Network for Computational Nanotechnology (NCN)
Quantum spins in the solid-state: An atomistic material-to-device modeling approach
Rajib Rahman Purdue University The Future of Electronics?
Optimization: Materials & Designs
New Variables: Spins
ITRS
New Paradigms: Quantum Logic Modeling challenge: Beyond Moore’s Law?
Atomistic Modeling Approach
Spintronics/Magnetics Emerging materials
Quantum ‘Logic/Spintronics’
Image Sources 1. http://funnano.kaist.ac.kr/?p=295 2. http://research.physics.berkeley.edu/lanzara/researc h/ti.html 3. http://qeg.mit.edu/research.php 4. https://phys.org/news/2015-09-stability-electron- qubits.html 5. http://www.iht.uni- stuttgart.de/forschung/spinplasm.php 6. http://jqi.umd.edu/news/searching-spin-liquids
Atomistic Modeling Approach
Group IV & III-Vs
2D TMDs
Magnetic Materials
Open System: NEGF
Spin-orbit, E-field, B-field, strain
Closed System: Schrodinger
Atomistic H: Tight-Binding 4 Beyond Moore’s Law?
Atomistic Modeling Approach
Spintronics/Magnetics Emerging materials
Quantum ‘Logic/Spintronics’ Quantum computing primer
1982: Feynman proposed a model for quantum computing.
1 Qubit: Superposition 2 Qubit: Entanglement
For N qubits, all 2N states are used in parallel. 30 qubit more powerful than a supercomputer.* Prime factoring, FFT, search, quantum simulation.
Semiconductor Hardware: nanoscale spins
*Error correction ~ 100-1000 qubits Source: Modified from ibmcai.com
QC Promises massive speedup for difficult problems. History: Semiconductor (Si) Quantum Computing
1998: Loss, Divincenzo proposal - QDs 1998: Kane proposal – donors in Si
Two promising proposals for semiconductor qubits! Kane’s Quantum Computer
Electrical control of hyperfine and exchange
Exchange(J) e- Hyperfine(A) e- e-
P+ P+ P+
Utilize Si:P for quantum computing. Wavefunction control. History: Semiconductor (Si) Quantum Computing
1998: Kane proposal – donors in Si.
2008: Single donor states observed in transport.
• Energy levels different from bulk donor • Modeling showed the levels were Stark shifted • Indirect evidence of wavefunction control
Single donors probed in experiments. History: Semiconductor (Si) Quantum Computing 1998: Kane proposal – donors in Si.
2008: Single donor states observed in transport.
2010: Readout of single spins + spin lifetime measurement.
2012: Single atom transistor. Single atom electron qubit. History: Semiconductor (Si) Quantum Computing 1998: Kane proposal – donors in Si.
2008: Single donor states observed in transport.
2010: Readout of single spins + spin lifetime measurement.
2012: Single atom transistor. Single atom electron qubit.
2014: First atomic scale imaging of donor wavefunctions.
Experiment Theory
• FFT of tunnel currents to STM tip.
• Theory confirmed dopant states were imaged.
• Explained various features.
Single donor wavefunctions imaged with atomic resolution. History: Semiconductor (Si) Quantum Computing 1998: Kane proposal – donors in Si.
2008: Single donor states observed in transport.
2010: Readout of single spins + spin lifetime measurement.
2012: Single atom transistor. Single atom electron qubit.
2014: First atomic scale imaging of donor wavefunctions.
2014: Theory guided engineering of long lifetimes.
Engineering spin lifetimes in silicon. Spin relaxation in semiconductors
• Spin polarization: N↑, N↓
• Decay of spin polarization: spin relaxation length/time
• Relaxation mechanisms: spin-orbit
Source: http://www.escience.cn/people/YanpingLiu/research.html
Spin relaxation in quantum computing: Spin lifetime T1 Atomistic methodology (no fitting parameters)
• Spin-orbit interaction (atomic orbital) Spin-Orbit • Acoustic phonons (atomistic deformation potential) phonon θ
Parameter-free calculations of spin relaxation times. Comparison with experiment
Donor numbers
1P1e
Old theory (1P1e) Electron numbers
2P3e
Morello group, Nature 467, 687 (2010) Simmons group, Nature Communications 4, 2017 (2013)
Unexplained T1 times from experiments. Atomistic Approach Explains Experiment
4P5e 1P1e
Old theory (1P1e) 5 4P3e B
4P1e Long T1
Theory: Electron and donor number variations => Orders of magnitude variation in T1. 10 times improvement. History: Semiconductor (Si) Quantum Computing 1998: Kane proposal – donors in Si.
