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$\mathcal{PT}$ and anti-$\mathcal{PT}$ phase transitions in a trimerized Su--Schrieffer--Heeger chain with nonreciprocal Rashba spin-orbit coupling
Authors:
Milad Jangjan,
Linhu Li,
Longwen Zhou,
Mir Vahid Hosseini
Abstract:
We theoretically investigate a one-dimensional trimerized Su--Schrieffer--Heeger chain with three sublattices per unit cell subjected to a nonreciprocal Rashba spin-orbit coupling. Invoking a spin-flip symmetry, the non-Hermitian Hamiltonian decomposes into two independent spin sectors, enabling a spin-resolved analysis of non-Hermitian skin effects and system symmetries. We identify a rich phase…
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We theoretically investigate a one-dimensional trimerized Su--Schrieffer--Heeger chain with three sublattices per unit cell subjected to a nonreciprocal Rashba spin-orbit coupling. Invoking a spin-flip symmetry, the non-Hermitian Hamiltonian decomposes into two independent spin sectors, enabling a spin-resolved analysis of non-Hermitian skin effects and system symmetries. We identify a rich phase diagram consisting of four bulk phases and two edge-state phases. The bulk phases include fully $\mathcal{PT}$-unbroken (real-spectrum) and fully anti-$\mathcal{PT}$-unbroken (imaginary-spectrum) regimes, as well as two mixed phases where one band remains on the real or imaginary axis while the other two form complex-conjugate pairs. The two edge-state phases correspond to topological edge modes with either $\mathcal{PT}$-unbroken (real) or anti-$\mathcal{PT}$-unbroken (imaginary) energies. Using non-Bloch band theory and Cardano's method, we derive closed-form expressions for phase boundaries and establish the bulk-edge correspondence for each spin sector. Calculations of Berry phase and directional inverse participation ratios confirm our analytical predictions. Our results provide a minimal platform for realizing spin-resolved non-Hermitian topology and edge-selective symmetry preservation, in which the bulk and edge states belong to distinct symmetry classes.
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Submitted 20 August, 2026;
originally announced August 2026.
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High Harmonic Spectroscopy from Lower-Order to Higher-Order Topological Insulators
Authors:
Bryan Lorenzo,
Carlos Batista,
Milad Jangjan,
Dasol Kim,
Jean Menotti,
Feng Liu,
Wenlong Gao,
Shambhu Ghimire,
Camilo Granados,
Alexis Chacon
Abstract:
Over the past decades, high-harmonic spectroscopy (HHS) has emerged as a powerful tool for all-optical probing of topological properties of solids. There are outstanding questions regarding universal nature of the spectral features of harmonics in their relationship to the non-trivial topological properties. Here, we present a systematic theoretical study of HHS in topological materials, including…
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Over the past decades, high-harmonic spectroscopy (HHS) has emerged as a powerful tool for all-optical probing of topological properties of solids. There are outstanding questions regarding universal nature of the spectral features of harmonics in their relationship to the non-trivial topological properties. Here, we present a systematic theoretical study of HHS in topological materials, including lower-order and higher-order topological insulators (LOTIs and HOTIs), focusing on observables such as helicity, circular dichroism, ellipticity dependence, and channel-resolved intensity yields. Using the Haldane, Kane-Mele, and breathing Kagome lattice models, we theoretically extend all-optical approaches from the LOTI to the HOTI regime by explicitly incorporating contributions from bulk, edge, and it corner states. Depending on the crystalline system, our calculations suggest that these observables can encode topological information through distinct modifications of the HHG spectra in topological phases. In particular, we identify significant enhancements of the harmonic intensity yields, reaching up to two orders of magnitude relative to trivial phases, together with distinct spectral signatures associated with edge and corner contributions revealed through channel-resolved intensity yields. These results show that channel-resolved HHS provides a promising route for probing topological states in both LOTIs and HOTIs.
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Submitted 24 May, 2026; v1 submitted 21 August, 2025;
originally announced August 2025.
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Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
Authors:
Milad Jangjan,
Linhu Li,
Luis E. F. Foa Torres,
Mir Vahid Hosseini
Abstract:
We theoretically investigate topological features of a one-dimensional Su-Schrieffer-Heeger lattice with modulating non-Hermitian on-site potentials containing four sublattices per unit cell. The lattice can be either commensurate or incommensurate. In the former case, the entire lattice can be mapped by supercells completely. While in the latter case, there are two extra lattice points, thereby m…
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We theoretically investigate topological features of a one-dimensional Su-Schrieffer-Heeger lattice with modulating non-Hermitian on-site potentials containing four sublattices per unit cell. The lattice can be either commensurate or incommensurate. In the former case, the entire lattice can be mapped by supercells completely. While in the latter case, there are two extra lattice points, thereby making the last cell incomplete. We find that an anti-PT transition occurs at exceptional points of edge states at certain parameters, which does not coincide with the conventional topological phase transition characterized by the Berry phase, provided the imaginary on-site potential is large enough. Interestingly, when the potential exceeds a critical value, edge states appear even in the regime with a trivial Berry phase. To characterize these novel edge states we present topological invariants associated with the system's parity. Finally, we analyze the dynamics for initial states with different spatial distributions, which exhibit distinct dynamics for the commensurate and incommensurate cases, depending on the imaginary part of edge state energy.
