h‖ ≈ 0.36 m₀ �

Fano Factor ~ 0.38

Findings

• Sapphire mass tensor: nearly isotropic
• Sapphire Hole tensor Anisotropic
• Band extrema: CBM & VBM at Γ
• Intervalley Scattering is not needed

Big Finding�“In Al₂O₃, electron charges are spatially localized, and optical excitation across the band gap drives charge transfer from O to Al. The resulting carrier distorts the surrounding ionic lattice, inducing a polarization field — a phenomenon known as a polaron”[Electronic Band Structure of Al₂O₃, with Comparison to AlON and AlN].���

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k-space energy bands of Sapphire

Then, what is a polaron?

_{Experimental Charge Transport in Sapphire in Literature}

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The results, including low-temperature mobilities > 10 000 cm²/V s, are compatible with a large-polaron description of the conduction electrons. [Measurement of the Frequency-Dependent Conductivity in Sapphire]

Across different excitation regimes—from intrinsic (Shan et al.) to highly excited (Storchak et al.)—polaron-phonon scattering remains the transport-limiting mechanism. [Quantum transport of electronic polarons in sapphire]

Temperature dependence of the muonium formation rate in Al₂O₃

Sapphire Scattering Rate

Large Polarons Properties

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• E_ST is the structural energy: Energy cost to distort the lattice around the electron
• E_POL polaron binding energy: How deeply the electron is bound in the polaron potential well
• E_EL is the electronic energy: the energy of the electron in its localized state. [OPTICAL, THERMAL AND POLARON ENERGY LEVELS IN α-Al2O3]

How the electron couples� to the lattice

Fröhlich coupling constant

Polaron Mass

• Long-range electron-photon interaction
• Polaron radius >> lattice parameter
• Coherent motion
• Free carrier mobility >> 1cm²/Vs
• Mobility decreasing with temperature�

What distinguishes a polaron from a charge?

Large ‘Fröhlich’ polarons

Polarons in Sapphire: Charge Transport at Low T

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Why is it important to model polarons in G4CMP?

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• Polaron dynamics may modify carrier mobility, drift velocity, charge collection efficiency, and Neganov–Luke phonon production, directly impacting detector response.
• The anisotropic nature of sapphire can produce direction-dependent polaron transport, potentially affecting charge propagation and TES/KID signal formation.
• Incorporating large-polaron transport into G4CMP may improve detector-response simulations, reducing systematic uncertainties in energy reconstruction and recoil discrimination.

Dark Matter

Polaron formation, trapping, and hopping at defects may contribute to:

• Charge noise
• TLS activation
• Microwave dielectric loss
• Reduced qubit coherence times (T₁, T₂)

Anisotropic polaron effective masses may lead to:

• Direction-dependent charge transport
• Orientation-dependent dielectric loss
• Crystal-orientation effects on qubit performance

QIS

Polarons in Sapphire: Charge Transport at Low T

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We need to develop anisotropic polaron transport models in G4CMP to quantify the impact of sapphire substrate properties on microwave loss and qubit decoherence.

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• Polaron dynamics may modify carrier mobility, drift velocity, charge collection efficiency, and Neganov–Luke phonon production, directly impacting detector response.
• The anisotropic nature of sapphire can produce direction-dependent polaron transport, potentially affecting charge propagation and TES/KID signal formation.
• Incorporating large-polaron transport into G4CMP may improve detector-response simulations, reducing systematic uncertainties in energy reconstruction and recoil discrimination.

Dark Matter

Polaron formation, trapping, and hopping at defects may contribute to:

• Charge noise
• TLS activation
• Microwave dielectric loss
• Reduced qubit coherence times (T₁, T₂)

Anisotropic polaron effective masses may lead to:

• Direction-dependent charge transport
• Orientation-dependent dielectric loss
• Crystal-orientation effects on qubit performance

QIS

This motivates incorporating polaron physics into G4CMP.

Why is it important to model polarons in G4CMP?

Polarons in Sapphire: Charge Transport at Low T

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We need to develop anisotropic polaron transport models in G4CMP to quantify the impact of sapphire substrate properties on microwave loss and qubit decoherence.

