Research: Cuprates



      Research on the High Tc superconductors is generally a sordid affair. This is partly due to the rapid decrease in funding, but it mainly has to do with the myriad of theories and bad data/experiments that dominate the literature. When High Tc materials were discovered in the 80’s they promised to bring about rapid advances in material science, industry and technology. However after 30 years of research, the underlying mechanism for the pairing remains unknown, there have been very limited advances in Tc, mostly made through trial and error, there exists a vast number of theories about the material, all of which have enough free parameters to be tuned to take into account any new data and funding has plummeted. On top of this, since the materials are all ceramics, it is almost impossible to make any useful fabracated devices out of them and all superconducting circuits are still made using classical BCS superconductors. Much work has gone into incorporating them into superconducting wires, however and this seems to be successful. Despite this grim outlook, they still are a fascinating and complex system.

       My research in the High Tc’s has been focused on one particular compound. Bi2Sr2CaCu2O8+x. This compound, otherwise known as Bi-2212, is a member of the cuprates and is a two CuO layer compound. These CuO 2D layers are where the superconducting pairing happens and are important to understanding the mechanism in this family. Now Bi-2212 and its single CuO layered brethren are some of the most heavily SI-STM studied members of the Cuprates. The reason for this is simple, they cleave. In order to get a clean surface for the vast majority (I would argue all) of SI-STMs the sample must be cleaved in a cryogenic temperature vacuum. This prevents surface contamination and allows samples to be studied for at least upwards of a year (longest time period I know of and that run was ended by an external error). SI-STM studies only a very small area of the sample, at max say about 200 nm2, so crystal size is not important in SI-STM studies. Although the sample must be large enough to be physically handled and mounted, usually ~1 mm2. Up until recently the larges Bi-2212 crystal size was limited to a few millimeters, which was fine for SI-STM, but made other bulk measurements problematic. This makes it difficult to determine the local phenomena’s relationship to the materials bulk properties.

      SI-STM reveals that the electronic structure of Bi-2212 is very disordered and it contains several spatial excitations. This presents a very complicated picture, one that traditional theoretical techniques have trouble coping with. The analysis is further complicated by the presence of setup condition errors that distort the data and require careful processing in order to sort the underlying electronic structure present in the data from these effects. Due to the complicated nature of the data I have spent my time on ways to reduce the complexity of the data through the use of simple phenomenological models. The goal of these are to reduce the complex 3D data sets to a series of 2D maps that capture all the information needed to reproduce the LDOS(E). As my research has progressed I have also tried to determine the energy ranges/signatures of the spatial excitations and determine their relationship to the 2D parameter maps. My last project in this field was the development of a general algorithm for extracting scattering k-space locations in the systems. This technique takes its inspiration from inverse techniques designed to recover missing information in inverse FFTs. As well as previous projects trying to rectify the differences between angle resolved photoemission spectroscopy (ARPES) and SI-STM.

Since I tend to ramble a bit I have broken up the Bi-2212 section into the following categories

The Spectra: An overview of what high quality SI-STM measures. I will also talk a little about setup effects here as far as the individual spectra are concerned.

Understanding Local Phenomena: My first published work on Bi-2212 used a simple historical phenomenological model to measure lifetimes and energy gaps as a function of doping. This work led to the development of a more complete phenomenological model, the Tripartite model, that is based on phenomena that the first model did not contain and energy scales measured from the spatial excitations.

The Spatial Excitations: My work with the local phenomena led to questions about the spatial excitations and how the local was related to the global. This work led to the Tripartite model and inspired me to develop a general method of understanding spatial excitations in the SI-STM data.

Tripartite Model: Striving to improve on my previous work in reducing the complexity of the data, I developed a Tripartite model that allows the spatial excitations and the LDOS(E) spectra to be fit/explained with a single model. This model also allows the answering of several questions about the spatial excitations energy ranges and their relationship to local LDOS(E) features. The Tripartite model also answers questions about the root cause of the disorder present and its effects on the local and spatial phenomena.

Constrained Monte Carlo Reconstruction (CMCR) of the scattering: In order to compare the LDOS(E) features to the spatial excitations I developed a general algorithm which allows the determination of the k-space origins of the scattering from any spatial excitation pattern. This method also allows a unique scattering length scale to be measured and shows how the scattering changes as a function of energy and doping.

Phase Diagram: All my work can be summed up in a simple phase diagram of the low temperature electronic states of Bi-2212 as measured by SI-STM. This phase diagram has three regions, each of which has a signature in the spatial modulations and also in the LDOS(E).

Other Measures of Disorder: This is a brief section with references to other probes measurements of disorder in the cuprates, Bi-2212 specifically.

SI-STM groups who study these materials.



The Spectra


Understanding Local Phenomina


The Spatial Excitations


The Triparite Model


Constrained Monte Carlo Reconsuction


Phase Diagram


Other Measures of Disorder

      There has been an ongoing argument about the disordered nature of the cuprates. Here is a list of references showing other disorder in the cuprates in in Bi-2212 specifically. Some of these can measure disorder that matches that seen in SI-STM.


Crocker, J. et al. “NMR studies of pseudogap and electronic inhomogeneity in Bi2Sr2CaCu2O8+δ.” Physical Review B 84, 224502 (2011).

Grafe, H.-J. et al. “Charge order and low frequency spin dynamics in lanthanum cuprates revealed by Nuclear Magnetic Resonance.” The European Physical Journal Special Topics 188, 89–101 (2010).

