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Cuprate Superconductors: Puzzle of the Pseudogap April 7, 2011

Posted by cmmPBlogs in : Condensed Matter and Materials Physics (CMMP) , 1 comment so far

by Philip Phillips, University of Illinois Urbana-Champaign

It has now been 25 years since superconductivity was discovered in the copper-oxide ceramics (hereafter cuprates). One thing we have learned since then is that these materials defy explanation within the standard paradigms of solid state physics. In metals such as mercury, superconductivity emerges from a normal state in which the interactions between the electrons can be ignored. The only interaction which is relevant is that arising from the ions. When two ions move closer together, the electrons experience a net attraction which gives rise to charge 2e charge carriers.

In the cuprates, superconductivity emerges from the pseudogap state in which there is a depression of the single particle density of states in the absence of superconductivity. Straightforward application of the standard superconducting paradigm to a state of matter with no states at the chemical potential yields a vanishing superconducting transition temperature.

However, the transition temperature in the cuprates can be as high as 140K. Hence, something else must be going on in these materials. The experiments by He, et al [1] are designed to unlock the secrets of this mysterious pseudogap phase which sets in at a temperature T^\ast as shown in the figure below.


Phase diagram and anomalous transport in the cuprate high-temperature superconductors. Heuristic phase diagram as a function of holes doped into the copper-oxide plane. The pseudogap and strange metal are characterized by a depletion of the density of states and a T-linear resistivity, respectively. The pseudogap terminates at a zero-temperature critical point or quantum critical point (QCP). To the right is a Fermi liquid (conventional theory of metals) where weak-coupling accounts become valid. We currently have no theory of superconductivity in a state of matter that is a non-Fermi liquid. Even the most recent constructions of superconductivity using tools from string theory that are designed to get at strong correlations in quantum systems yield superconductivity [2] only from the Fermi liquid state. This is truly unfortunate and points to how rudimentary our understanding of superconductivity really is.

The phenomena surrounding the pseudogap in the cuprates used to be fairly simple. In zero magnetic field, lightly doped cuprates possess an incomplete Fermi surface, termed a Fermi arc, in the normal state. That is, the Fermi surface which is present in the overdoped, more conventional Fermi liquid regime is destroyed on underdoping leaving behind only a Fermi arc.

In actuality, the situation is much worse. That the Fermi arc does not represent a collection of well-defined quasiparticle excitations has been clarified by Kanigel, et al. [3] who showed that in Bi_2Sr_2CaCu_2O_{8-\delta}, the length of the Fermi arc shrinks to zero as T/T^* tends to zero. Consequently, the only remnant of the arc at T=0 is a quasiparticle in the vicinity of (\pi/2,\pi/2) and hence the consistency with nodal metal phenomenology.

Recently, however, new ingredients have been added to the pseudogap story in the underdoped regime which, on the surface, are difficult to reconcile with Fermi arcs. At high magnetic fields, quantum oscillations, indicative of a closed 2 Fermi surface, have been observed [4] in Y123 and Tl-2201 through measurements of the Hall resistivity, Shubnikovde Haas effect, and the magnetization in a de Haas-van Alphen experiment. Also attracting much attention is the recent experimental evidence for nematic order [5, 6] ( a state with broken translational symmetry but still possessing translational symmetry) at the onset of the pseudogap onset temperature, T^\ast.

The paper by He, et al. [1] reports a series of measurements (as others have previously [7]) which point to the pseudogap regime being driven by a phase transition. The most puzzling of these experiments is the Kerr effect which requires the breaking of time-reversal symmetry. The authors claim, however, that the magnitude of this effect is too small for it to be the dominant cause of the pseudogap. If this is so, then perhaps the order which is seen is really an epiphenomenon having no causal connection to the pseudogap. What then of the transport anisotropies which have been attributed to nematic order?

Interestingly, the models [8, 9] proposed to explain the Kerr effect do not result in transport anisotropies. It might turn out that the transport anisotropies observed in the Nernst signal are a red-herring, afterall since the orthorhombic lattice symmetry of the cuprates already has asymmetric x and y axes.

While trying to understand the origin of competing order in the pseudogap state is important, it is entirely likely that order has nothing to do with the efficient cause of the pseudogap, the suppression of the single-particle density of states at the chemical potential. Such a claim has been made recently by Yazdani and collaborators [10] who also observed electronic inhomogeneities at the onset of the pseudogap state. They state explicitly, “While demonstrating that the fluctuating stripes emerge with the onset of the pseudogap state and occur over a large part of the cuprate phase diagram, our experiments indicate that they are a consequence of pseudogap behavior rather than its cause.” [10]

I think it is in this context that the He, et al. [1] experiments must be placed. The disassociation of order from the origin of the pseudogap is not entirely surprising. After all, the phase diagram of the cuprates does tell us that the single theory of these systems must above the superconducting dome explain the pseudogap and at higher temperatures the strange metal. Hence, focusing on the pseudogap independent of the strange metal amounts to not facing up to the nature of the charge vacuum of the high-temperature phase.

