 |
|
|
|
Quantum Phase Transitions
Week 10, 14th March - 18th March, 2005
Blogger: Mike Norman, Dirk Morr, Andrey
Chubukov
As this was the week before the March meeting,
we had a rather full program due to additional visitors. We started our
week with Dirk Morr (University of Illinois at Chicago) giving the
lunch blackboard talk on Monday on "Quantum Photography and Quantum
Music". On Tuesday Andy Millis (Columbia University) presented a talk
on "Mott physics in high Tc materials". On Wednesday morning, Bob
Schrieffer, a former director of ITP, gave a
talk on the Heisenberg-Kondo spin glass. He considered frustrated
magnets with long-range, RKKY-type oscillating exchange interaction and
discused his computations of spin correlation functions. On
Thursday, we had a lively
discussion on various aspects of strongly correlated electron systems.
The experimental talk of the week on "Hall Effect Across a Quantum
Critical Point" was given by Silke Paschen on Friday.
Participants
Blackboard Seminar
Experimental
Seminar
Thursday Discussion
Participants
present.
Click on participant to read questions that they have posed
Abrahams, Elihu
Blumberg, Girsh
Chubukov, Andrey
Efetov, Kostya
Feldman, Dima
Geshkenbein, Vadim
Kroha, Johannes
Larkin, Anatoli
Marenko. Maxim
Monien, Hartmut
Morr, Dirk
Norman,
Michael |
Paschen, Silke
Pepin,
Catherine
Shankar, Ramamurti
Si, Qimiao
Turlakov, Misha
Weng, Zheng-Yu
Yakovenko,Victor
Yang, Kun
Ye, Jinwu
Zarand, Gergely
|
Top
Dr. Dirk
K. Morr,
University if Illinois at Chicago |
Quantum
Photograpgy and Quantum Sound
or
How to take pictures and make music in the quantum world[Aud][Cam] |
The formation of optical images or sound is fundamentally related to
the
properties of waves. Experimental advances over the last few years have
made it possible to use the wave-like nature of electrons in condensed
matter systems to form quantum images (also called quantum mirages) in
solids. Dirk Morr began his talk by reviewing some of the
groundbreaking experiments that have demonstrated this possibility. In
particular, Manoharan et al. have shown that it is possible to form a
quantum image of a Kondo-resonance (a distinct feature in the density
of states which Dirk labeled a "quantum candle") inside an
elliptic quantum corral (see Fig.1).
In order to form this ellipse, Manoharan et al placed magnetic Co
atoms on the surface of Cu(111). An additional Co atom was placed into
one of the foci of the corral, and a Kondo resonance was observed near
this Co atom by measuring the density-of-states using a scanning
tunneling microscope. An image of the Kondo resonance was observed in
the empty focus of the quantum corral, demonstrating the possibility
for quantum imaging in condensed matter systems. This effect can be
easily understood classically, since waves emanating from the focus of
an ellipse are reflected specularly by the walls of the ellipse and are
refocused into the empty focus where they create an image. This
classical effect was demonstrated in 1825 by Weber and Weber by using
waves in an elliptic container filled with Hg. Quantum mechanically,
quantum imaging is possible through the formation of eigenmodes inside
the corral (eigenmodes are the eigenstates of the "particle in a box"
problem. The eigenmodes associated with a quantum corral has in general
a finite lifetime since the particle can leave the inside of the
corral).
Dirk then presented some theoretical results of his group on the
possibility of quantum imaging in quantum corrals that reside on the
surface of conventional and unconventional superconductors.
In particular, he demonstrated that one can use impurity bound (Shiba)
state induced by a magnetic impurities in an s-wave superconductor as a
new type of quantum candle. Placing a magnetic impurity in the focus of
a corral consisting of non-magnetic impurities, Dirk showed that an
image of both peaks associated with the bound state are formed in the
empty focus (see Fig.2).
Dirk then showed that multiple quantum images of the impurity bound
state peaks can be formed in quantum corrals of different geometry,
such as triangular ones. Moreover, in these corrals, it is possible to
"destroy" the impurity bound state by placing the impurity into one of
the nodes of the low-energy eigenmodes. In this case the bound state
cannot be formed since it cannot satisfy the boundary conditions
established by the corral's wall, or said differently, since it cannot
couple to a low-energy eigenmode. This constitutes an important result
since it shows that non-magnetic impurity (which form the corral
wall) can fully suppress the pair-breaking effect of a magnetic
impurity through quantum interference.
Dirk then showed that if more than one impurity is placed into the
inside of a triangular corral, selection rules emerge that govern the
formation of quantum images. In particular, for three magnetic
impurities, it is possible to observe only two (or four) of the
expected six impurity peaks in the density of states. Finally, Dirk
demonstrated that quantum interference effects between two (or more)
magnetic impurities can lead to the breaking of a Cooper pair and a
change in the ground state polarization of the entire superconductor
from S=0 to S=1/2. This change occurs via a level crossing, and thus
corresponds to a (local) first order quantum phase transition.