2008: Single donor states observed in transport.
2010: Readout of single spins + spin lifetime measurement.
2012: Single atom transistor. Single atom electron qubit.
2014: First atomic scale imaging of donor wavefunctions.
2014: Theory guided engineering of long lifetimes. 2015: Realization of Kane’s single qubit.
Manipulating single spins in silicon. Reminder: Kane’s Single Qubit
Single Qubit:
e- Hyperfine(A)
P+
Utilize Si:P for quantum computing! Wavefunction control. Theory of control for single qubit
Hyperfine coupling
Spin-orbit Stark Effect: Rahman et. al. PRB 80, 155301(2009).
E(MV/m) Agreed well with expt. in Princeton
Quantitative theory of donor spin control. History: Semiconductor (Si) Quantum Computing 1998: Kane proposal – donors in Si. 2008: Single donor states observed in transport. 2010: Readout of single spins + spin lifetime measurement. 2012: Single atom transistor. Single atom electron qubit. 2014: First atomic scale imaging of donor wavefunctions. 2014: Theory guided engineering of long lifetimes. 2014: Realization of the Kane single qubit. 2015 - : Next Challenge: Kane Two qubit gate (exchange). Exchange(J) e- e-
P+ P+
Entangling two spins in silicon. History: Semiconductor (Si) Quantum Computing
1998: Loss, Divincenzo proposal - QDs 1998: Kane proposal – donors in Si
Two promising proposals for semiconductor qubits! History: Semiconductor Quantum Computing
1998: Loss-Divincenzo proposal – Quantum Dot Qubit
By 2015: One & two-qubit gates realized in GaAs, Si.
2016-: Challenges: 1) Performance of two-qubit gates 2) Multi-qubit scalability
Contributions: 1) Qubit properties (g-factors, T2*) will vary between QDs. 2) Mitigation strategies.
Role of spin-orbit (SO) interaction
Towards realization of many qubits with quantum dots. Electronic states in Si Quantum Dots g-factors: Important for qubit manipulation
Energy
v- v+ hfv+= gv+μB
EVS
v+ v- hfv- = gv-μB
B-field
fv± = ESR frequencies,
gv± = valley g-factor, Veldhorst et. al. PRB 92, 201401 (2015).
g-factor shifts usually result from SO. But SO is thought negligible in Si.
Experiments found g-factors of the two valleys are different. 22 Spin-orbit coupling in tight-binding
p-orbitals (IV, III-Vs) Atomistic treatment of SO
SOC in atomic orbital basis
Define geometry atom by atom
Rashba/Dresselhaus (other SOCs) fall out automatically.
No adhoc fitting parameters unlike k.p.
Atomistic description of SOC is comprehensive & general. 23 TB results: Valley dependent g-factors in Si QDs
TB: g-factor (Ideal/flat surface)
How about interface roughness?
How robust are g-factors in Si?
G3 SET
Step disorder: Zandvliet et. al., PRB 48 (1993)
24 g-factors with interface steps
Bext along [110]
g- > g+ g- < g+
25 Experimental confirmation: g-factor variations
Al2O3 G G G G G Atomistic simulation Al R 4 3 2 1 C SET Exp SiO2 2DEG Q Q Q 28Si 3 2 1
Bext along [110] g- > g+ g- < g+
Observations: • g-factors vary between dots • g-factor magnitudes flip between valleys g- > g+ g- < g+
Predictions confirmed by experiment: g-factor variations. Why? Dresselhaus-like SOC in silicon
Bext along [110]
New findings: • Dresselhaus-like SOI (β) dominates in Si QDs. • β varies in sign and magnitude with step location.
Dresselhaus-like SOC in Si surface. 27 Strategies to mitigate varability
Bext along [110]
Step disorder β g±
Possible 1) Reduce disorder by interface engineering solutions: 2) Reduce β
How to reduce β? 28 Strategy: anisotropic Dresselhaus SOC
Our novel finding: Strategy: • Contribution of β is anisotropic • Are there magic angles where β is minimum?
[110]
[100]
Reorient B-field direction in experiments.
g-factor variations are strongly suppressed for B[100]. No effect of step disorder anymore. 29 * Strategy to improve T2
Other implications?
* T2 : time to loose quantum information
Obstacle to quantum information: * • small T2
Possible solution: • Reduce β => reduce effect of charge noise
• Can anisotropy be used again? [100] - - [010] [100] [010]
Anisotropic dephasing time: - - • Large increase in T2* along [100]/[010]/[100]/[010]
Prediction: ~30 times improvement in T2* may be possible. 30 History: Semiconductor Quantum Computing
1998: Loss-Divincenzo proposal – Quantum Dot Qubit
By 2015: One & two-qubit gates realized in GaAs, Si.