It is in this regime that the strong correlations conspire to produce the anomalous properties of the normal state. As neither the pseudogap nor the strange metal appear necessarily as T=0 states of matter in the cuprate phase diagram, the standard guiding principle of model building in which only T=0 states are relevant fails in this problem.

Nonetheless, the relevant physics should emerge from correct implementation of the Wilsonian program. As Wilson has taught us, high and low-energy physics are linked through a series of recursion equations that arise once the high-energy degrees of freedom are integrated out. In weakly interacting systems (Hg for example), such an integration simply renormalizes the coupling constants in the low-energy sector. However, in strongly interacting systems, new degrees of freedom can be generated [11].

The theoretical resolution of the normal state of the cuprates rests in demonstrating how the degrees of freedom that are generated upon integrating out the high-energy scale mediate the strange metal and at lower temperatures the pseudogap regime. While significant progress has been made on this problem recently [11], the associated phenomena found by He, et al.[1] relating to the origin of time-reversal symmetry breaking have not been addressed. This stands as an open problem.

[1] R. He, et al., Science 331, 1579 (2011)
[2] T. Hartman and S. A. Hartnoll, arXiv:1003.1918
[3] A. Kanigel, et al. Nat. Phys. 2, 447 (2006)
[4] L. Taillefer, arxiv:0901.2313
[5] R. Daou, et al. arxiv:0909.4330
[6] D. Haug, et al., Phys. Rev. Lett. 103, 017001 (2009)
[7] B. Fauque, Phys. Rev. Lett. 96, 197001 (2006)
[8] Aji, V., et al., Phys. Rev. B 81, 064515 (2010)
[9] S. Chakravarty, et al., Phys. Rev. B 63, 094503 (2001)
[10] C. V. Parker, et al., Nature 468, 677 (2010)
[11] P. Phillips, Rev. Mod. Phys. 82, 1719 (2010)


Industrial Masters and Internship Program at University of Oregon February 26, 2011

Posted by admin in : Chemical and Biological Physics (CBP), Condensed Matter and Materials Physics (CMMP), History, Policy and Education (HPE), Photonics and Optics (POP), Technology Transfer, Business Development and Entrepreneurism (TBE) , add a comment

You can earn a Masters degree and a salary one year through the University of Oregon’s Masters Industrial Internship Program. This program provides students with the real-world knowledge and skills necessary to be successful in an industrial environment.

The best way to judge the success of the Industrial Masters Program may be its history and its list of corporate partners. Over the last 13 years, approximately 90% of the students that have completed internships through this program have received offers for regular employment from their host company. We also have an impressive group of corporate partners such as Nike, Intel, IBM, Fairchild Semiconductor, Hewlett Packard, the Army Research Lab, ESI, Nanometrics, FEI Company, nLight, DataLogic and SolarWorld.

Through this program students have the opportunity to earn a degree from a leading research university and also learn what is required to be successful after graduation. We focus on the science and help you develop professional business skills that will allow you to be successful throughout your career.

The course work and labs are designed to help students become more effective problem solvers and will assist in developing your communication, collaboration and leadership skills. The labs are built to give students an opportunity to have experiences that closely mirror those they’ll find in industry.

The UO’s Masters Industrial Internship Program awards MS degrees in Chemistry or Applied Physics. Students entering the program typically have bachelor degrees in one of the following areas: Chemistry, Biochemistry, Physics, Chemical Engineering, Mechanical Engineering, or Electrical Engineering.

You can choose to focus in one of four core areas:

• Photovoltaic & Semiconductor Device Processing

• Optical Materials & Devices

• Polymers & Coatings

• Organic Synthesis & Organometallics

Internships/co-ops typically pay from $2,400 – $5,400 per month. Though internships are not guaranteed, the program has historically placed 98% of its students in internships and the program staff assists in every way to ensure you are a very competitive candidate for available opportunities.

To find out more please visit: internship.uoregon.edu

We are excited to talk to you about the program and life in Oregon–and to help you plan a visit to campus. The University of Oregon is located in Eugene in Oregon’s Willamette Valley. We’re a short drive from the Pacific Ocean, the Cascade Mountains and a two hour drive from Portland – the second largest city in the Pacific Northwest.

