R. B. Laughlin

Hidden order in the cuprates

We propose that the enigmatic pseudogap phase of cuprate superconductors is characterized by a hidden broken symmetry of

EVIDENCE FOR QUASIPARTICLE DECAY IN PHOTOEMISSION FROM UNDERDOPED CUPRATES

{d}_{{x}^{2}\ensuremath{-}{y}^{2}}

Magnetic Induction of d + i d Order in High-Tc Superconductors

-type. The transition to this state is rounded by disorder, but in the limit that the disorder is made sufficiently small, the pseudogap crossover should reveal itself to be such a transition. The ordered state breaks time-reversal, translational, and rotational symmetries, but it is invariant under the combination of any two. We discuss these ideas in the context of ten specific experimental properties of the cuprates, and make several predictions, including the existence of an as-yet undetected metal-metal transition under the superconducting dome.

Fractional vortices as evidence of time-reversal symmetry breaking in high-temperature superconductors.

I argue that the {open_quotes}gap{close_quotes} recently observed at the Brillouin zone face of cuprate superconductors in photoemission by Marshall {ital et al.}[Phys.Rev.Lett.{bold 76}, 4841 (1996)] and Ding {ital et al.}[Nature {bold 382}, 54 (1996)] is evidence for the decay of the injected hole into a spinon-holon pair. {copyright} {ital 1997} {ital The American Physical Society}

Primitive and composite ground states in the fractional quantum hall effect

I propose that the phase transition in Bi2Sr2CaCu2O8 recently observed by by Krishana et al [Science 277, 83 (1997)] is the development of a small d-xy superconducting order parameter phased by pi/2 with respect to the principal d-(x2-y2) one to produce a minimum energy gap delta. The violation of both parity and time-reversal symmetry allows the development of a magnetic moment, the key to explaining the experiment. The origin of this moment is a quantized boundary current of I = 2 e delta / h at zero temperature.

Elementary Theory: the Incompressible Quantum Fluid

We argue that recent experiments by Kirtley et al. may show evidence of time-reversal symmetry breaking in

Multiple bosonic mode coupling in the electron self-energy of (La2-xSrx)CuO4

{\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{O}_{7}

QUANTUM PHASE TRANSITIONS AND THE BREAKDOWN OF CLASSICAL GENERAL RELATIVITY

at crystal grain boundaries. We illustrate this through a Ginzburg-Landau model calculation. Further experimental tests are proposed.

Perspectives A critique of two metals

Our theory of the Fractional Quantum Hall Effect is reviewed. Arguments are presented that the fractionally charged quasiparticles associated with the effect are fermions. Wavefunctions for the 27 and 25 states are proposed, and estimates for the cohesive energies and gaps of these states are given.

The quantum criticality conundrum

In this lecture, I shall outline what I believe to be the correct fundamental picture of the fractional quantum Hall effect. The principal features of this picture are that the 1/3 state and its daughters are a new type of many-body condensate, that there are analogs of electrons and holes in the integral quantum Hall effect which in this case carry fractional charge, that the Hall plateau observed in experiments is due to localization of these fractionally charged quasiparticles, and that the rules for combining quasiparticles to make daughter states and excitons are simple. The key facts the theory has to explain are these: 1. The effect occurs when electrons are at a particular density, determined by the magnetic field strength. The separation between neighboring electrons locks in at particular values. 2. The fractional quantum Hall effect looks to the eye like the integral quantum Hall effect, except that the Hall conductance, in the case of the 1/3 step, is 1/3 e 2 /h. There is a plateau. Changing the electron density a small amount does not alter the Hall conductance, but changing it a large amount does. 3. The 1/3 effect turns on in GaAs at about 1 K when the magnetic field is 15 Tesla. 4. The effect occurs only in the cleanest samples. Excessive dirt destroys it. 5. Other fractions (2/5, 2/7, …) also occur but they are more easily destroyed by dirt and require lower temperatures to be observed. The most ‘stable’ states have small denominators.