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• Polaron dynamics may modify carrier mobility, drift velocity, charge collection efficiency, and Neganov–Luke phonon production, directly impacting detector response.
• The anisotropic nature of sapphire can produce direction-dependent polaron transport, potentially affecting charge propagation and TES/KID signal formation.
• Incorporating large-polaron transport into G4CMP may improve detector-response simulations, reducing systematic uncertainties in energy reconstruction and recoil discrimination.

Dark Matter

Polaron formation, trapping, and hopping at defects may contribute to:

• Charge noise
• TLS activation
• Microwave dielectric loss
• Reduced qubit coherence times (T₁, T₂)

Anisotropic polaron effective masses may lead to:

• Direction-dependent charge transport
• Orientation-dependent dielectric loss
• Crystal-orientation effects on qubit performance

QIS

This motivates incorporating polaron physics into G4CMP.

Why is it important to model polarons in G4CMP?

Hole Mass Tensor in G4CMP

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Hole Mass Tensor

Polaron Formation

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Polaron Formation

m(α)

(KE+Δ-ℏω)

Polarons Transport

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Polaron Transport

Polarons Scattering

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Scattering Rate

Polarons Scattering

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Scattering Rate

Acoustic

Optical

Impurities

Polarons in G4CMP

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Incorporate Hole Mass Tensor

Initial e-h pairs

Polaron Formation Class

Polaron Kinematics

Polaron Boundary Properties

Two new particles: electron and hole polaron

Emission of Phonons

Implement new classes to transport polarons

Enable absorption probabilities on the boundary

Optical Polaron Scattering

Polarons in G4CMP

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Incorporate Hole Mass Tensor

Initial e-h pairs

Polaron Formation Class

Polaron Kinematic

Polaron Boundaries Properties

Two new particles: electron and hole polaron

Emission of Phonons

Implement new classes to transport polarons

Enable absorption probabilities on the boundary

Optical Polaron Scattering

Why is this a good option?

• Full control of polaron physics
• Expansion to incorporate new physics of exotic particles
• Independent of updates to electron and hole transport

Hole Mass Tensor in G4CMP

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Light Mass in this direction

Heavy Mass in this direction

θ

Substrate

hmass_tensor 0.36 6.3 6.3

emass 0.24 0.23 0.23

Polaron Formation in G4CMP

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m(α)

(KE+Δ-ℏω)

Polaron Formation in G4CMP

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m(α)

(KE+Δ-ℏω)

Polaron Transport in G4CMP

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Isotropic polaron mass.�Transport consistency check

Per-event agreement plus the correct x1.20 mass enhancement confirm the isotropic polaron mass model is implemented correctly.

Polaron Boundaries Properties

Polaron Scattering in G4CMP

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WORKING ON THIS!

Superconductor in G4CMP

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To understand the quantum device response, phonon simulation in the superconductor along with quasiparticle propagation in G4CMP is needed.

Phys. Rev. B 60, 3072 (1999). doi:10.1103/PhysRevB.60.3072

• We have incorporated the phonons in G4CMP for Nb, Al and Ta. (paper in preparation)

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Nb

Experimental validation of phonon transport for Nb using G4CMP.

Al

Ta

Liquid Helium-4 in G4CMP

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Acknowledgments

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This material is based upon work supported by the U.S. Department of Energy, QuantiSED 2.0, National Quantum Information Science Research Centers, and Illinois Institute Of Technology.

Polarons in G4CMP

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Parameters for Charge Transport in Sapphire

# Charge carrier parameters

bandgap 8.6 eV

pairEnergy 27.0 eV

fanoFactor 0.382

vsound 11200.0 m/s

vtrans 6040.0 m/s

hmass_tensor 0.36 6.3 6.3 # per m(electron)

emass 0.24 0.23 0.23 # per m(electron)

valleyDir 0 0 1

# Intervalley scattering (matrix elements)

alpha 0.3 /eV

acDeform_e 19 eV

acDeform_h 4 eV�Frohlich 1.2 # unitless�BindingEnergy 0.72 eV

ivDeform 1e8 1.0e8 eV/cm # We do not need this

ivEnergy 48.0e-3 59.7e-3 63.3e-3 78.1e-3 109.0e-3 112e-3 eV #

neutDens 1e17 /cm3

epsilon 13.2

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Optical Scattering Rate (Polarons)

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Fröhlich Hamiltonian

Matrix element

Fröhlich coupling constant

Fermi’s Golden Rule for emission

Momentum Conservation

Scattering Rate