For more information:

Lynde Ritzow, Associate Director Masters Industrial Internship Program

T: (541) 346-6835

E: lynde@uoregon.edu

W: internship.uoregon.edu

Simply Harmonic Jello – Fun Physics for Thanksgiving November 23, 2010

Posted by admin in : Acoustics (ACOU), Condensed Matter and Materials Physics (CMMP), History, Policy and Education (HPE), Physics Education Research (PER) , add a comment

Jello is fun and delicious any time of year, and everyone has seen it “wiggling” and “jiggling”.  With a simple stopwatch and counting the frequency of the wiggles, serving jello brings up a special opportunity to work a physics experiment into your snack and dinner menu.

Those wiggles and jiggles can be described as simple harmonic motion, i.e., the force causing the displacement (motion) is proportional to the displacement itself, F = -kx .

Consider a square block of wiggling jello on a flat plate.  If the jello is set into vibrating motion by a shear force that acts on the top of the jello, static friction will keep the bottom of the jello fixed in place on the plate.   The displacement (or deformation) of the top of the jello due to the shear force is some distance, x . This displacement divided by the original dimension is called the shear strain.

From Giancoli, Physics for Scientists and Engineers

If you measure the wiggling rate, i.e., count the number of back and forth excursions per unit time, this frequency can be related to the a physical property of the jello called the shear modulus.

The shear modulus, G relates the shear force, F , and shear strain, \frac{x}{h}   by  

G = \frac{Fh}{Ax}   or F = \frac{GAx}{h}

where  A is the area of the top of the block.

Because the center of mass oscillates with half the displacement of the top,

F=\frac{1}{2} k_e x ,

and the effective force constant is given by

k_{e} = 2\frac{ F}{x} = \frac{2GA}{h} .

The frequency of the vibrations for any simple harmonic oscillator is

f =\frac{1}{2 \pi} \sqrt{\frac{k_e}{m}}

where m is the  mass oscillating object, in this case the piece of jello.  The piece of jello can be weighed directly (converting from weight to mass) or given by the density of the jello multiplied by its volume m= \rho Ah .

So the wiggling frequency of jello is  \frac{1}{2 \pi} \sqrt{\frac{\frac{2GA}{h}}{\rho Ah}} or \frac{1}{2 \pi h}{\sqrt{ \frac{2G}{\rho}} .

Thus the shear modulus of jello can be determined from the measured vibrational frequency by G= 2 \rho ( \pi f h)^2 .

You can try this experiment at home and even study how the shear modulus changes with how you make the jello, i.e., with water, vinegar, juice, soda, or alcohol. And you can investigate how temperature changes the shear modulus.

Post your results here as a comment.   Check back for updates and useful data.

Updates

Units? When doing any calculation in science it is important to keep in mind the units of the factors in used in the equations.  The units have to be consistent throughout, and the final derived units of your calculation should be consistent with quantity that you are trying to calculate.  It is easy to mix up units if you make length measurements using English units, and mass measurements in the metric system for example.   Even when using the metric system throughout, one could easily make the mistake of mixing CGS units with MKS units.  Always check your units.

The density of jello? Understanding what jello is and how it is made is an interesting lesson in biochemistry, particularly protein structure and function.

The more general name for jello is gelatin.  (Jell-0 is a brand name for the foodstuff – edible gelatin – that has become synonymous with the food itself.) Gelatin is made from the connective tissue proteins of cows or pigs. It is made first by breaking down the cellular structure of the connective tissues.  Then collagen proteins from these tissues are isolated, denatured and subsequently rendered to a powdered form.  Sweeteners, flavoring agents, dyes and other additives are added to this powder to make the familiar gelatin dessert.  To make jello you have to add boiling water to the powder which dis-aggregates the proteins.   Cooling the mixture re-aggregates the proteins.   The final jello mold will be a complex solid mixture of proteins, water, air, and chemical additives.

This leads us to consider the density of jello, which like the biological tissue from which it comes, is mostly water.

Water’s density is 1 \frac{g}{cm^3} = 1000 \frac{kg}{m^3} .  So the density has to be close to water.  But the various additives result in partial molar volumes that contract or expand the total volume.   The final volume depends on the thermodynamic nature of the additives and their relative concentrations.  So while it is easy to think that in any given volume of jello there are constituents that are heavier than water, and that the density should be greater than 1 g/cm^3 , the complex mixture of additives could result in the overall density being less than 1 g/cm^3 .  The most prudent thing to do is to take a well measured cube of jello, calculate its volume (or use volume displacement), weigh it, then calculate its density.

