Absence of Floating Phase in Superconductors with Time-reversal Symmetry Breaking on any Lattice
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929258131095552 |
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| author | Yuan, Andrew C. |
| author_facet | Yuan, Andrew C. |
| contents | Due to the interplay of multi-component order parameters (e.g., a twisted bilayer superconductor with inter-layer Josephson coupling or a frustrated ($n\ge 3$)-band superconductor), a superconductor can possess a $U(1)\times \mathbb{Z}_2$ symmetry, corresponding to the superconducting $T_c$ and time-reversal symmetry breaking transition $T_\text{TRSB}$, respectively. It was then conjectured that in this class of Hamiltonians, there exists a vast parameter regime $\mathcal{O}$ such that the system exhibits vestigial TRSB, i.e., $T_\text{TRSB} > T_c$, while at the boundary $\partial \mathcal{O}$, the system possesses a single phase transition $T_\text{TRSB}=T_c$. In this paper, we provide evidence towards this conjecture by mathematically eliminating the possibility of a floating phase, i.e., $T_\text{TRSB} < T_c$, for the strong coupling regime. More specifically, we prove that the correlation functions of $U(1)$ spins are bounded above by that of $\mathbb{Z}_2$ spins for all temperatures and lattice structures (e.g., $\mathbb{Z}^d$ for all $d$). In particular, this guarantees the existence of high-$T_c$ TRSB (and consequently topological) superconductivity in a large class of Hamiltonians. Note that the same property can also be proven for a certain parameter regime ($Δ\ge 4/5$) of the generalized XY model on any lattice structure, despite belonging to an entirely distinct class of $U(1)\times \mathbb{Z}_2$ Hamiltonians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06988 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Absence of Floating Phase in Superconductors with Time-reversal Symmetry Breaking on any Lattice Yuan, Andrew C. Statistical Mechanics Superconductivity Mathematical Physics Due to the interplay of multi-component order parameters (e.g., a twisted bilayer superconductor with inter-layer Josephson coupling or a frustrated ($n\ge 3$)-band superconductor), a superconductor can possess a $U(1)\times \mathbb{Z}_2$ symmetry, corresponding to the superconducting $T_c$ and time-reversal symmetry breaking transition $T_\text{TRSB}$, respectively. It was then conjectured that in this class of Hamiltonians, there exists a vast parameter regime $\mathcal{O}$ such that the system exhibits vestigial TRSB, i.e., $T_\text{TRSB} > T_c$, while at the boundary $\partial \mathcal{O}$, the system possesses a single phase transition $T_\text{TRSB}=T_c$. In this paper, we provide evidence towards this conjecture by mathematically eliminating the possibility of a floating phase, i.e., $T_\text{TRSB} < T_c$, for the strong coupling regime. More specifically, we prove that the correlation functions of $U(1)$ spins are bounded above by that of $\mathbb{Z}_2$ spins for all temperatures and lattice structures (e.g., $\mathbb{Z}^d$ for all $d$). In particular, this guarantees the existence of high-$T_c$ TRSB (and consequently topological) superconductivity in a large class of Hamiltonians. Note that the same property can also be proven for a certain parameter regime ($Δ\ge 4/5$) of the generalized XY model on any lattice structure, despite belonging to an entirely distinct class of $U(1)\times \mathbb{Z}_2$ Hamiltonians. |
| title | Absence of Floating Phase in Superconductors with Time-reversal Symmetry Breaking on any Lattice |
| topic | Statistical Mechanics Superconductivity Mathematical Physics |
| url | https://arxiv.org/abs/2308.06988 |