|
|
Blackboard
Discussion. 10am Monday, February
28
Dr. Andrew Millis Columbia University
Recent
Developments on Cuprates[Audio][Cam]
|
Andy Millis (Columbia
University) gave a theory talk on the role of Mott physics in high Tc
materials. The cuprates are doped Mott insulators, and Mott physics is
well known to play the major role very near half-filling (the parent
compounds of high Tc materials are Mott insulators and also Heisenberg
antiferromagnets). Andy addressed the issue how strong is the
suppression of double occupancy at a finite doping, and whether the new
correlations associated with Mott physics show up in the charge
response throughout the whole interesting range of dopings in
hole-doped and electron-doped materials. He discussed earlier studies
the one-band Hubbard model, e.g., of Tremblay and co-authors, who
argued that in electron-doped materials, Hubbard U is weaker than in
hole-doped materials. He then presented the results on his own DMFT
calculations of the integrated optical spectral weight in the normal
state of Hubbard model with nearest-neighbor hopping. His conclusion
differs from that of Tremblay et al. Andy and his student have found
that U is larger than the bandwidth W for hole-doped and for
electron-doped materials. For hole-doped materials, his calculations
yield U/W ~ 2 (i.e., U ~ 15-20 t). For electron-doped materials, U is
somewhat smaller, but still is larger than the bandwidth. Millis argued
that for such large U, one-band description of the charge transport is
likely not enough even near optimal doping as inter-band scattering
should contribute to charge transport. He estimated the effect of
inter-band scattering to be about 50% near optimal doping. He argued
that, at present, there is not enough data on optical conductivity to
track the effects of Mott correlations vs doping.
|
|
Top
|
|
Experimental
Seminar,
10.00 Friday, March 18
Dr. Silke
Paschen - Max Planck Institute - Dresden
|
Hall Effect
Across a Quantum Critical Point [Audio][Cam] |
Silke discussed
her recently published results in the journal Nature regarding the Hall
effect near the magnetic quantum critical point in YbRh2Si2.
She first presented the overall temperature dependence of the Hall
number, which is highly non-trivial due to the presence of skew
scattering. Once this is factored out, though, she finds that the
Hall number at high temperatures and low temperatures near zero field
are the same. This implies that the Fermi surface topology in the
zero field magnetic ground state is the same as at high temperatures,
which would be consistent with the f electrons not participating in the
Fermi surface.
She then discussed applying a field to reach the field tuned quantum
critical point. The linear field Hall response at low fields changes at
the critical field to a less steep slope, implying an increase in the
Hall number from 2 to 3. She took this as possible evidence that
the f electrons in the paramagnetic phase now participate in the Fermi
surface. One issue with the Hall measurements is that the same field is
being used to tune to the quantum critical point, and also provide the
linear response field. To investigate this, she performed a cross
field experiment where the tuning field and the linear response field
were applied in perpendicular directions. These results are
consistent with the previous results, again implying a Hall number
change from 2 to 3 across the critical point.
By doing
temperature sweeps, she was able to sweep out a phase diagram.
This shows that
the crossover field in the Hall number, although degenerate with the
quantum critical point at T=0, moves to higher fields with increasing
T, unlike the Neel temperature which moves to lower fields. This,
plus the fact that the ordered moment of 0.002 Bohr magnetons seems far
too small to be responsible for the large Hall number change, implies
that the Hall anomaly has nothing to do with the magnetic phase line,
but is rather a property of the quantum critical point itself.
The crossover line sharpens with reduced T, but the crossover is still
smooth at the lowest temperatures studied (16 mK).
Andy Millis
argued that this could be a consequence of the fact that at low
temperatures, the crossover straddles the boundary between the Neel
state and the paramagnetic state. Finally, she mentioned unpublished
results on the longitudinal resistance which shows only an anomaly at
the Neel temperature, and not at the Hall anomaly. All agreed
that this was rather strange, since if the Fermi surface topology
changes, one would expect changes in the longitudinal resistance as
well.
(a lively discussion after the talk with Silke Paschen, Qimiao Si, Andy
Schofield, Andy Millis, and Dirk Morr)
|
Top |
|
Discussion:
4:30 pm Thursday, March , 17th Founders Room.
Dima Feldman discussed a quantum phase transition far from
equilibrium in a one-dimensional conductor with an applied voltage.
This system was assumed to be non-dissipative, and corresponds to a
one-channel quantum wire. Such a system, in the absence of an applied
voltage, can be driven into a ferromagnetic state via a second order
phase transition by tuning the density of states. Dima discussed the
question of how the nature of the quantum phase transition is changed
if the applied voltage is non-zero. Considering an Ising spin symmetry,
and employing a bosonization approach, Dima demonstrated that the
universality class of the transition changes in the vicinity of the QPT
due to a non-zero voltage. In particular, the transition becomes
mean-field like with an effective dimension D=6, instead of D=1+1 in
the absence of a voltage. The correlation function of the magnetization
decays as 1/x^2, as expected for a Luttinger liquid, reflecting that
the magnetization is a conserved quantity.
Jinwu Ye then discussed the Bose-Hubbard model on a
honeycomb lattice at half-filling. In order to discuss its physical
properties, Jinwu used a bipartition of the lattice, combined with a
duality transformation to vortices on a triangular lattice with a
pi-flux. Jinwu argued that this model is appropriate to describe the
system D2/Kr/graphite. He finds that this model exhibits a
superconducting and an insulating phase.
Doug Scalapino presented a series of comments on Andy
Millis' talk on Tuesday. In particular, Doug raised the question of the
relationship between the Drude weight and the value of U/t, that Any
focused on in his talk. Doug argued that the Drude weight, D, is the
sum of a "kinetic energy" term and a term describing the
current-current correlations. Under the assumption that the Drude
weight, which goes into the superfluid density, scales linearly with
doping away from half-filling, Dough showed that the results of his
quantum Monte-Carlo calculations are consistent with a value of U/t=8,
which is about half of the value that was obtained by Andy on the basis
of DMFT calculations. The value of U/t determines whether the t-J
model, or the SDW paramagnon approach is the correct starting point for
the description of the cuprate superconductors.
Top |
Return to
main page.
|
|
|
|
|
