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class=\"wp-block-heading\">\u7570\u5e38Hall\u52b9\u679c\u306e\u5e7e\u4f55\u5b66\u7684\u5074\u9762\u3068\u4e0d\u7d14\u7269\u6563\u4e71\u5c40\u5728\u52b9\u679c\u306b\u3088\u308bHall\u4f1d\u5c0e\u7387\u306e\u91cf\u5b50\u5316<\/h4>\n\n\n\n<p>\u3000\u4f1d\u5c0e\u4f53\u306b\u78c1\u5834\u3092\u304b\u3051\u305f\u72b6\u614b\u3067\u96fb\u6d41\u3092\u6d41\u3059\u3068\u3001\u96fb\u6d41\u3068\u78c1\u5834\u306e\u4e21\u65b9\u306b\u5782\u76f4\u306a\u65b9\u5411\u306b\u8d77\u96fb\u529b\u304c\u751f\u3058\u308b\u73fe\u8c61\u3092Hall\u52b9\u679c\u3068\u547c\u3073\u307e\u3059\u3002\u307e\u305f\u3001\u5f37\u78c1\u6027\u91d1\u5c5e\u3067\u306f\u5916\u90e8\u78c1\u5834\u3060\u3051\u3067\u306a\u304f\u3001\u78c1\u5316\u306b\u4f9d\u5b58\u3057\u305f\u540c\u69d8\u306e\u73fe\u8c61\u3082\u89b3\u6e2c\u3055\u308c\u3001\u3053\u308c\u3092\u533a\u5225\u3057\u3066\u7570\u5e38Hall\u52b9\u679c\u3068\u547c\u3073\u307e\u3059\u3002\u7570\u5e38Hall\u52b9\u679c\u304c\u751f\u3058\u308b\u4ed5\u7d44\u307f\u306b\u306f\u3001\u96fb\u5b50\u306b\u5bfe\u3059\u308b\u30b9\u30d4\u30f3\u4f9d\u5b58\u6563\u4e71\u306b\u3088\u308b\u5916\u56e0\u7684\u6a5f\u69cb\u3068\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u30d0\u30f3\u30c9\u3092\u5f62\u6210\u3059\u308b\u96fb\u5b50\u72b6\u614b\u306e\u7279\u6b8a\u6027\u306b\u8d77\u56e0\u3059\u308b\u5185\u56e0\u7684\u6a5f\u69cb\u304c\u3042\u308a\u307e\u3059\u3002\u3044\u305a\u308c\u306e\u6a5f\u69cb\u306b\u304a\u3044\u3066\u3082\u3001\u30b9\u30d4\u30f3\u8ecc\u9053\u76f8\u4e92\u4f5c\u7528\u304c\u91cd\u8981\u306a\u5f79\u5272\u3092\u62c5\u3063\u3066\u3044\u307e\u3059\u3002<br>\u3000\u3053\u3053\u3067\u306f\u5185\u56e0\u7684\u6a5f\u69cb\u306b\u6ce8\u76ee\u3057\u3001\u96fb\u5b50\u72b6\u614b\u306e\u7279\u6b8a\u6027\u3092\u5e7e\u4f55\u5b66\u7684\u4f4d\u76f8\u306e\u6982\u5ff5\u3092\u901a\u3058\u3066\u7406\u89e3\u3059\u308b\u3053\u3068\u3067\u3001\u3053\u306e\u6a5f\u69cb\u304c\u3088\u308a\u52b9\u679c\u7684\u306b\u50cd\u304f\u305f\u3081\u306e\u6761\u4ef6\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3057\u305f\u3002\u3053\u306e\u77e5\u898b\u306f\u7269\u8cea\u8a2d\u8a08\u306b\u304a\u3044\u3066\u91cd\u8981\u306a\u6307\u91dd\u3068\u306a\u308a\u5f97\u307e\u3059\u3002\u307e\u305f\u3001\u4e0d\u7d14\u7269\u6563\u4e71\u306b\u3088\u308b\u5c40\u5728\u52b9\u679c\u306b\u3088\u308a\u3001\u96fb\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u30d0\u30f3\u30c9\u5168\u4f53\u306e\u6301\u3064\u4f4d\u76f8\u5e7e\u4f55\u5b66\u7684\u306a\u7279\u6027\u304c\u9855\u5728\u5316\u3057\u3001\u5f37\u78c1\u5834\u4e2d\u306e2\u6b21\u5143\u96fb\u5b50\u7cfb\u306b\u304a\u3051\u308b\u91cf\u5b50Hall\u52b9\u679c\u3068\u540c\u69d8\u306e\u4ed5\u7d44\u307f\u3067\u30012\u6b21\u5143\u5f37\u78c1\u6027\u91d1\u5c5e\u306b\u304a\u3044\u3066\u3082Hall\u4f1d\u5c0e\u7387\u306e\u91cf\u5b50\u5316\u304c\u8d77\u3053\u308a\u5f97\u308b\u3053\u3068\u3092\u7406\u8ad6\u7684\u306b\u793a\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<div class=\"wp-block-group is-content-justification-center is-nowrap is-layout-flex