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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.13215 |
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| _version_ | 1866916402581995520 |
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| author | Wei, Miaomiao Wang, Bin Wang, Jian |
| author_facet | Wei, Miaomiao Wang, Bin Wang, Jian |
| contents | Gauge invariance is a fundamental principle that must be preserved in quantum transport. However, when a complex potential is incorporated into the Hamiltonian, we find that the current described by the well-established Landauer-B$\ddot{u}$ttiker formula no longer satisfies gauge invariance. Using the non-equilibrium Green's function (NEGF) method, we derive a current expression for a multi-probe system that includes a complex potential in the scattering region. We observe that an additional current term arises compared to the Landauer-B$\ddot{u}$ttiker formula, which leads to a violation of gauge invariance. To address this, we propose two phenomenological methods for redistributing the conductance to restore gauge invariance in non-Hermitian systems. These methods are applied to various trivial and nontrivial non-Hermitian quantum states, confirming the necessity of gauge-invariant treatments in non-Hermitian systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13215 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gauge invariant quantum transport theory for non-Hermitian systems Wei, Miaomiao Wang, Bin Wang, Jian Mesoscale and Nanoscale Physics Gauge invariance is a fundamental principle that must be preserved in quantum transport. However, when a complex potential is incorporated into the Hamiltonian, we find that the current described by the well-established Landauer-B$\ddot{u}$ttiker formula no longer satisfies gauge invariance. Using the non-equilibrium Green's function (NEGF) method, we derive a current expression for a multi-probe system that includes a complex potential in the scattering region. We observe that an additional current term arises compared to the Landauer-B$\ddot{u}$ttiker formula, which leads to a violation of gauge invariance. To address this, we propose two phenomenological methods for redistributing the conductance to restore gauge invariance in non-Hermitian systems. These methods are applied to various trivial and nontrivial non-Hermitian quantum states, confirming the necessity of gauge-invariant treatments in non-Hermitian systems. |
| title | Gauge invariant quantum transport theory for non-Hermitian systems |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2409.13215 |