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Register a new userqeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
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Bloch wavefunctions in solids form a representation of crystalline symmetries. Recent studies revealed that symmetry representations in band structure can be used to diagnose the topological properties of weakly interacting materials. In this work, we introduce an open-source program qeirreps that computes the representation characters in a band structure based on the output file of Quantum ESPRESSO. Our program also calculates the Z4 index, i.e., the sum of inversion parities at all time-reversal invariant momenta, for materials with inversion symmetry. When combined with the symmetry indicator method, this program can be used to explore new topological materials.
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Quantum ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). Quantum ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. Quantum ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively-parallel architectures, and a great effort being devoted to user friendliness. Quantum ESPRESSO is evolving towards a distribution of independent and inter-operable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
We present a semiclassical approximation to the scattering wavefunction $Psi(mathbf{r},k)$ for an open quantum billiard which is based on the reconstruction of the Feynman path integral. We demonstrate its remarkable numerical accuracy for the open rectangular billiard and show that the convergence of the semiclassical wavefunction to the full quantum state is controlled by the path length or equivalently the dwell time. Possible applications include leaky billiards and systems with decoherence present.
Anticipated breakthroughs in solid-state quantum computing will rely on achieving unprecedented control over the wave-like states of electrons in crystalline materials. For example, an international effort to build a quantum computer that is topologically protected from decoherence is focusing on carefully engineering the wave-like states of electrons in hybrid devices that proximatize an elemental superconductor and a semiconductor nanostructure[1-6]. However, more than 90 years after Bloch derived the functional forms of electronic waves in crystals[7](now known as Bloch wavefunction) rapid scattering processes have so far prevented their direct experimental reconstruction, even in bulk materials. In high-order sideband generation (HSG)[8-15], electrons and holes generated in semiconductors by a near-infrared (NIR) laser are accelerated to high kinetic energy by a strong terahertz field, and recollide to emit NIR sidebands before they are scattered. Here we reconstruct the Bloch wavefunctions of two types of holes in gallium arsenide by experimentally measuring sideband polarizations and introducing an elegant theory that ties those polarizations to quantum interference between different recollision pathways. Because HSG can, in principle, be observed from any direct-gap semiconductor or insulator, we expect the method introduced in this Article can be used to reconstruct Bloch wavefunctions in a large class of bulk and nanostructured materials, accelerating the development of topologically-protected quantum computers as well as other important electronic and optical technologies.
Bi2Se3 is a topological insulator with metallic surface states residing in a large bulk bandgap. It is believed that Bi2Se3 gets additional n-type doping after exposure to atmosphere, thereby reducing the relative contribution of surface states in total conductivity. In this letter, transport measurements on Bi2Se3 nanoribbons provide additional evidence of such environmental doping process. Systematic surface composition analyses by X-ray photoelectron spectroscopy reveal fast formation and continuous growth of native oxide on Bi2Se3 under ambient conditions. In addition to n-type doping at the surface, such surface oxidation is likely the material origin of the degradation of topological surface states. Appropriate surface passivation or encapsulation may be required to probe topological surface states of Bi2Se3 by transport measurements.
Topological insulators are exotic material that possess conducting surface states protected by the topology of the system. They can be classified in terms of their properties under discrete symmetries and are characterized by topological invariants. The latter has been measured experimentally for several models in one, two and three dimensions in both condensed matter and quantum simulation platforms. The recent progress in quantum simulation opens the road to the simulation of higher dimensional Hamiltonians and in particular of the 4D quantum Hall effect. These systems are characterized by the second Chern number, a topological invariant that appears in the quantization of the transverse conductivity for the non-linear response to both external magnetic and electric fields. This quantity cannot always be computed analytically and there is therefore a need of an algorithm to compute it numerically. In this work, we propose an efficient algorithm to compute the second Chern number in 4D systems. We construct the algorithm with the help of lattice gauge theory and discuss the convergence to the continuous gauge theory. We benchmark the algorithm on several relevant models, including the 4D Dirac Hamiltonian and the 4D quantum Hall effect and verify numerically its rapid convergence.
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