wp-container-core-group-is-layout-4 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"393\" height=\"350\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/t2g\u6a21\u578b.png\" alt=\"\" class=\"wp-image-36\" style=\"width:223px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/t2g\u6a21\u578b.png 393w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/t2g\u6a21\u578b-300x267.png 300w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/><figcaption class=\"wp-element-caption\">t2g\u6a21\u578b<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"422\" height=\"383\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/t2g\u6a21\u578b\u306eBerry\u66f2\u7387.png\" alt=\"\" class=\"wp-image-37\" style=\"width:251px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/t2g\u6a21\u578b\u306eBerry\u66f2\u7387.png 422w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/t2g\u6a21\u578b\u306eBerry\u66f2\u7387-300x272.png 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><figcaption class=\"wp-element-caption\">\u7b2c5\u30d0\u30f3\u30c9\u306eBerry\u66f2\u7387\u306e\u30d0\u30f3\u30c9\u4ea4\u5dee\u306b\u3088\u308b\u5909\u5316<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-content-justification-center is-nowrap is-layout-flex wp-container-core-group-is-layout-5 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"416\" height=\"224\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/Haldane\u6a21\u578b.png\" alt=\"\" class=\"wp-image-38\" style=\"width:241px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/Haldane\u6a21\u578b.png 416w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/Haldane\u6a21\u578b-300x162.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><figcaption class=\"wp-element-caption\">Haldane\u6a21\u578b<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"416\" height=\"410\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5c40\u5728\u52b9\u679c\u306b\u3088\u308bHall\u4f1d\u5c0e\u7387\u306e\u91cf\u5b50\u5316.png\" alt=\"\" class=\"wp-image-39\" style=\"width:260px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5c40\u5728\u52b9\u679c\u306b\u3088\u308bHall\u4f1d\u5c0e\u7387\u306e\u91cf\u5b50\u5316.png 416w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5c40\u5728\u52b9\u679c\u306b\u3088\u308bHall\u4f1d\u5c0e\u7387\u306e\u91cf\u5b50\u5316-300x296.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><figcaption class=\"wp-element-caption\">\u62e1\u5f35Haldane\u6a21\u578b\u306b\u304a\u3051\u308bHall\u4f1d\u5c0e\u7387\u306e\u91cf\u5b50\u5316<\/figcaption><\/figure>\n<\/div>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"http:\/\/dx.doi.org\/10.1143\/JPSJ.71.19\" data-type=\"link\" data-id=\"http:\/\/dx.doi.org\/10.1143\/JPSJ.71.19\">&#8220;Topological Nature of Anomalous Hall Effect in Ferromagnets&#8221;<br>Masaru Onoda, and Naoto Nagaosa,<br>Journal of the Physical Society of Japan 71 (1) 19 &#8211; 22 (2002)<\/a><\/p>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"http:\/\/dx.doi.org\/10.1103\/PhysRevLett.90.206601\" data-type=\"link\" data-id=\"http:\/\/dx.doi.org\/10.1103\/PhysRevLett.90.206601\">&#8220;Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets: Quantum Hall Effect in Metals&#8221;<br>Masaru Onoda and Naoto Nagaosa<br>Physical Review Letters 90 (20) 206601-1 &#8211; 206601-4 (2002)<\/a><\/p>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"http:\/\/dx.doi.org\/10.1143\/JPSJ.73.2624\" data-type=\"link\" data-id=\"http:\/\/dx.doi.org\/10.1143\/JPSJ.73.2624\">&#8220;Anomalous Hall Effect and Skyrmion Number in Real and Momentum Spaces&#8221;<br>Masaru Onoda, Gen Tatara, and Naoto Nagaosa<br>Journal of the Physical Society of Japan 73 (10) 2624 &#8211; 2627 (2004)<\/a><\/p>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<h4 class=\"wp-block-heading\">\u30b9\u30d4\u30f3Hall\u52b9\u679c\u304a\u3088\u3073\u91cf\u5b50\u30b9\u30d4\u30f3Hall\u52b9\u679c\u306b\u304a\u3051\u308b\u30b9\u30d4\u30f3\u6d41\u30fb\u30b9\u30d4\u30f3\u84c4\u7a4d\u3068\u4e0d\u7d14\u7269\u306b\u3088\u308b\u5c40\u5728\u52b9\u679c<\/h4>\n\n\n\n<p>\u3000\u524d\u8ff0\u306e\u3088\u3046\u306b\u3001\u96fb\u5b50\u306f\u96fb\u8377\u306e\u307b\u304b\u306b\u3082\u3001\u81ea\u8ee2\u904b\u52d5\u306b\u985e\u4f3c\u3057\u305f\u30b9\u30d4\u30f3\u3068\u547c\u3070\u308c\u308b\u81ea\u7531\u5ea6\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002\u30b9\u30d4\u30f3Hall\u52b9\u679c\u3068\u306f\u3001\u8868\u9762\u7684\u306b\u306fHall\u52b9\u679c\u306b\u304a\u3051\u308b\u96fb\u8377\u3092\u30b9\u30d4\u30f3\u306b\u7f6e\u304d\u63db\u3048\u305f\u3088\u3046\u306a\u73fe\u8c61\u3068\u3057\u3066\u73fe\u308c\u3001\u96fb\u6d41\u3068\u76f4\u4ea4\u3059\u308b\u65b9\u5411\u306b\u30b9\u30d4\u30f3\u84c4\u7a4d\u304c\u751f\u3058\u308b\u3068\u3044\u3046\u3082\u306e\u3067\u3059\u3002\u3055\u3089\u306b\u3001\u91cf\u5b50Hall\u52b9\u679c\u306b\u5bfe\u5fdc\u3059\u308b\u73fe\u8c61\u3068\u3057\u3066\u91cf\u5b50\u30b9\u30d4\u30f3Hall\u52b9\u679c\u304c\u77e5\u3089\u308c\u3066\u304a\u308a\u3001\u30b9\u30d4\u30f3Hall\u52b9\u679c\u3068\u540c\u69d8\u306b\u30b9\u30d4\u30f3\u8ecc\u9053\u76f8\u4e92\u4f5c\u7528\u304c\u91cd\u8981\u306a\u50cd\u304d\u3092\u3057\u307e\u3059\u3002\u30b9\u30d4\u30f3\u8ecc\u9053\u76f8\u4e92\u4f5c\u7528\u306e\u305f\u3081\u3001\u30b9\u30d4\u30f3\u306f\u96fb\u8377\u3068\u7570\u306a\u308a\u4fdd\u5b58\u91cf\u3067\u306f\u306a\u304f\u3001\u30b9\u30d4\u30f3Hall\u4f1d\u5c0e\u7387\u3068\u30b9\u30d4\u30f3\u84c4\u7a4d\u306e\u95a2\u4fc2\u306f\u3001Hall\u4f1d\u5c0e\u7387\u3068Hall\u8d77\u96fb\u529b\u306e\u95a2\u4fc2\u3088\u308a\u3082\u305a\u3063\u3068\u8907\u96d1\u306a\u3082\u306e\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u975e\u5e73\u8861\u5b9a\u5e38\u72b6\u614b\u306b\u304a\u3051\u308b\u5b9f\u7a7a\u9593\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u7528\u3044\u3066\u3001\u6709\u9650\u7cfb\u306e\u30b9\u30d4\u30f3Hall\u52b9\u679c\u30fb\u91cf\u5b50\u30b9\u30d4\u30f3Hall\u52b9\u679c\u306b\u304a\u3051\u308b\u30b9\u30d4\u30f3\u6d41\u3068\u30b9\u30d4\u30f3\u84c4\u7a4d\u306e\u69d8\u5b50\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3057\u305f\u3002<br