Spontaneous time-reversal symmetry breaking plays an important role in studying strongly correlated unconventional superconductors.When two superconducting gap functions with different symmetries compete,the relative ...Spontaneous time-reversal symmetry breaking plays an important role in studying strongly correlated unconventional superconductors.When two superconducting gap functions with different symmetries compete,the relative phase channel(θ_(-)≡θ_(1)-θ_(2))exhibits an Ising-type Z_(2) symmetry due to the second order Josephson coupling,where θ_(1,2) are the phases of two gap functions.In contrast,the U(1) symmetry in the channel of θ_(+)≡(θ_(1)+θ_(2))/2 is intact.The phase locking,i.e.,ordering of θ_(-),can take place in the phase fluctuation regime before the onset of superconductivity,i.e.,when θ_(+) is disordered.If θ_(-) is pinned at ±π/2,then timereversal symmetry is broken in the normal state,otherwise,if θ_(-)=0,or,π,rotational symmetry is broken,leading to a nematic normal state.In both cases,the order parameters possess a 4-fermion structure beyond the scope of mean-field theory,which can be viewed as a high order symmetry breaking.We employ an effective two-component XY-model assisted by a renormalization group analysis to address this problem.As a natural by-product,we also find the other interesting intermediate phase corresponds to ordering of θ_+ but with θ_(-)disordered.This is the quartetting,or,charge-4e,superconductivity,which occurs above the low temperature Z_(2)-breaking charge-2e superconducting phase.Our results provide useful guidance for studying novel symmetry breaking phases in strongly correlated superconductors.展开更多
In a superconducting topological insulator, a superconducting vortex line can trap a one-dimensional topological band with localized Majorana zero modes at the ends. Here, we study the effect of hexagonal warping and ...In a superconducting topological insulator, a superconducting vortex line can trap a one-dimensional topological band with localized Majorana zero modes at the ends. Here, we study the effect of hexagonal warping and its corresponding symmetry-breaking effect on vortex phase transition. We perform both analytical calculations based on a semiclassical formula and numerical calculations based on full quantum mechanics using the Bogoliubov-de Gennes equation. We find that the hexagonal warping term extends the topological region of the vortex line as the chemical potential changes and leads to MZMs, even in the absence of topological surface states.展开更多
Unconventional antiferromagnets(AFMs)with non-relativistic spin-splitting,such as the recently discovered altermagnet,have recently gained significant interest due to their potential for novel quantum phenomena and sp...Unconventional antiferromagnets(AFMs)with non-relativistic spin-splitting,such as the recently discovered altermagnet,have recently gained significant interest due to their potential for novel quantum phenomena and spintronic applications.The compensated magnetization in unconventional AFMs is protected by spin-space symmetries.In this work,we explore the symmetrybreaking effects and identify three distinct mechanisms for inducing net spin magnetizations in unconventional AFMs with collinear or non-collinear spins:(1)finite size effect,(2)extrinsic spin canting effect,and(3)irradiation with circularly polarized light.We show that the induced spin magnetizations are controllable and manifest as diverse intriguing phenomena.For the finite size system,the confined direction of a two-dimensional AM creates quantum-well-like subbands that determine the spin magnetization.This effect can be experimentally probed by measuring the spin density of states and the spin-polarization of Andreev-bound states within planar Josephson junctions.In the case of spin canting effect,it leads to peculiar anisotropic and non-monotonic behaviors in the superconducting proximity effect.Lastly,with circularly polarized light,spin magnetization is driven by the polarized light and the chirality of non-collinear magnetic order,thus offering a direct means of detecting the chirality of magnetic order in real materials.Our findings provide valuable insight into understanding and probing the spin magnetization in unconventional AFM materials.展开更多
基金supported by a startup funding of UCSD and the National Science Foundation (Grant No. DMR-2238360)supported by the National Natural Science Foundation of China (Grant Nos. 12234016, and 12174317)supported by the New Cornerstone Science Foundation。
