arXiv subjects

Wei-Han Hsiao

Publications and source records attributed to Wei-Han Hsiao.

16 recordsLinked to original sources

arXiv2025

Precise correspondence between the p-wave chiral superfluid and the spinless bosonic superfluid in the lowest Landau level

We establish a precise formal correspondence between a spinless p-wave chiral fermionic superfluid and a spinless bosonic superfluid in a strong magnetic field by correctly accounting for superfluid vorticity in the effective theory of the former. In the literature, this vorticity term incompletely manifests as the magnetic field. This paper demonstrates this substitution can be understood as a truncation within the relevant expansion scheme, accompanied by field redefinitions. The components discarded in this truncation are critical for restoring the Berry phase term in the effective theory, encapsulating both systems in the same master Lagrangian. Beyond clarifying the structure of the Berry phase, this formalism allows for solving the bosonic system in the lowest Landau level (LLL) by analogy. Specifically, we show that, in the linear regime, the Maxwell equations governing these systems are identical when the vortex crystal is reformulated using an auxiliary electromagnetic field. This approach offers a unified perspective on these systems and yields solutions that are rotationally covariant, gauge invariants, and physically interpretable.

cond-mat.mes-hall↗

arXiv2024

Gauge field fluctuation corrected QED3 effective action by fermionic particle-vortex duality

We present a non-perturbative framework for incorporating gauge field fluctuations into effective actions of QED3 in the infrared using fermionic particle-vortex duality. This approach is demonstrated through the applications to models containing N species of 2-component Dirac fermions in solvable and interpretable electromagnetic backgrounds, focusing on N = 1 or 2. For the N = 1 model, we establish a correspondence between fermion Casimir energy at finite density and the magnetic Euler-Heisenberg Lagrangian, and further evaluate the corrections to their amplitudes. This predicts amplification of charge susceptibility and reduction of magnetic permeability. We additionally provide physical interpretations for each component of our calculation and offer alternative derivations based on energy density measurements in different characteristic lengths. For N = 2, we show that magnetic catalysis is erased in a U(1)xU(1) QED3, indicating no breakdown of chiral symmetry. Reasoning is offered based on the properties of the lowest Landau level wave functions.

hep-th↗

arXiv2024

Chiral anomaly in (1+1) dimensions revisited: complementary kinetic perspective and universality

We reinvestigate the classic example of the chiral anomaly in (1+1) dimensional spacetime. By reviewing the derivation of charge conservation using the semiclassical Boltzmann equation, we show that chiral anomalies could emerge in (1+1) dimensions without Berry curvature corrections to the kinetic theory. The pivotal step depends only on the asymptotic behavior of the distribution function of the quasiparticle--and thus its dispersion relation--in the limit of $\mathbf p\to\pm\infty$ rather than the detailed functional form of the dispersion. We address two subjects motivated by this observation. First, we reformulate (1+1)-dimensional chiral anomaly using kinetic theory with the current algebra approach and the gradient expansion of the Dirac Lagrangian, adding a complementary perspective to existing approaches. Second, we demonstrate the universality of the chiral anomaly across various quasiparticle dispersions. For two-band models linear in the temporal derivative, with Fujikawa's method we show it is sufficient to have a chirality-odd strictly monotonic dispersion in order to exhibit the chiral anomaly.

hep-th↗

arXiv2024

Geometrically constrained particle dynamics revisited: Equation of motion in terms of the normal curvature of the constraint manifold

We revisit the problem of the particle dynamics subject to a geometric holonomic constraint of codimension 1 in spatial dimensions d =2 and 3. In the absence of dissipation, we show that by solving the Lagrangian multiplier in a general fashion, the external potential independent part, the net normal force, of the equation of motion corresponds to precisely to the curvature of the trajectory on the constraint space multiplied by twice the kinetic energy. The tangent the trajectory is the instantaneous velocity. In d = 3, this term equals the second fundamental form II of the constraint surface evaluated on the unit tangent vector in the direction of velocity. Using these result we establish the relation between constrained particle dynamics with geodesic equations and derive intriguing kinematic implications using theorems from fundamental differential geometry.

physics.class-ph↗

arXiv2023

Electromagnetic fluctuation and collective modes in relativistic bosonic superfluid in mixed dimensions

In Gaussian approximation, we investigate the marginal electromagnetic fluctuation in models of charged relativistic bosonic superfluids in three and two spatial dimensions at zero temperature. The electromagnetism is modeled by the ordinary Maxwell term and the non-local pseudo-electrodynamics action in these dimensions respectively. We explore the collective excitations in these systems by integrating the superfluid velocity fields. In (3+1) dimensions, we derive the roton mode reminiscent of what was discovered in the context of the free relativistic Bose-Einstein condensate as a generalization of the Higgs mode and determine the necessary and sufficient condition for the roton to exist. In (2+1) dimensions, besides solving the dispersion relation for the surface plasmon, we prove there cannot be roton-like excitation in this model as opposed to its (3+1) dimensional counterpart, and additionally derive the asymptotic lines of the dispersion in the limits of long wavelength and short distance.

