Single electron control in n-type semiconductor quantum dots using non-Abelian holonomies generated by spin orbit coupling

We propose that n-type semiconductor quantum dots with the Rashba and Dresselhaus spin orbit interactions may be used for single electron manipulation through adiabatic transformations between degenerate states. All the energy levels are discrete in quantum dots and possess a double degeneracy due to time reversal symmetryin the presence of the Rashba and/or Dresselhaus spin orbit coupling terms. We find that the presence of double degeneracy does not necessarily give rise to a finite non-Abelian (matrix) Berry phase. We show that a distorted two-dimensional harmonic potential may give rise to non-Abelian Berry phases. The presence of the non-Abelian Berry phase may be tested experimentally by measuring the optical dipole transitions.Comment: accepted in Phys. Rev.

Numerical calculation of the complex berry phase in non-Hermitian systems

We numerically investigate topological phases of periodic lattice systems in tight-binding description under the influence of dissipation. The effects of dissipation are effectively described by $\mathcal{PT}$-symmetric potentials. In this framework we develop a general numerical gauge smoothing procedure to calculate complex Berry phases from the biorthogonal basis of the system's non-Hermitian Hamiltonian. Further, we apply this method to a one-dimensional $\mathcal{PT}$-symmetric lattice system and verify our numerical results by an analytical calculation.Comment: 7 pages, 3 figures, minor modifications in the final versio

Multiple Unpinned Dirac Points in Group-Va Single-layers with Phosphorene Structure

Emergent Dirac fermion states underlie many intriguing properties of graphene, and the search for them constitute one strong motivation to explore two-dimensional (2D) allotropes of other elements. Phosphorene, the ultrathin layers of black phosphorous, has been a subject of intense investigations recently, and it was found that other group-Va elements could also form 2D layers with similar puckered lattice structure. Here, by a close examination of their electronic band structure evolution, we discover two types of Dirac fermion states emerging in the low-energy spectrum. One pair of (type-I) Dirac points is sitting on high-symmetry lines, while two pairs of (type-II) Dirac points are located at generic $k$-points, with different anisotropic dispersions determined by the reduced symmetries at their locations. Such fully-unpinned (type-II) 2D Dirac points are discovered for the first time. In the absence of spin-orbit coupling, we find that each Dirac node is protected by the sublattice symmetry from gap opening, which is in turn ensured by any one of three point group symmetries. The spin-orbit coupling generally gaps the Dirac nodes, and for the type-I case, this drives the system into a quantum spin Hall insulator phase. We suggest possible ways to realize the unpinned Dirac points in strained phosphorene.Comment: 30 pages, 6 figure

Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems

For open systems described by the quantum Markovian master equation, we study a possible extension of the Clausius equality to quasistatic operations between nonequilibrium steady states (NESSs). We investigate the excess heat divided by temperature (i.e., excess entropy production) which is transferred into the system during the operations. We derive a geometrical expression for the excess entropy production, which is analogous to the Berry phase in unitary evolution. Our result implies that in general one cannot define a scalar potential whose difference coincides with the excess entropy production in a thermodynamic process, and that a vector potential plays a crucial role in the thermodynamics for NESSs. In the weakly nonequilibrium regime, we show that the geometrical expression reduces to the extended Clausius equality derived by Saito and Tasaki (J. Stat. Phys. {\bf 145}, 1275 (2011)). As an example, we investigate a spinless electron system in quantum dots. We find that one can define a scalar potential when the parameters of only one of the reservoirs are modified in a non-interacting system, but this is no longer the case for an interacting system.Comment: 28 pages, 3 figures. 'Remark on the fluctuation theorem' has been revised in ver. 2. Brief Summary has been added in Sec. 1 in ver.

Chirality in Quantum Computation with Spin Cluster Qubits

We study corrections to the Heisenberg interaction between several lateral, single-electron quantum dots. We show, using exact diagonalization, that three-body chiral terms couple triangular configurations to external sources of flux rather strongly. The chiral corrections impact single qubit encodings utilizing loops of three or more Heisenberg coupled quantum dots.Comment: 5 pages, 2 figure

Interaction Driven Quantum Hall Wedding cake-like Structures in Graphene Quantum Dots

Quantum-relativistic matter is ubiquitous in nature; however it is notoriously difficult to probe. The ease with which external electric and magnetic fields can be introduced in graphene opens a door to creating a table-top prototype of strongly confined relativistic matter. Here, through a detailed spectroscopic mapping, we provide a spatial visualization of the interplay between spatial and magnetic confinement in a circular graphene resonator. We directly observe the development of a multi-tiered "wedding cake"-like structure of concentric regions of compressible/incompressible quantum Hall states, a signature of electron interactions in the system. Solid-state experiments can therefore yield insights into the behaviour of quantum-relativistic matter under extreme conditions

An Aharonov-Bohm interferometer for determining Bloch band topology

The geometric structure of an energy band in a solid is fundamental for a wide range of many-body phenomena in condensed matter and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. In analogy to an Aharonov-Bohm interferometer that measures the magnetic flux penetrating a given area in real space, we realize an atomic interferometer to measure Berry flux in momentum space. We demonstrate the interferometer for a graphene-type hexagonal lattice, where it has allowed us to directly detect the singular $\pi$ Berry flux localized at each Dirac point. We show that the interferometer enables one to determine the distribution of Berry curvature with high momentum resolution. Our work forms the basis for a general framework to fully characterize topological band structures and can also facilitate holonomic quantum computing through controlled exploitation of the geometry of Hilbert space.Comment: 5+5 page