Reported densities for  jello have ranged from 0.98 - 1.3 g/cm^3 (with sugar-free variants being on the low end), while for scientific gelatin (without all the food additives) the density has been reported to be 1.3 g/cm^3 .

Two NSBP Members Win Major Awards September 2, 2009

Posted by admin in : Condensed Matter and Materials Physics (CMMP), History, Policy and Education (HPE) , add a comment
Professor Adrienne Stiff-Roberts wins Presidential Early Career Award

Dr. Adrienne Stiff-Roberts was recently awarded one of the Presidential Early Career Awards for Scientists and Engineers (PECASE).

The PECASE awards were commissioned by President Clinton to
honor and support the extraordinary achievements of young scientists and engineers at the outset of their independent research careers. These Presidential awards are the highest honor bestowed by the United States government on outstanding scientists and engineers just beginning their independent careers.

Dr. Stiff-Roberts is an assistant professor of electrical and computer engineering at Duke University. Her research involves the design, fabrication, and characterization of opto-electronic/photonic devices, particularly those in the infrared spectrum.  She also does research on multifunctional sensors featuring hybrid nanomaterials.

She is a graduate of Spelman College and the University of Michigan.
Professor Nadya Mason wins Denise Denton Award

Dr. Nadya Mason is the 2009 winner of the Denise Denton Emerging Leader Award.   Dr. Mason is currently and assistant professor of physics at the University of Illinois Urbana-Champaign.   She is co-chair of the NSBP Condensed Matter and Materials Physics Section.

Given by the Anita Borg Institute for Women and Technology (ABI),  the Denice Denton Emerging Leader Award is given each year to a junior non-tenured faculty member under the age of 40 at an academic or research institution pursuing high-quality research in any field of engineering or physical sciences while contributing significantly to promoting diversity in his/her environment.  The Denice Denton Award is underwritten by Microsoft.

Dr. Mason’s research focuses on electron behavior in low-dimensional, correlated materials, where enhanced novel interactions are expected to give novel results.  She is particularly interested in the effect of reduced dimensionality and correlations on electron coherence, and uses novel fabrication techniques to study quantum properties of carbon nanotubes, quantum dots and wires.   She has several publications in top-flight journals including Nature, Science and Physical Review Letters.

In addition to her research, Dr. Mason is a spokesperson for increasing diversity in physics and for creating a climate in academia that embraces and supports minorities and women.

She is a graduate of Harvard University and Stanford University.

Doing Business with DOE February 10, 2009

Posted by NPPblogs in : Acoustics (ACOU), Astronomy and Astrophysics (ASTRO), Atomic, Molecular and Optical Physics (AMO), Chemical and Biological Physics (CBP), Condensed Matter and Materials Physics (CMMP), Cosmology, Gravitation, and Relativity (CGR), Earth and Planetary Systems Sciences (EPSS), Fluid and Plasma Physics (FPP), Mathematical and Computational Physics (MCP), Nuclear and Particle Physics (NPP), Photonics and Optics (POP), Physics Education Research (PER) , add a comment

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ARE YOU LOOKING FOR?

· Paid undergraduate science research internships?

· Summer research positions for faculty and student teams at a national laboratory?

· Careers with the Federal government or national laboratories?

· Graduate fellowships and Post-Doc appointments?

The Department of Energy is looking for you…

Come see us in the DOE Pavilion

Learn how you can work alongside scientists and engineers experienced at mentoring who want to transfer science knowledge by collaborative research. These programs are for undergraduate students from four year institutions, community colleges, or for students who are preparing to become K-12 science, math or technology teachers and for undergraduate faculty. Internships are available at all DOE national labs.

Up to 8 qualified undergraduate students will be considered for placement in the summer of 2009. The laboratories also have graduate and post-doc opportunities. We look forward to seeing you in Nashville! Please come join us at Booth 304 and the other booths in the DOE Pavilion in the Exhibit Hall Thursday and Friday or at any of the following activities and workshops:

Physics Diversity Summit: Discussion with Bill Valdez, Director, Office of Workforce Development for Teachers and Scientists

Date: Wednesday, February 11

Time: 2:00 PM

Workshop: Brookhaven National Laboratory –On Using Photons

Date: Thursday, February 12

Time: 2:00 – 3:30 PM and 4:00 – 5:30 PM

Workshop: Oakridge National Laboratory—On Using Neutrons

Date: Friday, February 13
Time: 3:00 PM – 4:30 PM; 5:00-6:30 PM

Doing Business with Department of Energy—Research and Grants

Date: Friday, February 13

Time: 3:00 – 4:30 PM