cond-mat.other↗

arXiv2022

Band geometry from position-momentum duality at topological band crossings

We show that the position-momentum duality offers a transparent interpretation of the band geometry at the topological band crossings. Under this duality, the band geometry with Berry connection is dual to the free-electron motion under gauge field. This identifies the trace of quantum metric as the dual energy in momentum space. The band crossings with Berry defects thus induce the dual energy quantization in the trace of quantum metric. For the $\mathbb Z$ nodal-point and nodal-surface semimetals in three dimensions, the dual Landau level quantization occurs owing to the Berry charges. Meanwhile, the two-dimensional (2D) Dirac points exhibit the Berry vortices, leading to the quantized dual axial rotational energies. Such a quantization naturally generalizes to the three-dimensional (3D) nodal-loop semimetals, where the nodal loops host the Berry vortex lines. The $\mathbb Z_2$ monopoles bring about additional dual axial rotational energies, which originate from the links with additional nodal lines. Nontrivial band geometry generically induces finite spread in the Wannier functions. While the spread manifest quantized lower bounds from the Berry charges, logarithmic divergences occur from the Berry vortices. The band geometry at the band crossings may be probed experimentally by a periodic-drive measurement.

cond-mat.mes-hall↗

arXiv2021

Thermoelectric properties and Wiedemann-Franz like relations in mixed-dimensional QEDs from particle-vortex dualities

We consider the thermoelectric properties of the mixed-dimensional quantum electrodynamics of the relativistic Dirac fermion and Wilson-Fisher boson. These models are self-dual, and can form non-trivial many-body phases depending on the values of chemical potential, background magnetic field and the electromagnetic fine-structure constant. Using particle-vortex duality, we derive a variety of thermoelectric relations for strongly-interacting phases with classic paradigms such as the Wiedemann-Franz law and the Mott's relation in the dual weakly interacting regimes. Besides, at the self-dual point, for the fermionic theory we find the ratio of thermal conductivity of electrical conductivity depends on the determinant of the Seebeck tensor and the phenomenological parameter Hall angle $θ_H$. As for the bosonic theory, the dual fermion description explains how its Seebeck tensor varies depending on the dynamic regime characterized by $θ_H$.

cond-mat.str-el↗

arXiv2021

Dual Haldane sphere and quantized band geometry in chiral multifold fermions

We show that the chiral multifold fermions present a dual Haldane sphere problem in momentum space. Owing to the Berry monopole at the degenerate point, a dual Landau level emerges in the trace of quantum metric, with which a quantized geometric invariant is defined through a surface integration. We further demonstrate potential manifestations in the measurable, physical observables. With a lower bound derived for the finite spread of Wannier functions, anomalous phase coherence is identified accordingly for the flat band superconductivity. We briefly comment on the stability of these results under perturbations. Potential experimental probes of the quantum metric are also discussed.

cond-mat.mes-hall↗

arXiv2021

Time-reversal odd transport in bilayer graphene: Hall conductivity and Hall viscosity

We consider the time-reversal odd dynamics of the bilayer graphene at low energies in the quantum Hall regime. A generating functional for the effective action that captures the electromagnetic response to all orders in momentum and frequency is presented and evaluated to the third order in the space-time gradient $\mathcal O(\partial^3)$. In addition, we calculate the Hall viscosity and derive an explicit relationship with the $q^2$ coefficient of the Hall conductivity. It is reminiscent of the Hoyos--Son relation in the Galilean invariant systems, which can be recovered in the limit of large filling factor $N$.

cond-mat.mes-hall↗

arXiv2020

Landau quantization of multilayer graphene on a Haldane sphere

We consider the problem of multilayer graphene on a Haldane sphere and determine the Landau level spectrum for this family of systems. This serves as a generalization of the Landau quantization problem of ordinary non-relativistic Haldane sphere and spherical graphene, or Dirac-like particles on a sphere. The Hamiltonian is diagonalized in a concise algebraic fashion exploiting two mutually commuting SU(2) algebras of the problem. Additionally, using exact wave functions we demonstrate computation of Haldane pseudopotentials in the second Landau level. These exact solutions add to the current toolkits of the numerical studies on fractional quantum Hall effects in systems of graphite multilayers.

cond-mat.mes-hall↗

arXiv2020

Multipath Division Multiple Access for 5G Millimeter Wave Cellular Systems

Future 5G communication systems require more demanding performances than the existing cellular communication systems, e.g., 10 to 100 Mbps user data rate and much larger cellular spectrum efficiency. The well-used multiple access methods like CDMA and OFDMA are hard to achieve these challenging requirements simultaneously even with advanced signal processing techniques and base station cooperation. Recently, massive MIMO has gain much attention since it provides large signal dimensions that can be used to improve future 5G cellular system performance. This tutorial paper describes a recently proposed multiple access scheme called multipath division multiple access (MDMA) based on massive antennas and multipath channel characteristics in millimeter wave band, which offers uniform user data rate and achieves high cellular spectrum efficiency for 5G systems. We describe the fundamental principle and show the uplink and downlink block diagrams, control signaling and the call setup process. Besides, benefits of using MDMA as a multiple access scheme are discussed. Finally, practical concerns are addressed for future research directions.