2016-: Challenges: 1) Performance of two-qubit gates 2) Multi-qubit scalability
• Dresselhaus at silicon surface. • Mitigate variations in g, T2*. • Improve T2* 30 times.
Towards realization of many qubits with quantum dots. Atomistic description of SOC: Magnetic/Spintronic Materials Giant SO Materials (heavier Transition Metals): Ta, W, Pt
Ralph/Buhrman groups
Topological Insulators (Large SO, spin-polarized bands):
Bi2Te 3, Bi2Se3,Bi2Sb3)
Kang Wang group
Atomistic methods can help engineer SOC couplings in spintronic devices Atomistic description of SOC: Magnetic/Spintronic Materials 2D materials (Adatoms, intercalation): Graphene, TMDs
III-V materials: InAs, InSb, GaSb Kouwenhoven • Topological Qubits (Majorana) group • E-field manipulation of qubits • Hole qubits
Manfra/Marcus Atomistic methods can help engineer SOC couplings in spintronic devices Beyond Moore’s Law?
Atomistic Modeling Approach
Spintronics/Magnetics Emerging materials
Quantum ‘Logic/Spintronics’ Beyond Si: 2D Material tunnel FETs
LEAST: Steep transistor design with NEMO5 Thinnest channel
Good gate control
Smaller tunneling distance
Large ON currents
H. Ilatikhameneh et. al., JxCDC 1, 12-18 (2015). T. Ameen et. al., Scientific Reports (2016).
ON-currents too low for most TMD TFETs. Black Phosphorus is promising. Comparison with experiment
Experiment: Appenzeller group
Good experiment-theory agreement of black phosphorus I-V. Scaling Lch in TFETs InAs NW TFET
1) Low m* for high ION 2) High m* for low IOFF
Most TFETs do not scale well below 10 nm. Anisotropic m*: L-shaped BP TFET
Perspective view Top view
Low m* Channel
High m*
Proposal of a new 38BP TFET. L-shaped BP TFET performance
Successful scaling to 2nm gate lengths
Low m*
High m*
L-shaped BP TFET can scale down to few nm. 39 Beyond Moore’s Law?
Atomistic Modeling Approach
Spintronics/Magnetics Emerging materials
Quantum ‘Logic/Spintronics’ Applications spintronics/magnetics e-n spins: hyperfine coupling Topological Insulators / magnetic materials
P+ P+ “Spin battery”, Y. Chen group 2017: hyperfine, e-n dynamics.
STM imaging atomic scale Magnetic Impurities
Mn in GaAs
N/Co in graphene
TI states
41/27 Yazdani group 2006 Applications in spintronics/magnetics
e-e direct exchange coupling Engineering magnetism: exchange • Direct, RKKY, Super-exchange • Ab-initio/wavefunction level description Exchange(J) of exchange coupling desired. e- e-
P+ P+
Spin lifetimes Spin-orbit coupling
Can we engineer material properties for long spin lifetimes? 42/27 Atomistic “Material-to-Device” Component for Spintronics Atomistic Component: Spin Purdue Expertise: Spin
DFT: First principles Theory ~ <200 atoms Device Level: m* Novel materials Material-to- description of devices, device interface: compact models, EM- NEGF, Drift-diffusion, LLG TB, Wannier: Semi- Exchange, spin- Circuit/architecture empirical / mapping orbit, hyperfine, level: Spin circuits, SPICE ~ 1-20 million atoms magnetic dipole, Material & Device spin relaxation, E/B-fields, strain, spin currents disorder, full band Experiment + computational Material growth NEGF: Spin Transport device modeling
Spin currents (with SO) Device Fabrication -Leads, scattering, spin
injection/relaxation Measurement
Proposal: Atomistic spin component43/27 for material to device interface Conclusion: Material-to-device framework
Experimental partners
(Simmons, Rogge, Dzurak, Morello)
Delft/Intel (Vandersypen, Veldhorst)
• Atomistic material-to-device framework has led donor based U. Wiscon-Madison (Eriksson) quantum computing in silicon. (Appenzeller, Chen,
Seabaugh, Fay, Jena) • Understanding spin-orbit at the atomic scale challenges our old knowledge.
Publications: 8 Nature (family), 2 Science Advances, 5 PRLs, 3 Nanoletters, 3 Sci. Reps.44 /27Total 55 journals.