Related papers: Discrete Quantum Geometry and Intrinsic Spin Hall …
Using THz spectroscopy in external magnetic fields we investigate the low-temperature charge dynamics of strained HgTe, a three dimensional topological insulator. From the Faraday rotation angle and ellipticity a complete characterization…
We explore potentials that break time-reversal symmetry to confine the surface states of 3D topological insulators into quantum wires and quantum dots. A magnetic domain wall on a ferromagnet insulator cap layer provides interfacial states…
This pedagogical piece provides a surprisingly simple demonstration that the quantized Hall conductivity of correlated insulators is given by the many-body Chern number, a topological invariant defined in the space of twisted boundary…
We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, $p$. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin $S=1/2$, charge $+e$ fermionic dimers. The model…
Free gasses of spinless fermions moving on a lattice-symmetric geometric background are considered. Their topological properties at zero temperature can be used to classify their Fermi seas and associated boundaries. The flat orbifolds…
Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, $\mathcal C^2$ smooth surface embedded in $\mathbb{R}^3$. We assume that the surface is asymptotically flat in the sense that…
We study the transition between sharp and smooth density distributions at the edges of Quantum Hall Liquids in the presence of interactions. We find that, for strong confining potentials, the edge of a $\nu=1$ liquid is described by the…
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. Existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external…
Measuring bipartite fluctuations of a conserved charge, such as the particle number, is a powerful approach to understanding quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional…
We construct two infinite sequences of immersions of the 3-sphere into 4-space, parameterized by the Dynkin diagrams of types A and D. The construction is based on immersions of 4-manifolds obtained as the plumbed immersions along the…
In a quasi two-dimensional electron system with non-zero layer thickness, a parallel magnetic field (B||) can couple to the out-of-plane electron motion and lead to a severe distortion and eventual disintegration of the Fermi contour. Here…
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…
We consider quantum Einstein gravity in three dimensional de Sitter space. The Euclidean path integral is formulated as a sum over geometries, including both perturbative loop corrections and non-perturbative instanton corrections coming…
We calculate the intrinsic spin Hall conductivity \sigma^{\mathrm{sH}} of a two-dimensional electron system within a generalized Rashba model, showing that it is, in general, finite and model-dependent. Considering arbitrary band…
We elaborate that $s$-wave and $d$-wave superconductors described by mean field theories possess a nontrivial quantum geometry. From the overlap of two quasihole states at slightly different momenta, one can define a quantum metric that…
We consider the reconstruction expected for the Fermi surface of underdoped YBa2Cu3O6+x in the case of a collinear spin-density wave with a characteristic vector Q=(pi[1+/-2 delta],pi), assuming an incommensurability delta~0.06 similar to…
The weak-field Hall conductivity in metals is interpreted in terms of the curvature of the Fermi surface in the main part. In the appendix the orbital magnetic-susceptibility and the magneto-conductivity in metals are discussed focusing on…
The quantum spin Hall effect (QSHE), a hallmark of topological insulators, enables dissipationless, spin-polarized edge transport and has been predicted in various two-dimensional materials. However, challenges such as limited scalability,…
After recalling briefly some basic properties of the quantum group $GL_q(2)$, we study the quantum sphere $S_q^2$, quantum projective space $CP_q(N)$ and quantum Grassmannians as examples of complex (K\"{a}hler) quantum manifolds. The…
Spin-polarized band structure of the three-dimensional quantum spin Hall insulator $\rm Bi_{1-x}Sb_{x}$ (x=0.12-0.13) was fully elucidated by spin-polarized angle-resolved photoemission spectroscopy using a high-yield spin polarimeter…