arXiv subjects

Canon Sun

Publications and source records attributed to Canon Sun.

7 recordsLinked to original sources

arXiv2025

Strain-induced Berry phase in chiral superconductors

We study the topology of the order parameter in the intermediate phase between the superconducting and time-reversal symmetry breaking transitions of a $p_x+ip_y$ superconductor under strain. The application of in-plane strain reduces the underlying crystal symmetry and lifts the degeneracy of the critical temperature between the $p_x$ and $p_y$ orbitals, resulting in a Dirac cone structure in the thermodynamic phase diagram. When the strain is varied adiabatically along a closed path enclosing the Dirac cone, the order parameter acquires a Berry phase of $\pi$, which originates from a half rotation of the superconducting gap function. This half rotation leaves a topological signature in the superfluid stiffness tensor, making it directly observable through the geometry of vortices and the upper critical field.

cond-mat.supr-con↗

arXiv2024

Topological Landau Theory

We present an extension of Landau's theory of phase transitions by incorporating the topology of the order parameter. When the order parameter comprises several components arising from multiplicity in the same irreducible representation of symmetry, it can possess a nontrivial topology and acquire a Berry phase under the variation of thermodynamic parameters. To illustrate this idea, we investigate the superconducting phase transition of an electronic system with tetragonal symmetry and an attractive interaction involving two partial waves, both transforming in the trivial representation. By analyzing the time-dependent Ginzburg-Landau equation in the adiabatic limit, we show that the order parameter acquires a Berry phase after a cyclic evolution of parameters. We study two concrete models -- one preserving time-reversal symmetry and one breaking it -- and demonstrate that the nontrivial topology of the order parameter originates from thermodynamic analogs of gapless Dirac and Weyl points in the phase diagram. Finally, we identify an experimental signature of the topological Berry phase in a Josephson junction.

cond-mat.supr-con↗

arXiv2024

Topological linear response of hyperbolic Chern insulators

We establish a connection between the electromagnetic Hall response and band topological invariants in hyperbolic Chern insulators by deriving a hyperbolic analog of the Thouless-Kohmoto-Nightingale-den Nijs (TKNN) formula. By generalizing the Kubo formula to hyperbolic lattices, we show that the Hall conductivity is quantized to $-e^2C_{ij}/h$, where $C_{ij}$ is the first Chern number. Through a flux-threading argument, we provide an interpretation of the Chern number as a topological invariant in hyperbolic band theory. We demonstrate that, although it receives contributions from both Abelian and non-Abelian Bloch states, the Chern number can be calculated solely from Abelian states, resulting in a tremendous simplification of the topological band theory. Finally, we verify our results numerically by computing various Chern numbers in the hyperbolic Haldane model.

cond-mat.mes-hall↗

arXiv2023

Superfluid phase transition of nanoscale-confined helium-3

We theoretically investigate the superfluid phase transition of helium-3 under nanoscale confinement of one spatial dimension realized in recent experiments. Instead of the 3x3 complex matrix order parameter found in the three-dimensional system, the quasi two-dimensional superfluid is described by a reduced 3x2 complex matrix. It features a nodal quasiparticle spectrum, regardless of the value of the order parameter. The origin of the 3x2 order parameter is first illustrated via the two-particle Cooper problem, where Cooper pairs in the $p_x$ and $p_y$ orbitals are shown to have a lower bound state energy than those in $p_z$ orbitals, hinting at their energetically favorable role at the phase transition. We then compute the Landau free energy under confinement within the mean-field approximation and show that the critical temperature for condensation of the 3x2 order parameter is larger than for other competing phases. Through exact minimization of the mean-field free energy, we show that mean-field theory predicts precisely two energetically degenerate superfluid orders to emerge at the transition that are not related by symmetry: the A-phase and the planar phase. Beyond the mean-field approximation, we show that strong-coupling corrections favor the A-phase observed in experiment, whereas weak-coupling perturbative renormalization group predicts the planar phase to be stable.

cond-mat.supr-con↗

arXiv2020

$\mathbb{Z}_2$ Topologically Obstructed Superconducting Order

We propose a class of topological superconductivity in which the pairing order is $\mathbb{Z}_2$ topologically obstructed in a three-dimensional time-reversal invariant system. When two Fermi surfaces are related by time-reversal and mirror symmetries, such as those in a $\mathbb{Z}_2$ Dirac semimetal, the inter-Fermi-surface pairing in the weak-coupling regime inherits the band topological obstruction. As a result, the pairing order cannot be well-defined over the entire Fermi surface and forms a time-reversal invariant generalization of U($1$) monopole harmonic pairing. A tight-binding model of the $\mathbb{Z}_2$ topologically obstructed superconductor is constructed based on a doped $\mathbb{Z}_2$ Dirac semimetal and exhibits nodal pairings. At an open boundary, the system exhibits a time-reversal pair of topologically protected surface states.

cond-mat.supr-con↗

arXiv2019

Vortices in a Monopole Superconducting Weyl Semi-metal

A monopole harmonic superconductor is a novel topological phase of matter with topologically protected gap nodes that result from the non-trivial Berry phase structure of Cooper pairs. In this work we propose to realize a monopole superconductor by the proximity effect between a time-reversal broken Weyl semi-metal and an $s$-wave superconductor. Furthermore, we study the zero-energy vortex bound states in this system by projection methods and by exact solutions. The zero modes exhibit a non-trivial phase winding in real space as a result of the non-trivial winding of the order parameter in momentum space. By mapping the Hamiltonian to the $(1+1)$d Dirac Hamiltonian, it is shown that the zero modes, analogous to the Jackiw-Rebbi mode, are protected by the index theorem. Finally, we propose possible experimental realizations.

cond-mat.supr-con↗

arXiv2018

Monopole Charge Density Wave States in Weyl Semimetals

We study a new class of topological charge density wave states exhibiting monopole harmonic symmetries. The density-wave ordering is equivalent to pairing in the particle-hole channel due to Fermi surface nesting under interactions. When electron and hole Fermi surfaces carry different Chern numbers, the particle-hole pairing exhibits a non-trivial Berry phase inherited from band structure topology independent of concrete density-wave ordering mechanism. The associated density-wave gap functions become nodal, and the net nodal vorticity is determined by the monopole charge of the pairing Berry phase. The gap function nodes become zero-energy Weyl nodes of the bulk spectra of quasi-particle excitations. These states can occur in doped Weyl semimetals with nested electron and hole Fermi surfaces enclosing Weyl nodes of the same chirality in the weak coupling regime. Topologically non-trivial low-energy Fermi arc surface states appear in the density-wave ordering state as a consequence of the emergent zero-energy Weyl nodes.

cond-mat.str-el↗