Chen, B., Mukhopadhyay, S., Halperin, W., Guptasarma, P. & Hinks, D. “Evidence for intrinsic impurities in the high-temperature superconductor Bi2Sr2CaCu2O8+δ from O17 nuclear magnetic resonance.” Physical Review B 77, 052508 (2008).

Mukuda, H. et al. “Genuine Phase Diagram of Homogeneously Doped CuO 2 Plane in High- T c Cuprate Superconductors.” Journal of the Physical Society of Japan 77, 124706 (2008).

Alloul, H., Bobroff, J., Mahajan, A., Mendels, P. & Yoshinari, Y. “NMR studies of the original magnetic properties of the cuprates: effect of impurities and defects.” AIP Conf. Proc. 483 161–171 (1999)

Takigawa, M. & Mitzi, D. “NMR Studies of Spin Excitations in Superconducting Bi2Sr2CaCu2O8+δ Single Crystals.” Physical Review Letters 73, 1287–1290 (1994).



Bonnoit, C. J. et al. “Probing electronic order via coupling to low energy phonons in superconducting Bi2Sr2-xLaxCuO6+d.” 5 (2012).  Cond-Mat/1202.4994

Poccia, N. et al. “Spatial inhomogeneity and planar symmetry breaking of the lattice incommensurate supermodulation in the high-temperature superconductor Bi2Sr2CaCu2O8+y.” Physical Review B 84, 100504 (2011).


Specific Heat:

Here the standard paper is Tallon and Loramas specific heat measurement as a function of doping. This they interpret as proving that the samples are electronically homogeneous. However the two theory papers that follow show that their results are entirely consistent with SI-STM observations.

Lorama, J. W., Mirza, K. A., Cooper, J. R. & Tallon, J. L. “SPECIFIC HEAT EVIDENCE ON THE NORMAL STATE PSEUDOGAP.” Journal of Physics and Chemistry of Solids 59, 2091–2094 (1998).

Andersen, B., Melikyan, A., Nunner, T. & Hirschfeld, P. “Thermodynamic transitions in inhomogeneous d-wave superconductors.” Physical Review B 74, 060501 (2006).

Wilson, J. A. “Examination of the claim by Loram and Tallon that the energy-resolved STM results, in their apparent inhomogeneity, misrepresent the true bulk behaviour of the HTSC cuprates.” 22 (2006).



Chen, W., Andersen, B. & Hirschfeld, P. “Theory of resistivity upturns in metallic cuprates.” Physical Review B 80, 134518 (2009).

Fruchter, L., Raffy, H., Bouquet, F. & Li, Z. “Contribution of disorder to the Hall effect in Bi2Sr2CuO6+δ.” Physical Review B 75, 092502 (2007).

Abdel-Jawad, M. et al. “Anisotropic scattering and anomalous normal-state transport in a high-temperature superconductor.” Nature Physics 2, 821–825 (2006).

Sun, X. et al. “Electronic Inhomogeneity and Breakdown of the Universal Thermal Conductivity of Cuprate Superconductors.” Physical Review Letters 96, 017008 (2006).

Nunner, T. & Hirschfeld, P. “Microwave conductivity of d-wave superconductors with extended impurities.” Physical Review B 72, 014514 (2005).

Dordevic, S. V, Komiya, S., Ando, Y. & Basov, D. N. “Josephson plasmon and inhomogeneous superconducting state in La2-xSrxCuO4.” Physical review letters 91, 167401 (2003).

Turner, P. et al. “Observation of Weak-Limit Quasiparticle Scattering via Broadband Microwave Spectroscopy of a d-Wave Superconductor.” Physical Review Letters 90, 237005 (2003).


Vortex Pinning:

Shaidiuk, V., Ammor, L. & Ruyter, A. “Experimental Study on Plasticity of Current-driven Vortex Lattices Interacting with Disorder in Bi2Sr2CaCu2O8 Single Crystal.” Physics Procedia 36, 675–680 (2012).

Horvat, J., Wang, X. . & Dou, S. “Vortex pinning in heavily Pb-doped Bi2212 crystals.” Physica C: Superconductivity 324, 211–219 (1999).

Darminto, D. et al. “Different roles of anisotropy and disorder on the vortex matter of Bi2Sr2CaCu2O8+δ single crystal.” Physica C: Superconductivity 378-381, 479–482 (2002).

Dolan, G., Chandrashekhar, G., Dinger, T., Feild, C. & Holtzberg, F. “Vortex Structure in YBa2Cu3O7 and Evidence for Intrinsic Pinning.” Physical Review Letters 62, 827–830 (1989).

Tachiki, M. & Takahashi, S. “Strong vortex pinning intrinsic in high-Tc oxide superconductors.” Solid State Communications 70, 291–295 (1989).


Neutron Scattering:

Birgeneau, R. J., Stock, C., Tranquada, J. M. & Yamada, K. “Magnetic Neutron Scattering in Hole-Doped Cuprate Superconductors.” Journal of the Physical Society of Japan 75, 111003 (2006).

Fong, H. F. et al. “Neutron scattering from magnetic excitations in Bi2Sr2CaCu2O8+x.” Nature 398, 588–591 (1999).



Ishikado, M., Kojima, K. M. & Uchida, S. “Electronic inhomogeneity and optical response of Bi2212.” Physica C: Superconductivity 470, 1045–1047 (2010).



Sonier, J. E. ”High-field μSR studies of superconducting and magnetic correlations in cuprates above T(c).” Journal of physics. Condensed matter : an Institute of Physics journal 22, 203202 (2010).


Other Groups of Note

Hudson Group

McElroy Group

Hoffman Group

J.C. Davis Group