Patrick A. Lee

The Quantum Hall Effect

The discovery of the quantum Hall effect was great event in the development of low\|dimension condensed matter physics. The discovery of the fractional quantum Hall effect has opened a new era of research into poly\|body phenomena and will affect many branches of physics. Two Nobel prizes have been awarded in this field, which has aroused the interest of many people. The discovery of the Hall effect by Edwin Hall in 1897, the quantum Hall effect by Klaus von Klitzing in 1980, the fractional quantum Hall effect by Danial Chee Tusi and Horst L.Stormer, and the experimental verification of the fractional quantum Hall effect are reviewed.

Low-temperature transport through a quantum dot: The Anderson model out of equilibrium.

Abstract : The infinite-U Anderson model is applied to non-equilibrium transport through a quantum dot containing two spin levels weakly coupled to two leads. At low temperatures, the Kondo peak in the equilibrium density of states is split upon the application of a voltage bias. The split peaks, one at the chemical potential of each lead, are suppressed by non-equilibrium dissipation. In a magnetic field, the Kondo peaks shift away from the chemical potentials by the Zeeman energy, leading to an observable peak in the differential conductance when the non-equilibrium bias equals the Zeeman energy. Infinite-U Anderson model, Kondo peak, Zeeman energy, Low-temperature transport through a quantum dot, Kondo effect.

Majorana Fermion Induced Resonant Andreev Reflection

We describe experimental signatures of Majorana fermion edge states, which form at the interface between a superconductor and the surface of a topological insulator. If a lead couples to the Majorana fermions through electron tunneling, the Majorana fermions induce resonant Andreev reflections from the lead to the grounded superconductor. The linear tunneling conductance is 0 (2e(2)/h) if there is an even (odd) number of vortices in the superconductor. Similar resonance occurs for tunneling into the zero mode in the vortex core. We also study the current and noise of a two-lead device.

Spin-filtered edge states and quantum Hall effect in graphene.

Electron edge states in graphene in the quantum Hall effect regime can carry both charge and spin. We show that spin splitting of the zeroth Landau level gives rise to counterpropagating modes with opposite spin polarization. These chiral spin modes lead to a rich variety of spin current states, depending on the spin-flip rate. A method to control the latter locally is proposed. We estimate Zeeman spin splitting enhanced by exchange, and obtain a spin gap of a few hundred Kelvin.

Theory of underdoped cuprates.

We develop a slave-boson theory for the

Zero-Bias Peaks in the Tunneling Conductance of Spin-Orbit-Coupled Superconducting Wires with and without Majorana End-States

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Unusual Superconducting State of Underdoped Cuprates

model at finite doping which respects an

Dissipative Quantum Hall Effect in Graphene near the Dirac Point

\mathrm{SU}(2)

U(1) Gauge Theory of the Hubbard Model: Spin Liquid States and Possible Application to kappa-(BEDT-TTF)~2Cu~2(CN)~3

symmetry\char22{}a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain

Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films

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