KITP - 7

Quantum Phase Transitions

Week 7, 21st-25th February, 2005

Bloggers: Dirk Morr, Mike Norman, Hilbert von Lohneysen
Edited: Mike Norman

We started off the week with a great experimental talk on Tuesday by Andy MacKenzie on bilayer ruthenates. This was followed on Wednesday with an interesting talk by Peter Wolfle on the incoherent metal phase of hole doped Mott insulators, addressed using dynamical mean field theory. We closed the week off with a discussion session concerning our ignorance in regards to quantum critical metamagnets.

Participants
Blackboard Seminar
Experimental Seminar
Thursday Discussion

Participants present. Click on participant to read questions that they have posed

Bedell, Kevin
Belitz, Dietrich
Carbotte, Jules
Ingersent, Kevin
Larkin, Anatoli
Lavagna, Mireille
Marenko. Maxim
Morr, Dirk
Nicol, Elisabeth
Norman, Michael

Pepin, Catherine
Shaginyan, Vasily
Tewari, Sumanta
Vojta, Thomas
von Lohneysen, Hilbert
Woelfle, Peter
Ye, Jinwu
Young, Peter

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Blackboard Discussion. 10am Wednesday, February 23rd.

Dr. Peter Wolfle, Universitat Karlsruhe	Incoherent Metals[Aud][Cam]
	Local spectral function from extended DMFT for the t-J model at a hole doping of 1% as a function of the superexchange, J (left). As J is cranked up, a pseudogap develops. Hall response as a function of doping. Note the strong low T upturn, and the strong doping dependence. From: Haule, Rosch, Wolfle, PRB 68, 155119 (2003)
Motivation: As the motivation for his talk, Peter argued that the unconventional physical properties displayed by the pseudo-gap and strange metal regions in the phase diagram of the high-temperature superconductors are those of a hole-doped Mott insulator. In general, one needs to distinguish between two schools of thought: 1) A description of the pseudo-gap and strange metal region based on Landau's quasiparticle concept is still possible, leading to a strongly modified Fermi liquid, or the appearance of novel quasi-particles, such as spinons or holons. 2) The qp-concept has to be abandoned, and the system can only be described by highly incoherent excitations. Peter argued that the results presented in this talk support the latter approach. Mott-Hubbard Insulator and the Metal-Insulator transition near half-filling Starting from the Hubbard Hamiltonian, Peter discussed the nature of the metal insulator transition near half-filling. At half-filling, the Dynamical Mean Field Theory (DMFT) (work done by Vollhardt, Kotliar, etc..), is used to map the problem onto a quantum impurity problem assuming that the system is spin frustrated and thus does not undergo a magnetic transition. The main result of this approach was that at small U, the system is metallic, while with increasing U, a "Kondo-type" resonance appears at the chemical potential, and the system eventually undergoes a first order transition into an insulating state. At finite doping (work done by D.S. Fisher, Kotliar, Moeller, etc...) and U much larger than the bandwidth, a new state appears at the top of the lower Hubbard band. Because of the first-order nature of the transition, there exists a metal-insulator coexistence region in the phase diagram for doping <1% and at temperatures below 100-200K. Incoherent Metal Phase Peter then described a different approach to capture the physics of the pseudo-gap which is based on the Extended Dynamical Mean Field Theory (EDMFT) of the t-J model. Peter showed that the t-J Hamiltonian can be mapped onto an effective quantum impurity problem. Here, one assumes that the fermionic and bosonic self-energies are momentum independent, and determines the fermionic and bosonic Greens functions self-consistently. In order to solve the quantum impurity problem, one introduces a pseudoparticle representation. Within a generalized non-crossing approximation, one derives a functional from which the self-energies are obtained. Peter discussed several results of this approach, two examples of which are shown in the figures. Of particular interest is that a pseudogap opens in the local spectral functions with increasing J, and that the resistivity shows a linear temperature dependence.

