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Yen Lee Loh
Research Statement
My research involves strongly correlated quantum systems and how the mutual interaction of a large number of
particles leads to fascinating emergent behavior. I have worked on a diverse range of topics in condensed matter,
interconnected through the themes of magnetism, superconductivity, disorder, quantum criticality, and the
Coulomb blockade. Recently, I have also become interested in ultracold atom systems, which are versatile,
tunable, and open up a whole new world of possibilities for studying quantum phases and nonequilibrium
dynamics.
My previous work includes the following:
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Magnetic droplets near ferromagnetic quantum critical points: found a new logarithmic behavior of the
susceptibility
Coulomb blockade effects in granular metals: studied the renormalization of the charging energy
Disordered magnetism: developed the bond propagation algorithm to solve any planar random-bond Ising
model in polynomial time
Disordered superconductors: studied possibilities for enhancing Tc using inhomogeneity
Below is a description of my current work and future plans.
Superconductor-Insulator Transitions: A thin film of superconducting material (such as indium oxide or
aluminum) can undergo a transition to an insulating state as a function of thickness, disorder, or magnetic field.
The superconductor-insulator transition (SIT) is a quantum phase transition of a strongly correlated electron
system, for which several fundamental questions remain unanswered.
My colleagues and I have recently made significant progress in this
field. Our Bogoliubov-de Gennes (BdG) results suggest that even
superconductors with “homogeneous disorder” can spontaneously
develop inhomogeneity in the form of superconducting puddles (a type
of nanoscale emergent phenomenon). We have further refined this
picture using determinantal Quantum Monte Carlo (DQMC)
simulations, which include all thermal and quantum phase fluctuations.
Moreover, we have studied single-particle and two-particle spectral
functions across the disorder-tuned SIT using maximum entropy
methods for analytic continuation. We find that the single-particle gap
remains robust through the SIT, whereas the coherence peaks disappear
beyond the SIT (and above Tc). Therefore, it is the coherence peaks
Fig. 1: Energy scales across the SIT from
our DQMC simulations.
(and not the gap) that signal the presence of long-range
superconducting order. Furthermore, the “normal” state has a disorder-induced pseudogap that persists to
temperatures much higher than Tc. This naturally explains the discrepancy between tunneling and transport that
has baffled some experimentalists. The insulator is characterized by a gap-like structure in the two-particle
spctrum at a characteristic energy scale that decreases to zero at the SIT (unlike the single-particle gap). We have
also be able to correlate the features of the local density of states (LDOS) with the local pairing amplitude. These
results are of enormous importance for guiding tunneling and scanning probe experiments.
In the future, I plan to extend our calculations to transport and electrodynamic response, which, after all, are the
quantities that distinguish “superconductors” from “insulators”. I also plan to explore the possibility for
multiscale modeling where BdG on short scales is used to generate parameters for effective field theories on
longer scales. Finally, I have plans to connect the superconducting and insulating phases of our fermionic model
with those of bosonic models, which would complete the big picture. This will involve a synergy between
analytical and numerical work, and it may provide a valuable experience for graduate students.
Fulde-Ferrell-Larkin-Ovchinnikov states in ultracold atomic gases: It was proposed in the 1960s that the
competition between Cooper pairing and spin polarization can produce an exotic form of superconductivity,
known as a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, in which the pairing amplitude varies periodically in
space. However, the FFLO phase is as elusive as it is exciting; on the 3D continuum mean-field phase diagram it
occupies a tiny sliver, which disappears upon including fluctuations. On the experimental front, there have only
been a handful of reports of FFLO phases in condensed matter or cold atom systems, and these are based on
indirect evidence.
In a recent PRL I showed that optical lattices greatly enhance the
stability of Larkin-Ovchinnikov (LO) phases (where it is important
to distinguish more general LO solutions from the less favorable FF
ansatz), and identified this as due to a combination of Hartree shifts,
domain wall formation, and enhanced Fermi surface nesting. Within
my approximations, up to 80% of the fermions in a cubic optical
lattice in a harmonic trap can be involved in LO phases! Moreover,
LO phases (unlike FF phases) have polarization oscillations in space,
and sub-gap spectral weight in the frequency domain, that serve as
complementary signatures that may be the long-desired “smoking
gun” for direct experimental detection.
