New materialselectronic structure in 21st century

1
New materials/electronic structure in 21st century
Typical features - multi-component,
hierarchies - 0-3D (dots, chains, layers ... ) -
d- and f- elements - H proton as a quantum
part. - organic/inorganic/solid - bioinspired
Challenges - lack of a "unifying"
strategy - complexity - competition of
mechanisms quantum, temperature, etc -
single electron/quantum effects important
Solving these one-by-one, ie, by a
postdoc focused on a class of materials
for X years is ultimately inefficient Unifying
concept on which we all agree Schrodinger
equation Solve it in the many-body framework
(!)
with the original Hamiltonian
Lubos_Mitas_at_ncsu.edu
2
Computational Materials Research
Key goals - predict, design and
optimize new materials for 21st century
- complement, guide and/or replace experiment
- new science frontier from one-particle
to many-body Broad application areas
- new energy sources production/storage/processin
g of H - nanosystems based materials
- bioinspired materials and processes
waste is nonexistent Clear-cut example of
previous impact - 3rd most cited PRL
in all physics and history is Ceperley/Alder
Quantum Monte Carlo of homogeneous
electron gas Possibilities/breakthroughs with
500-fold increase in compute power - a
few meV accuracy for energy differences
- quantum effects, temperature, dynamics on the
same footing - nanosystems in action,
magnetism, supreconductivity in a wave
function framework - H (bonded,
solvated, ...) proton as a quantum particle
Lubos_Mitas_at_ncsu.edu
3
Quantum Monte Carlo a unique strategy/opportunity
for quantum many-body problems
Schrodinger equation in a propagator form
-sample the wave function by walkers in
space -boost the
efficiency with explicitly correlated trial
functions -propagate the walkers while enforcing
all required symmetries -evaluate the
expectation values of interest QMC -
new physics/paradigm work directly on many-body
effects - scalable, robust, highly
efficient on parallel architectures -
favorable scaling in of particles nominally
O( N3) and
implentation with almost O( N ) feasible
- accurate typically 95 of correlation
energy across systems
0.1 eV/1 accuracy/agreement with experiment
- benchmarks for other methods, consistent
results
Lubos_Mitas_at_ncsu.edu
4
QMC bottlenecks and advanatges next 5-10 years
Scientific - beyond the fixed-node
approximation, very active
research obtain 99 of correlation with
polynomial scaling - spin and
spatial degrees of freedom on the same footing
- responses to external fields and
spectral functions - from wave
functions to density matrices (temperature) Mix
of Science and Algorithmic/Computational
- more efficient and accurate building
of trial functions eg,
robust stochastic optimizations
- efficient coupling and data exchange with
one-particle approaches
Hardware/ 1. processor speed Software
2. parallelism 3.
stability (QMC can test it real well)
4. memory, communication, etc, relevant
but secondary
Lubos_Mitas_at_ncsu.edu
5
Qauntum Monte Carlo typical run
System 50 atoms, 200 electrons, desired
accuracy 0.1 - 0.2 eV Typical input
tens/hunderds of MB (initial/trial wave
function) Typical run - tens of processors
for days and weeks - MPI
- 10-100s walkers in
3N-dim. space per processor
- evolved for hundreds of steps
(independently, or
occasionally rebalanced) -
accumulate statistics from processors Typical
output - most of the data
reduced to simple physical quantities
- current walker configurations stored (tens
of MB per proc) - restartable
Lubos_Mitas_at_ncsu.edu
6
Materials with competing many-body effects
hexaborides CaB6, LaxCa1-xB6 , ...
5 La-doped CaB6 is a weak magnet up to 900K
(!) No d or f electrons - genuine itinerant
magnetism ? -
promising spintronics material ?

Undoped CaB6 insulator ? exitonic insulator ?
metal ? Experiments contardictory ARPES
insulator de Haas-van Alphen metal Optical,
etc metal, insulator
Calculations inconclusive DFT band overlap 1
eV (Swiss,...) DFT small gap (Japan) GW (DFT
pert. corr.) 1 eV gap (NL) GW small overlap
(Japan)
Can we predict the correct gap before the
experiment ?
Lubos_Mitas_at_ncsu.edu
7
CaB6 band structure in Hartree-Fock
Large gap of the order of 7 eV
Lubos_Mitas_at_ncsu.edu
8
CaB6 band structure in DFT - B3LYP
Gap is now only about 0.5 eV !
Lubos_Mitas_at_ncsu.edu
9
CaB6 band structure in DFT - PW91
1 eV overlap at the X point d-states
on Ca ! Fixed-node DMC gap
1.3(3) eV
X G

Lubos_Mitas_at_ncsu.edu
10
Predict a "nanomagnet" caged transition
elements TM_at_Si12 TMSc, Ti, ... 3d, 4d, 5d
Find the smallest stable "nanomagnet" made from
silicon and a
transition metal atom ...
- attempt to predict caged d-spin - no
success, hybridized, unstable
Experiment in Japan in '01!
W_at_Si12
APS March Meeting in '94 L. M.
Electronic structure of Mn_at_Si12
Lubos_Mitas_at_ncsu.edu