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We present a series of measurements based on K L,S →␲ ϩ ␲ Ϫ and K L,S →␲ 0 ␲ 0 decays collected in 1996 – 1997 by the KTeV experiment ͑E832͒ at Fermilab. We compare these four K→␲␲ decay rates to measure the direct CP violation parameter Re(⑀Ј/⑀)ϭ(20.7Ϯ2.8)ϫ10 Ϫ4. We also test CPT symmetry by measuring the relative phase between the CP violating and CP(More)
Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from(More)
Existence of the magnetic monopole is compatible with the fundamental laws of nature; however, this elusive particle has yet to be detected experimentally. We show theoretically that an electric charge near a topological surface state induces an image magnetic monopole charge due to the topological magneto-electric effect. The magnetic field generated by(More)
The quantum spin Hall (QSH) state is a topologically nontrivial state of quantum matter which preserves time-reversal symmetry; it has an energy gap in the bulk, but topologically robust gapless states at the edge. Recently, this novel effect has been predicted and observed in HgTe quantum wells and in this Letter we predict a similar effect arising in(More)
We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin(More)
Nonlocal transport through edge channels holds great promise for low-power information processing. However, edge channels have so far only been demonstrated to occur in the quantum Hall regime, at high magnetic fields. We found that mercury telluride quantum wells in the quantum spin Hall regime exhibit nonlocal edge channel transport at zero external(More)
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insula-tors have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the helical(More)
Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant topological insulator in three dimensions exhibits a topological magnetoelectric effect quantized in units of the fine(More)
We propose a topological order parameter for interacting topological insulators, expressed in terms of the full Green's functions of the interacting system. We show that it is exactly quantized for a time-reversal invariant topological insulator, and it can be experimentally measured through the topological magneto-electric effect. This topological order(More)
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract: We study chaos and scrambling in unitary channels by considering their en-tanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process(More)