eess.SP↗

arXiv2020

Self-Dual $ν=1$ Bosonic Quantum Hall State in Mixed Dimensional QED

We consider a (2+1) dimensional Wilson-Fisher boson coupled to a (3+1) dimensional U(1) gauge field. This theory possesses a strong-weak duality in terms of the coupling constant e, and is self-dual at a particular value of $e$. We derive exact relations between transport coefficients for a $ν=1$ quantum Hall state at the self-dual point. Using boson-fermion duality, we map the $ν=1$ bosonic quantum Hall state to a Fermi sea of the dual fermion, and observed that the exact relationships between transport coefficients at the bosonic self-dual point are reproduced by a simple random phase approximation, coupled with a Drude formula, in the fermionic theory. We explain this success of the RPA by pointing out a cancellation of a parity-breaking term in the fermion theory which occurs only at the self-dual point, resulting in the fermion self-dual theory explored previously. In addition, we argue n that the equivalence of self-dual structure can be understood in terms of electromagnetic duality or modular invariance, and these features are not inherited by the non-relativistic cousins of the present model.

cond-mat.mes-hall↗

arXiv2019

Universal collective modes in 2 dimensional chiral superfluids

In this work, we utilize semi-classical kinetic equations to investigate the order parameter collective modes of a class of 2 dimensional superfluids. Extending the known results for $p$-wave superfluids, we show for any chiral ground state of angular momentum $L\geq 1$, there exists a sub-gap mode with mass $\sqrt{2}\, Δ$ in the BCS limit, where $Δ$ is the magnitude of the ground state gap. We determine the most significant Landau parameter which contributes to the mass renormalization and show explicitly the renormalized modes become massless at the Pomeranchuk instability of the fermion vacuum. Particularly for $L=1$, we propose a continuous field theory to include the Fermi liquid effect in quadrupolar channel and produce the same result under consistent approximations. They provide potential diagnostics for distinguishing 2 dimensional chiral ground states of different angular momenta with order parameter collective modes and reveal another low energy degrees of freedom near nematic transition.

cond-mat.supr-con↗

arXiv2018

Quantum Phase Transitions in Proximitized Josephson Junctions

We study fermion-parity-changing quantum phase transitions (QPTs) in platform Josephson junctions. These QPTs, associated with zero-energy bound states, are rather widely observed experimentally. They emerge from numerical calculations frequently without detailed microscopic insight. Importantly, they may incorrectly lend support to claims for the observations of Majorana zero modes. In this paper we present a fully consistent solution of the Bogoliubov-de Gennes equations for a multi-component Josephson junction. This provides insights into the origin of the QPTs. It also makes it possible to assess the standard self energy approximations which are widely used to understand proximity coupling in topological systems. The junctions we consider are complex and chosen to mirror experiments. Our full proximity calculations associate the mechanism behind the QPT as deriving from a spatially extended, proximity-induced magnetic "defect". This defect arises because of the insulating region which effects a local reorganization of the bulk magnetization in the proximitized superconductor. Our results suggest more generally that QPTs in Josephson junctions generally do not require the existence of spin-orbit coupling and should not be confused with, nor are they indicators of, Majorana physics.

cond-mat.supr-con↗

arXiv2017

Duality and Universal Transport in a Mixed-Dimension Electrodynamics

We consider a theory of a two-component Dirac fermion localized on a (2+1) dimensional brane coupled to a (3+1) dimensional bulk. Using the fermionic particle-vortex duality, we show that the theory has a strong-weak duality that maps the coupling $e$ to $\tilde e=(8π)/e$. We explore the theory at $e^2=8π$ where it is self-dual. The electrical conductivity of the theory is a constant independent of frequency. When the system is at finite density and magnetic field at filling factor $ν=\frac12$, the longitudinal and Hall conductivity satisfies a semicircle law, and the ratio of the longitudinal and Hall thermal electric coefficients is completely determined by the Hall angle. The thermal Hall conductivity is directly related to the thermal electric coefficients.

cond-mat.mes-hall↗

arXiv2016

Majorana zero modes in spintronics devices

We show that topological phases should be realizable in readily available and well studied heterostructures. In particular we identify a new class of topological materials which are well known in spintronics: helical ferromagnet-superconducting junctions. We note that almost all previous work on topological heterostructures has focused on creating Majorana modes at the proximity interface in effectively two-dimensional or one-dimensional systems. The particular heterostructures we address exhibit finite range proximity effects leading to nodal superconductors with Majorana modes localized well away from this interface. To show this, we implement a Bogoliubov-de Gennes (BdG) proximity numerical scheme, which importantly, involves two finite dimensions in a three dimensional junction. Incorporating this level of numerical complexity serves to distinguish ours from alternative numerical BdG approaches which are limited by generally assuming translational invariance or periodic boundary conditions along multiple directions. With this access to the edges, we are then able to illustrate in a concrete fashion the wavefunctions of Majorana zero modes, and, moreover, address finite size effects. In the process we establish consistency with a simple analytical model.

cond-mat.supr-con↗