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.