{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"42a24b4a6978d8ac6f14d2473d0f0074b582872d444e8897817139c09fd48a0b","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["81d541d2cfe752af1232938c6108a52bf0aceca17e04720ed2db69ce7bf50e40","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"78b78f929453acb9ca240198940abeed2c2b529e54c4f3c3e0de5c642574bad9","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"amo.attosecond-electron-dynamics.hhg-berry-curvature","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"In crystals lacking mirror symmetry, electrons pushed by a field also drift sideways because of a geometric property of their bands called Berry curvature. Harmonics polarized at right angles to the laser might read this property out, if other effects can be excluded.","posed_since":"2017","precise":"In noncentrosymmetric materials (monolayer $\\mathrm{MoS_2}$, hBN, $\\alpha$-quartz) the anomalous velocity $v = -(e/\\hbar)\\ E\\ x\\ \\Omega(k)$, with $\\Omega(k)$ the Berry curvature, generates even-order harmonics polarized perpendicular to the drive. Question: can the perpendicular even-harmonic amplitudes and phases be inverted to give $\\Omega(k)$ along the driven trajectories with a stated accuracy, given interband contributions and propagation. An answer is a retrieval in a material with independently known Omega(k) that agrees within the stated uncertainty, or a proof that the inversion is not unique.","problem_ref":"81d541d2cfe752af1232938c6108a52bf0aceca17e04720ed2db69ce7bf50e40","references":"","settled_by":"A blind retrieval of $\\Omega(k)$ from harmonic data in a material whose Berry curvature is fixed by ab initio band theory and by an independent transport or optical measurement.","status_note":"Retrievals were reported in $\\alpha$-quartz (Luu and Woerner, Nature Communications 2018) and even harmonics attributed to Berry curvature in $\\mathrm{MoS_2}$ (2017); uniqueness and model dependence of the inversion remain debated.","title":"Can harmonic spectra measure Berry curvature of a crystal?","topic_ref":null},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"a37fe2b0ae9b5a92eb81e665c1388778e511f3b50452b57b85ae3e3b89781bc7","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"32157920e4eda159828e45d6ada4a6340eaf0610373a7e1541f20686ffd15f28","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"U_RHeYCWWSbSlLnKSHt-pQ9PnVep1Ul5fUKdAEmttrCnMIx4E-bPF2-yfyyiEsnrvlSjCaXUPj2nyyiI0nxxBA"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIMhV5IOTtoVmCjkXWraSmNA6vBhA3On4VQfIGhv_RXyjxIDHeAnwD8AYhA6t2AzzYNKZyC79U6nuoEOy8Hi3_LM_eCPAgT3ot0Bm0ACOokDt09zwRrFwVMWhPdPmUEnglRV5pOiYI8SAnrc800RciXZsBmIDoCAydKXnC7_MNHmJCixC8o0epfwjxIDzczB1V_QumD18VJXEb8V22Iebx6AwXLZN1Rwyd-1THCPEgcseiNfXxFBIeufEJqTShvyCMk0ov1XvjfCh2kuT5SOII8CAKRXVORCRjmM8WLf7MUR1bK6fhft9y98pH022iRbj3lQjwIEy6JN28xxcmaT8U-CrGm2ycCSQBCZNWkpcJmM3XNqJ2CPEgET84erh4QMqfDxFWGLBJaZS5EYFN7oYAm7iWbswJgxQI8CDsCcIzBovmyR1v7IXhYg1Z7m0X4dWZvLS_NU94HSk3sQjxIJdQdDsL3v2lA7qZb8kMJtOgaTQmbgchdPcS5lYJqDLnCPAgkPXX-naXR0fRIdS-sEDlzYmtMvSCNH42ESUF0QXb6NUI8CDQo_sIWZiWXaTGRSQBLmU-lHJKskYKqsjO1r02DhB8LAj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIpq6axd5_ydPMZiVqDNP05DSMdshUOlCZR0BWpfVw7E3xIKao1Mhlx6EuG4HwMeeUpCm5KXPpzmt6tm07ULQE4KlZCPEgZKRDG-q5vzFC6hZtVrsfc5bC_9g72KnZWNauLRhatnAI8CAyDfR3x89BUQBv3UeTTrZU1UonAGq1i0QL_1EaEKNs6AjxIKc2LuZdAGb_1YtivD4GOulgStTPQUX0-4_bF2bXlxSrCPAg-lTfW3Nfnw4WpfqG-pIoMH7r0f57JywXJVZjDKrIp78I8SA2egp0G2ge8pnr1JRslpoPLLFcM41Ju0LnbChmXPjjngjwIHExvyo7F9qj3z61fSDvdyatlouUDqqU4ATffdHOplJWCPEgXBC-vhHz95oq2yKKi3ggahpIP6-CNOC1MPNshHV0yjUI8CDKr-9A1x_uMQhhNTqvWvXpPsAsdseP-4IejtAraE3u4AjwIIgwugvlgSNOmTWMhquqetKjeLf0x7d1a1MH4KU52JbFCPAg3mczMYDKOd7Nhf3ojA9ZvuTsN66Y1NnyYTp9j8GKQNwI8SCvAiiN-Hrv7IEejd8wdUihoozu5KOvpoBFJ0vg3UnGAQj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"]},"log":{"leaf_index":"2190","tree_size":"3804","proof":["145f94b63c41cc579343c01fb3d0a6c8619ce8929f1cd84b9c8c86cf0a20c931","61e17d5cf702e11d942043a0ccf5448d2562d0b7c1d8aab5b296fc28d10f9762","61a08238dc21f1a61f9806891d1ca7e253cd175b3a7d8712e0a66b31118b77d0","dd05e05297015e4dc0aef054d3602c82aedaa7b2f0e00bc1c014fcd067b880b8","e92247d468abb46b659c02170bc0f7d429ae2b0044c86e9b95942c1c9f75ff7e","9c11194190be928ce5e60bec8c0009100dbe9ee1d681e748e41ca5a853138d17","6a6dd27141672b28efa1ee62891bc3591ef1954d1d4256adbabec756be6e0a64","9761eb0f4689d6e5f28934059787de8a9f8da3f799c91405afdf99769db5c00d","9f197ad4a050ba9a768c42080a12af180f8a85b30776c547c433648f943b3824","453fe2db8b5276d732edac85634e8be036b4709a91a2584f32a4b9edcc8ca9de","325287f5a43e4f3ad4072ec4bd53d43c50c1393021a056122e9cb0fad83b868f","3c578dccc15502c5f3efe228cadc99fee76ab536ed01f66b14d316fdcc157429"],"checkpoint":"pubphys.com/log/v1\n3804\nAK6t4qgu96+M9wScTrIlsJ10d/zhKVEtYguyM3aeJvo=\n\n— pubphys.com/log/v1 JFPwIPP8EtoxgcsQg7V7CwIdL4UKPqJtpv+eB8sFNJjyQHIdyA1VabmBsPyLqq2bLxJPn57rA6fQi8y0QDDjRXHvlQg=\n","promise":"pubphys.com/log/v1 promise\n748ba979774cc4ba99421913b28ad65f14a1b003f405ec26cee253fd5c0fe692\n2190\n2026-10-15T23:43:57Z\n2026-10-16T01:43:57Z\n\n— pubphys.com/log/v1 JFPwILnZ/Ch1GJOFllHbG+LkqObM2CED7ITPffheE3YEcMHQyJRmtZg/lUqJdkpmH5ev3Zej3PYE//gzM7eEhBQgHA8=\n"},"orcid_key_evidence":[],"attesting":null}