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Experimental Seminar, 12.30 Tuesday, 22nd February

Dr. Andrew MacKenzie
(St. Andrews University)

Bilayer Ruthenates [Slides][Aud][Cam]

Resistivity exponent (rho - rho₀ ~ T^alpha) versus field and temperature, with linear T behavior in rho near the critical field (8 T).

Rho versus field for various T for high purity samples. The "finger" is bounded on each side by a first order phase transition.

After a general introduction on lines (or more generally surfaces) of first-order transitions in a multi-parameter coordinate space, terminating in a (quantum) critical point (QCP) in the T=0 plane, Andy focused on the particular example of metamagnetism in Sr₃Ru₂O₇ where magnetic field and field angle with respect to the c axis are used as tuning parameters to find the QCP. The system is a highly anisotropic Fermi liquid rho_c/rho_a ~ 100) but is magnetically isotropic. Andy pointed out the exceptional sensitivity of the system's properties to impurities.

Near the metamagnetic transition around B = 8 T tne system at low T develops an intermediate phase in a narrow field range (~ 0.3 T), first seen in resistivity but later also in susceptibility, thermal expansion, etc. on the purest samples (rho ~ 0.5 µOhm cm). This phase is separated from the low-field paramagnetic and high-field magnetized phase by two lines of first-order transitions in the B-T plane. A possible scenario is a magnetoelastic coupling to the Fermi surface leading to a Pomeranchuk instability.

Resistivity anomaly versus field and field angle relative to the c axis.

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Discussion: 10 am Thursday, February 24th, Founders Room.

Present at the discussion were Dietrich Belitz, Jules Carbotte, Kevin Ingersent, Mireille Lavagna, Elisabeth Nicol, Mike Norman, Catherine Pepin, Bahman Roostaei, Vasily Shaginyan, Thomas Vojta, Veljko Zlatic, Hilbert von Lohneysen, Peter Wolfle, Maxim Marenko, Dirk Morr, and Andrew Mackenzie.

We took advantage of the presence of Andy MacKenzie and dealt with the question of metamagnetism. We decided to list what we and Andy felt were key issues in the field.

1. The role of disorder - What is responsible for the enhancement of the resistivity near the critical field? Why is this region of the phase diagram so sensitive to sample purity? Although these issues are most evident in the bilayer ruthenate, similar considerations apply to other materials like CeRu₂Si₂.

In this context, Catherine Pepin gave us a synopsis of the work she did with Indranil Paul concerning the novel form the Altshuler-Aronov disorder effects take near a ferromagnetic quantum critical point (see the discussion session from last week).

2. The model - Are we exploring the correct model? The "standard" model explored by Millis and Schofield is based on the Rhodes-Wolfarth theory for itinerant metamagnets, where at zero field, the Fermi energy is near a minimum in the density of states. This model has not only been used for the ruthenates, but also for UGe₂ and other materials of interest. This brought up a discussion of the role of van Hove singularities near the Fermi energy, and the question of nesting, which have both been raised in the context of the ruthenates.

But there are also other well known examples of metamagnetism. For instance, the one most studied in terms of classical critical phenomena has been the field induced spin flip transition in an antiferromagnet. And in rare earth metals, the most common example occurs when an excited magnetic crystal field state crosses a ground state singlet due to Zeeman splitting (the classic example of this being praesodynium). Are these other models worth exploring? Will they give us further insight into the problem of quantum critical metamagnets?

3. Universality - Interesting metamagnetic phenomena and associated non Fermi liquid behavior has been observed not only in the bilayer ruthenates, but also in UPt₃, URu₂Si₂, UGe₂, and MnSi. Is there some sort of universal behavior going on here? Again, questions of incommensurate magnetism and nesting were raised in this context.

4. Pomeranchuk Instabilities - Is Sr₃Ru₂O₇ undergoing a Pomeranchuk instability? How would one prove this? What effect would disorder have (presumably, it would be pair breaking as for a d-wave superconductor)? Are van Hove singularities important in this context?

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