Our research group focuses on condensed matter theory, studying the electronic properties of novel materials. Current group interests include high temperature superconductivity, strongly correlated electrons, liquid crystalline phases of electrons, and soft electronic matter.


We gratefully acknowledge support from the National Science Foundation, Research Corporation for Science Advancement, and the Purdue Research Foundation.

Spatial Complexity in Strongly Correlated Electronic Systems

Spatial Complexity

Inside the metals, semiconductors, and magnets of our everyday experience, electrons are uniformly distributed throughout the material. By contrast, electrons often form clumpy patterns inside of strongly correlated electronic systems (SCES) such as colossal magnetoresistance materials and high temperature superconductors. In copper-oxide based high temperature superconductors, scanning tunneling microscopy (STM) has detected an electron nematic on the surface of the material, in which the electrons form nanoscale structures which break the rotational symmetry of the host crystal. These structures may hold the key to unlocking the mystery of high temperature superconductivity in these materials, but only if the nematic also exists throughout the entire bulk of the material.

Using new methods we have developed for decoding these surface structures, we find that the nematic indeed persists throughout the bulk of the material. We furthermore find that the intricate pattern formation is set by a delicate balance between disorder, interactions, and material anisotropy, leading to a fractal nature of the cluster pattern. The methods we have developed can be extended to many other surface probes and materials, enabling surface probes to determine whether surface structures are confined only to the surface, or whether they extend throughout the material.

E. W. Carlson and K. A. Dahmen, "Using Disorder to Detect Locally Ordered Electron Nematics via Hysteresis," Nature Communications 2, 379 (2011).

S. Liu, B. Phillabaum, E. W. Carlson, K. A. Dahmen, N. S. Vidhyadhiraja, M. M. Qazilbash, and D. N. Basov, "Random Field Driven Spatial Complexity at the Mott Transition in VO2," Phys. Rev. Lett., 116, 036401 (2016).

High Temperature Superconductivity

Spatial Complexity

Superconductivity requires that electrons pair, and also become phase coherent. The transition temperature to superconductivity must be below both the energy scale of pairing, and the energy scale of phase coherence. The "catch 22" of raising the transition temperature is that raising one of these energy scales often results in the decrease of the other, and it is difficult to parametrically raise the transition temperature. This is seen empirically in the cuprate superconductors, where on the underdoped side, pairing (as measured by, e.g. the single particle tunneling gap) is strong but the phase stiffness energy scale (as measured by London penetration depth measurements) is weak. On the overdoped side, the situation is reversed, and as the phase stiffness energy scale rises, the paring scale is depressed.

E. W. Carlson, V. J. Emery, S. A. Kivelson, and D. Orgad, "Concepts in High Temperature Superconductivity," in The Physics of Conventional and Unconventional Superconductors, Vol. 2, ed. K.H. Bennemann and J.B. Ketterson (Springer-Verlag 2004)

Electronic Ising Nematic

Spatial Complexity

Stripes within the copper-oxygen plane tend to lock to favorable lattice directions. For certain ranges of dopings, stripes lock to the Cu-O bond direction. In a four-fold symmetric crystal, stripes can lock either "vertically" or "horizontally" in the copper-oxygen plane, giving a natural mapping to the Ising model, where, e.g., up spins correspond to vertical stripe patches, and down spins correspond to horizontal ones. Disorder in the form of dopant atoms between planes favors one or the other direction locally, and acts as a random field on the Ising pseudospin. We are studying the consequences of this mapping for macroscopic nonequilibrium properties such as anisotropic transport, and also for local probes such as scanning tunneling microscopy.

E. W. Carlson, K. A. Dahmen, E. Fradkin, S. A. Kivelson, "Hysteresis and Noise from Electronic Nematicity in High Temperature Superconductors," Phys. Rev. Lett, 96, 097003 (2006).

Vortex Smectic-A

Spatial Complexity

In anisotropic Type II superconductors, vortices have elongated cross sections, and anisotropic interactions. Anisotropic, repulsive objects generically give rise to liquid crystal phases. We predicted a new type of vortex phase in anisotropic superconductors, whereby the anisotropic Abrikosov lattice melts first into a smectic as temperature is raised, and then into the high temperature disordered phase. The vortex smectic forms an intermediate broken symmetry phase, where the vortices are liquid-like in one direction perpendicular to the external magnetic field, but lattice-like in the other. Because vortices melt first along the direction of short lattice constant, the intermediate phase has the symmetry of a smectic-A.

E. W. Carlson, A. H. Castro Neto, and D. K. Campbell, "Vortex Liquid Crystals in Anisotropic Type II Superconductors," Phys. Rev. Lett. 90, 087001 (2003)

Spin Waves in Striped Phases

Spatial Complexity

Certain nickelate materials and some cuprate materials show evidence of stripe phases, whereby holes doped into an antiferromagnet congregate in lines called charge stripes. Each charge stripe introduces a line defect in the form of a &pi phase shift in the parent antiferromagnetic texture, leading to the formation of spin stripes as well. The elementary excitations of fully ordered spin stripes are spin waves, observable as finite energy excitations in neutron scattering experiments. We have studied both site-centered stripes, where the charged domain walls like on Ni or Cu sites, and bond-centered stripes, where the charge lines lie between Ni or Cu sites, and developed a litmus test for ruling out site-centered stripes from low energy neutron data.

E. W. Carlson, D.-X. Yao, and D. K. Campbell, "Spin Waves in Striped Phases," Phys. Rev. B, 70, 064505 (2004).

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