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Submitted 16 June, 2024;
originally announced June 2024.
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Floquet topological phase transitions in a periodically quenched dimer
Authors:
Milad Jangjan,
Luis E. F. Foa Torres,
Mir Vahid Hosseini
Abstract:
We report on the theoretical investigation of the topological properties of a periodically quenched one-dimensional dimerized lattice where a piece-wise constant Hamiltonian switches from $h_1$ to $h_2$ at a partition time $t_p$ within each driving period $T$. We examine different dimerization patterns for $h_1$ and $h_2$ and the interplay with the driving parameters that lead to the emergence of…
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We report on the theoretical investigation of the topological properties of a periodically quenched one-dimensional dimerized lattice where a piece-wise constant Hamiltonian switches from $h_1$ to $h_2$ at a partition time $t_p$ within each driving period $T$. We examine different dimerization patterns for $h_1$ and $h_2$ and the interplay with the driving parameters that lead to the emergence of topological states both at zero energy and at the edge of the Brillouin-Floquet quasi-energy zone. We illustrate different phenomena, including the occurrence of both edge states in a semimetal spectrum, the topological transitions, and the generation of zero-energy topological states from trivial snapshots. The role of the different symmetries in our results is also discussed.
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Submitted 6 August, 2022;
originally announced August 2022.
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Topological properties of subsystem-symmetry-protected edge states in an extended quasi-one-dimensional dimerized lattice
Authors:
Milad Jangjan,
Mir Vahid Hosseini
Abstract:
We investigate theoretically the topological properties of dimerized quasi-one-dimensional (1D) lattice comprising of multi legs $(L)$ as well as multi sublattices $(R)$. The system has main and subsidiary exchange symmetries. In the basis of latter one, the system can be divided into $L$ 1D subsystems each of which corresponds to a generalized $SSH_R$ model having $R$ sublattices and on-site pote…
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We investigate theoretically the topological properties of dimerized quasi-one-dimensional (1D) lattice comprising of multi legs $(L)$ as well as multi sublattices $(R)$. The system has main and subsidiary exchange symmetries. In the basis of latter one, the system can be divided into $L$ 1D subsystems each of which corresponds to a generalized $SSH_R$ model having $R$ sublattices and on-site potentials. Chiral symmetry is absent in all subsystems except when the axis of main exchange symmetry coincides on the central chain. We find that the system may host zero- and finite-energy topological edge states. The existence of zero-energy edge state requires a certain relation between the number of legs and sublattices. As such, different topological phases, protected by subsystem symmetry, including zero-energy edge states in the main gap, no zero-energy edge states, and zero-energy edge states in the bulk states are characterized. Despite the classification symmetry of the system belongs to $BDI$ but each subsystem falls in either $AI$ or $BDI$ symmetry class.
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Submitted 24 March, 2022;
originally announced March 2022.
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Floquet engineering of topological metal states and hybridization of edge states with bulk states in dimerized two-leg ladders
Authors:
Milad Jangjan,
Mir Vahid Hosseini
Abstract:
We consider asymmetric and symmetric dimerized two-leg ladders, comprising of four different lattice points per unit cell, illuminated by circularly polarized light. In the asymmetric dimerized ladder case, rungs are not perpendicular to the ladder's legs whereas the rungs are perpendicular to the legs for the symmetric one. Using the Floquet theory, we obtain an effective Hamiltonian to study top…
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We consider asymmetric and symmetric dimerized two-leg ladders, comprising of four different lattice points per unit cell, illuminated by circularly polarized light. In the asymmetric dimerized ladder case, rungs are not perpendicular to the ladder's legs whereas the rungs are perpendicular to the legs for the symmetric one. Using the Floquet theory, we obtain an effective Hamiltonian to study topological properties of the systems. Depending on the dimerization strength and driving amplitude, it is shown that topologically protected edge states manifest themselves not only as a zero-energy band within the gap between conduction and valence band but also as finite-energy curved bands inside the gap of subbands. The latter one can penetrate into bulk states and hybridize with the bulk states revealing hybridized Floquet topological metal phase with delocalized edge states in the asymmetric ladder case. However, in the symmetric ladder, the finite-energy edge states while remaining localized can coexist with the extended bulk states manifesting Floquet topological metal phase.
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Submitted 4 September, 2020; v1 submitted 15 May, 2020;
originally announced May 2020.