Session B3: Invited Session: Frustration and Quantum Criticality

Superconductivity Near Quantum Critical Points

The study of itinerant-electron systems on the border of charge and spin density wave transitions at low temperatures is leading to an increasing number of discoveries of unusual forms of superconductivity and other types of quantum order. Examples will be reviewed of electron-electron pair instabilities in particular on the border of ferromagnetic, antiferromagnetic, ferroelectric and structural quantum phase transitions. The superconducting transition temperature in a number of nearly magnetic metals from heavy fermion compounds to the copper oxide superconductors appears to scale with the characteristic spin fluctuation temperature. These best known materials will be compared and contrasted with examples from other classes of materials in which the spin fluctuation temperature far exceeds the peak of the superconducting transition temperature in the temperature-pressure phase diagram near a magnetic quantum critical point.   

A Topological Spin Glass State of a Frustrated Magnet

We will present a simple way of understanding the physics of the kagome-triangular-kagome trilayer antiferromagnet by mapping the magnetic interactions onto a problem of an ordered tricolor and a disordered binary sign degree of freedom. By doing so, We will show a systematic way of constructing different classical ground states, and will identify possible zero-energy excitations that involve ``partial but extended'' numbers of spins in the system. Due to the unique properties of the ground state, we argue that a topological spin glass is the ground state for the quasi-two-dimensional frustrated magnet.   

On Short Ranged Resonating Valence Bond Liquids

Over 40 years ago, P W Anderson proposed the short ranged resonating valence bond state as an alternative to Neel order in antiferromagnets with strong fluctuations---in hindsight, the first proposal for a topologically ordered $Z_2$ spin liquid. In the last year, convincing numerical evidence has accumulated for the existence of such $Z_2$ spin liquids in short ranged Hamiltonians on simple lattices in two dimensions. I will sketch the intellectually productive historical route between these two developments and survey what we now know about the physics of the short ranged RVB and allied states of matter.   

Critical Behavior of a Strongly-Interacting 2D Electron System

Two-dimensional (2D) electron systems that obey Fermi liquid theory at high electron densities are expected to undergo one or more transitions to spatially and/or spin-ordered phases as the density is decreased, ultimately forming a Wigner crystal in the dilute, strongly-interacting limit. Interesting, unexpected behavior is observed with decreasing electron density as the electrons' interactions become increasingly important relative to their kinetic energy: the resistivity undergoes a transition from metallic to insulating temperature dependence; the resistance increases sharply and then saturates abruptly with increasing in-plane magnetic field; a number of experiments indicate that the electrons' effective mass exhibits a substantial increase approaching a finite ``critical'' density. There has been a great deal of debate concerning the underlying physics in these systems, and many have questioned whether the change of the resistivity from metallic to insulating signals a phase transition or a crossover. In this talk, I will report measurements [1] that show that with decreasing density $n_s$, the thermopower $S$ of a low-disorder 2D electron system in silicon exhibits a sharp increase by more than an order of magnitude, tending to a divergence at a finite, disorder-independent density $n_t$, consistent with the critical form $(-T/S) \propto (n_s - n_t)^x$ with $x = 1.0 \pm 0.1$ ($T$ is the temperature) [2]. Unlike the resistivity which may not clearly distinguish between a transition and crossover behavior, the thermopower provides clear evidence that a true phase transition occurs with decreasing density to a new low-density phase. \\[4pt] [1] Work done with S. Li and B. Wen (City College of NY), A. Mokashi and S. V. Kravchenko (Northeastern U.), A. A. Shashkin and V. T. Dolgopolov (ISSP, Chernogolovka).\\[0pt] [2] A. Mokashi, S. Li, B. Wen, S. V. Kravchenko, A. A. Shashkin and V. T. Dolgopolov, and M. P. Sarachik, Phys. Rev. Lett. {\bf 109}, 096405 (2012).