Fig. 2: Schematic of the LO phase in a
harmonic trap corresponding to a slice
through the phase diagram.
More recently, we have been working on low-dimensional systems, where FFLO is thought to be most likely. I
initiated a comparison of BdG, DQMC, Stochastic Green Function (SGF) QMC, and time-dependent DMRG
results in 1D, which has led us to an interpretation of the 1D FFLO state in terms of fluctuating domain walls.
Not only does this help us to understand the static correlation functions, it also manifests itself in the nature of the
dynamic quantities (spectral functions), which may be a powerful experimental probe for detecting FFLO states. I
am hoping to extend our DQMC work to quasi-1D to obtain some predictions about the FFLO phase diagram and
signatures for detection, which would be extremely useful to our experimental collaborators at Rice University.
Disordered Fulde-Ferrell-Larkin-Ovchinnikov states in thin film superconductors: LO physics may be more
widespread than conventionally thought. I have verified that BdG calculations for superconducting films in
parallel fields converge to LO-like solutions, and furthermore, I have shown that the density of states in a
“disordered LO” phase has significant weight within the gap due to Andreev bound states in domain walls, which
act somewhat like emergent magnetic impurities. This may, in fact, resolve a longstanding puzzle raised by
tunneling experiments on disordered superconducting films by Phil Adams and collaborators at LSU. In a parallel
field, over a significant range of fields below the Chandraksekhar-Clogston transition, the tunneling conductance
has a rather large value at zero bias. The conventional theory of a uniform superconductor, even after accounting
for magnetic impurities, misalignment, and orbital pairbreaking, is unable to explain this. I have argued that the
anomalous zero-bias conductance may be a signature of disordered LO physics, and it may persist even if LO
order is washed out by fluctuations.
Sodium tungsten bronzes: Work by D. D. Sarma at the Indian Institute of Science has revealed fascinating
behavior in the photoemission spectra of NaxWO3 across the metal-insulator transition driven by doping x. I plan
to perform calculations at successive levels of sophistication (with and without hopping, interaction, and disorder),
in order to obtain a coherent description of the whole series of experiments.
Nonequilibrium quantum dynamics: Cold atom systems offer the possibility of studying quantum dynamics of
isolated systems. Such systems support novel nonequilibrium phenomena such as a finite-temperature metalinsulator transition due to many-body localization, put forth by Basko, Aleiner, and Altshuler and taken up by
other authors. In particular, Vadim Oganesyan and David Huse have performed exact diagonalization studies on
small systems to look for such a transition. It may be possible to extend such calculations to significantly larger
systems using Chebyshev methods (following previous work by myself), which are natural for studying time
evolution and spectral functions, and are billions of times more accurate than equation-of-motion methods. I plan
to explore this possibility with Vadim.
In the past few weeks, experimentalists at Garching have managed to control the exact arrangement of atoms in a
2D optical lattice, and furthermore, they can even perform “spin” flips on individual atoms! If we can
successfully simulate the dynamics of such a system using Chebyshev methods, we will be very close to designing
a quantum computer.
In general, I am fascinated by emergent phenomena, from new types of ground states, elementary excitations and
hidden orders in strongly correlated electron materials to complex behavior in classical nonlinear systems. While
I believe that understanding the natural world is the primary goal of a physicist, I also look out for possible
improvements in theoretical and computational techniques that help in bridging the gap between theory and
experiment. I have found that my key strength is the ability to use a multipronged approach of various analytical
and numerical techniques to build up a solid understanding of the system being considered, and thereby gain a
thorough understanding of the physics. My research has reached a point where additional postdoc, graduate, and
undergrad manpower would be very useful in exploring different aspects of each problem. Where suitable, I
intend to leverage the Algorithms and Libraries in Physics Simulations (ALPS) package, which is a promising
collection of research-quality quantum Monte Carlo codes that can help graduate students get off to a quick start.
Finally, I have been fortunate for the opportunity to collaborate with many excellent theorists and experimentalists
including Mohit Randeria, Adrian Feiguin, Tom Lemberger, and Phil Adams, and to participate in writing DOE,
NSF, and OSC (Ohio Supercomputer Center) grant proposals with my supervisor, Prof. Nandini Trivedi.