文摘Spontaneous time-reversal symmetry breaking plays an important role in studying strongly correlated unconventional superconductors.When two superconducting gap functions with different symmetries compete,the relative phase channel(θ_(-)≡θ_(1)-θ_(2))exhibits an Ising-type Z_(2) symmetry due to the second order Josephson coupling,where θ_(1,2) are the phases of two gap functions.In contrast,the U(1) symmetry in the channel of θ_(+)≡(θ_(1)+θ_(2))/2 is intact.The phase locking,i.e.,ordering of θ_(-),can take place in the phase fluctuation regime before the onset of superconductivity,i.e.,when θ_(+) is disordered.If θ_(-) is pinned at ±π/2,then timereversal symmetry is broken in the normal state,otherwise,if θ_(-)=0,or,π,rotational symmetry is broken,leading to a nematic normal state.In both cases,the order parameters possess a 4-fermion structure beyond the scope of mean-field theory,which can be viewed as a high order symmetry breaking.We employ an effective two-component XY-model assisted by a renormalization group analysis to address this problem.As a natural by-product,we also find the other interesting intermediate phase corresponds to ordering of θ_+ but with θ_(-)disordered.This is the quartetting,or,charge-4e,superconductivity,which occurs above the low temperature Z_(2)-breaking charge-2e superconducting phase.Our results provide useful guidance for studying novel symmetry breaking phases in strongly correlated superconductors.
基金supported by the Air Force Office of Scientific Research(AFOSR)(Grant No.FA9550-14-1-0168)supported by the National Natural Science Foundation of China(Grant No.11674278)+1 种基金the National Basic Research Program of China(Grant No.2014CB921203)the CAS Center for Excellence in Topological Quantum Computation,and the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB28000000)
文摘In a superconducting topological insulator, a superconducting vortex line can trap a one-dimensional topological band with localized Majorana zero modes at the ends. Here, we study the effect of hexagonal warping and its corresponding symmetry-breaking effect on vortex phase transition. We perform both analytical calculations based on a semiclassical formula and numerical calculations based on full quantum mechanics using the Bogoliubov-de Gennes equation. We find that the hexagonal warping term extends the topological region of the vortex line as the chemical potential changes and leads to MZMs, even in the absence of topological surface states.
基金the support of the startup funds at HFNLthe Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302800)+3 种基金Anhui Initiative in Quantum Information Technologies(Grant No.AHY170000)supported by the start-up of Zhejiang Universitythe Fundamental Research Funds for the Central Universities(Grant No.226-2024-00068)funded by the Jane and Aatos Erkko Foundation and the Keele Foundation as part of the SuperC collaboration。
文摘Unconventional antiferromagnets(AFMs)with non-relativistic spin-splitting,such as the recently discovered altermagnet,have recently gained significant interest due to their potential for novel quantum phenomena and spintronic applications.The compensated magnetization in unconventional AFMs is protected by spin-space symmetries.In this work,we explore the symmetrybreaking effects and identify three distinct mechanisms for inducing net spin magnetizations in unconventional AFMs with collinear or non-collinear spins:(1)finite size effect,(2)extrinsic spin canting effect,and(3)irradiation with circularly polarized light.We show that the induced spin magnetizations are controllable and manifest as diverse intriguing phenomena.For the finite size system,the confined direction of a two-dimensional AM creates quantum-well-like subbands that determine the spin magnetization.This effect can be experimentally probed by measuring the spin density of states and the spin-polarization of Andreev-bound states within planar Josephson junctions.In the case of spin canting effect,it leads to peculiar anisotropic and non-monotonic behaviors in the superconducting proximity effect.Lastly,with circularly polarized light,spin magnetization is driven by the polarized light and the chirality of non-collinear magnetic order,thus offering a direct means of detecting the chirality of magnetic order in real materials.Our findings provide valuable insight into understanding and probing the spin magnetization in unconventional AFM materials.
