A study led by researchers at the U.S. Department of Energy's Oak Ridge
National Laboratory used the nation's fastest supercomputer to close in on
the answer to a central question of modern physics that could help conduct
development of the next generation of energy technologies.
"This is mostly about solving what's now a decades-old problem," said Thomas
Maier, an ORNL physicist who led the study with researchers from the
University of Tennessee and the Institute for Theoretical Physics ETH
Zurich. "If we can answer the question of what's the mechanism for
superconductivity in certain correlated electron systems and understand the
reasons for that behavior, then we can design materials to make the most of
that behavior."
Findings appeared in the Proceedings of the National Academy of Sciences.
The study used Summit, the Oak Ridge Leadership Computing Facility's
200-petaflop IBM AC922 supercomputing system, to simulate interactions among
a system of electrons within a solid. The simulations applied the Hubbard
model, the most straightforward model of a system of interacting electrons
in various dimensions, to explore how a class of copper alloys known as
cuprates act as superconductors that transmit electricity with no loss of
energy.
Cuprates can be used in power transmission and generation, high-speed
magnetic levitation, or maglev, trains and medical applications, but
generally display their full superconducting properties under extreme
cold—typically hundreds of degrees below freezing. Explaining this
superconductivity could crack the code to deliver superconductivity at room
temperature and provide cheap, speedy and sustainable energy.
The Hubbard model, developed nearly 60 years ago and named for British
physicist John Hubbard, posits a system of electrons within a 2D lattice.
Each electron has a spin—either up or down, similar to the positive and
negative poles of a magnet—and no two electrons of the same spin can occupy
the same site. The first term of the model describes kinetic energy. In this
term, the electrons move or "hop" back and forth between adjacent sites in
the lattice and diagonally between their next nearest neighbors. The second
term describes interaction energy and the energy increase if two electrons
of opposite spin try to occupy a single site.
Hubbard didn't design the model to explain electron behavior in
superconductors like cuprates. Researchers have experimented with layers of
copper and oxygen in search of a room-temperature superconductor and
adjusted or "doped" the Hubbard model over the years to try to understand
superconducting properties.
The doped models remove electrons, leaving "holes" that encourage the
remaining electrons to form pairs that easily conduct electricity. Under the
right conditions, the holes fall in line to form stripes, believed by
scientists to compete with superconductivity, and the electrons form a wave
pattern, known as a charge and spin density wave.
But those models so far fail to reliably explain or predict
superconductivity in enough detail for practical use.
"The approaches we have to solve this problem are not exact, and the model
in theory would be infinite in size with many distinct phases, which
requires extremely large, complex calculations," Maier said. "Energy
differences can be tiny—less than a millielectron volt. We can try to
approximate all this in a finite-sized lattice, but that approach neglects
too many aspects and we end up with a lattice too small to draw the kind of
robust conclusions we're looking for. We need a simple model that describes
all the physics and consistently produces the same results."
Maier's team received an allocation grant of 900,000 node hours on Summit
via the DOE's Innovative and Novel Computational Impact on Theory and
Experiment, or INCITE, program
to explore the model in depth. The results revealed new insights into the
relationships between electron spin and charge stripes, including when
stripes form as superconductivity develops.
"These were some really heavy computations that couldn't be done anywhere
but on Summit," Maier said. "We kind of took a chance, but it paid off
because we finally had a machine that could support computations for a
system large enough to see the stripes. This method allowed us to show that
when the stripes show up in charge and spin, the superconducting
correlations form a similar wave-like pattern known as a pair-density wave.
The results could set a new standard for understanding this model."
The simulations don't spell out the secret to raising the temperature for
superconductivity. But the lessons learned point to targets for further
study as researchers zero in on how superconducting occurs.
"We know more each year than we did the last," Maier said. "Now we need to
explore other methods for solving the model and replicate the results. We're
closer now than ever before, and we want to get even closer."
Reference:
Peizhi Mai et al, Intertwined spin, charge, and pair correlations in the
two-dimensional Hubbard model in the thermodynamic limit, Proceedings of the
National Academy of Sciences (2022).
DOI: 10.1073/pnas.2112806119
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Physics