arXiv subjects

Junseo Jung

Publications and source records attributed to Junseo Jung.

4 recordsLinked to original sources

arXiv2026

Quaternion-Kahler geometry of time reversal symmetric crystals

Quantum geometry reveals how the shape of Bloch wave functions governs correlated quantum phenomena. Its standard formulation describes isolated complex bands, where Berry curvature is Abelian and ideal geometry is Kahler. However, time reversal symmetric crystals with spin require a different language since Kramers degeneracy pairs Bloch states and turns Berry curvature into a non-Abelian SU(2) field. Here we show that Kramers pair band geometry is quaternionic. A minimal Kramers pair defines a map into quaternion projective space, and its quaternionic quantum geometric tensor unifies the quantum metric with the three SU(2) Berry curvature components. The non-negativity of this tensor imposes local metric-curvature inequalities, whose saturation defines the non-Abelian counterpart of ideal Chern bands. In four dimensions, the ideal limit further yields an algebraic structure related to the four-dimensional quantum Hall effect. Our results promote ideal quantum geometry from the Abelian geometry of Chern bands to the quaternionic, non-Abelian geometry of time reversal symmetric quantum matter.

cond-mat.mes-hall↗

arXiv2024

Measurements of the quantum geometric tensor in solids

Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is at the core of modern physics. The Quantum Geometric Tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays a fundamental role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence very recently, giving rise to a new set of quantum geometric phenomena, such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts, and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. In this work, we develop a framework to measure the QGT (both quantum metric and Berry curvature) in crystalline solids using polarization-, spin-, and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in solids in the archetype kagome metal CoSn, which hosts topological flat bands. The key idea is to introduce another geometrical tensor, the quasi-QGT, whose components, the band Drude weight and orbital angular momentum, are experimentally accessible and can be used for extracting the QGT. Establishing such a momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.

cond-mat.mtrl-sci↗

arXiv2023

Quantum Geometry and Landau Levels of Quadratic Band Crossings

We study the relation between the quantum geometry of wave functions and the Landau level (LL) spectrum of two-band Hamiltonians with a quadratic band crossing point (QBCP) in two-dimensions. By investigating the influence of interband coupling parameters on the wave function geometry of general QBCPs, we demonstrate that the interband coupling parameters can be entirely determined by the projected elliptic image of the wave functions on the Bloch sphere, which can be characterized by three parameters, i.e., the major $d_1$ and minor $d_2$ diameters of the ellipse, and one angular parameter $ϕ$ describing the orientation of the ellipse. These parameters govern the geometric properties of the system such as the Berry phase and modified LL spectra. Explicitly, by comparing the LL spectra of two quadratic band models with and without interband couplings, we show that the product of $d_1$ and $d_2$ determines the constant shift in LL energy while their ratio governs the initial LL energies near a QBCP. Also, by examining the influence of the rotation and time-reversal symmetries on the wave function geometry, we construct a minimal continuum model which exhibits various wave function geometries. We calculate the LL spectra of this model and discuss how interband couplings give LL structure for dispersive bands as well as nearly flat bands.

cond-mat.mes-hall↗

arXiv2021

Wave-function geometry of band crossing points in two-dimensions

Geometry of the wave function is a central pillar of modern solid state physics. In this work, we unveil the wave-function geometry of two-dimensional semimetals with band crossing points (BCPs). We show that the Berry phase of BCPs are governed by the quantum metric describing the infinitesimal distance between quantum states. For generic linear BCPs, we show that the corresponding Berry phase is determined either by an angular integral of the quantum metric, or equivalently, by the maximum quantum distance of Bloch states. This naturally explains the origin of the $π$-Berry phase of a linear BCP. In the case of quadratic BCPs, the Berry phase can take an arbitrary value between 0 and $2π$. We find simple relations between the Berry phase, maximum quantum distance, and the quantum metric in two cases: (i) when one of the two crossing bands is flat; (ii) when the system has rotation and/or time-reversal symmetries. To demonstrate the implication of the continuum model analysis in lattice systems, we study tight-binding Hamiltonians describing quadratic BCPs. We show that, when the Berry curvature is absent, a quadratic BCP with an arbitrary Berry phase always accompanies another quadratic BCP so that the total Berry phase of the periodic system becomes zero. This work demonstrates that the quantum metric plays a critical role in understanding the geometric properties of topological semimetals.

cond-mat.mes-hall↗