>\u3000\u91cf\u5b50\u30b9\u30d4\u30f3Hall\u52b9\u679c\u306f\u91cf\u5b50Hall\u52b9\u679c\u3068\u540c\u69d8\u306b\u7279\u6b8a\u306a\u30a8\u30c3\u30b8\u72b6\u614b\u306e\u5b58\u5728\u3092\u793a\u5506\u3057\u3066\u304a\u308a\u3001\u305d\u306e\u5b58\u5728\u306f\u30d0\u30eb\u30af\u72b6\u614b\u306e\u4f4d\u76f8\u5e7e\u4f55\u5b66\u7684\u306a\u975e\u81ea\u660e\u6027\u3068\u95a2\u9023\u3057\u3066\u3044\u307e\u3059\u3002\u91cf\u5b50Hall\u52b9\u679c\u306e\u5834\u5408\u306b\u306f\u3001\u3053\u306e\u975e\u81ea\u660e\u6027\u304c\u4e0d\u7d14\u7269\u6563\u4e71\u306b\u3088\u308b\u5c40\u5728\u52b9\u679c\u306b\u304a\u3044\u3066\u9855\u8457\u306b\u73fe\u308c\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u3053\u3068\u3092\u8e0f\u307e\u3048\u3001\u91cf\u5b50\u30b9\u30d4\u30f3Hall\u52b9\u679c\u306b\u5bfe\u3059\u308b\u4e0d\u7d14\u7269\u306e\u5f71\u97ff\u3092\u89e3\u6790\u3057\u3001\u91cf\u5b50Hall\u52b9\u679c\u3084\u901a\u5e38\u306e\u30b9\u30d4\u30f3Hall\u52b9\u679c\u306b\u304a\u3051\u308b\u5c40\u5728\u52b9\u679c\u3068\u306e\u9055\u3044\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<div class=\"wp-block-group is-content-justification-center is-nowrap is-layout-flex wp-container-core-group-is-layout-7 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"666\" height=\"389\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u30b9\u30d4\u30f3\u6d41\u30fb\u30b9\u30d4\u30f3\u84c4\u7a4d.png\" alt=\"\" class=\"wp-image-40\" style=\"width:561px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u30b9\u30d4\u30f3\u6d41\u30fb\u30b9\u30d4\u30f3\u84c4\u7a4d.png 666w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u30b9\u30d4\u30f3\u6d41\u30fb\u30b9\u30d4\u30f3\u84c4\u7a4d-300x175.png 300w\" sizes=\"(max-width: 666px) 100vw, 666px\" \/><figcaption class=\"wp-element-caption\">\u91cf\u5b50\u30b9\u30d4\u30f3Hall\u7cfb\uff08\u4e0a\uff09\u3068\u30b9\u30d4\u30f3Hall\u7d76\u7e01\u4f53\uff08\u4e0b\uff09\u306b\u304a\u3051\u308b\u30b9\u30d4\u30f3\u6d41\uff08\u4e2d\uff09\u304a\u3088\u3073\u30b9\u30d4\u30f3\u84c4\u7a4d\uff08\u53f3\uff09<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-content-justification-center is-nowrap is-layout-flex wp-container-core-group-is-layout-8 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"499\" height=\"343\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u91cf\u5b50\u30b9\u30d4\u30f3Hall\u7cfb\u3068\u30b9\u30d4\u30f3Hall\u7d76\u7e01\u4f53\u306e\u9055\u3044.png\" alt=\"\" class=\"wp-image-41\" style=\"width:397px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u91cf\u5b50\u30b9\u30d4\u30f3Hall\u7cfb\u3068\u30b9\u30d4\u30f3Hall\u7d76\u7e01\u4f53\u306e\u9055\u3044.png 499w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u91cf\u5b50\u30b9\u30d4\u30f3Hall\u7cfb\u3068\u30b9\u30d4\u30f3Hall\u7d76\u7e01\u4f53\u306e\u9055\u3044-300x206.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><figcaption class=\"wp-element-caption\">\u91cf\u5b50\u30b9\u30d4\u30f3Hall\u7cfb\uff08QHS\uff09\u3068\u30b9\u30d4\u30f3Hall\u7d76\u7e01\u4f53\uff08SHI\uff09\u306e\u9055\u3044\u306e\u6982\u5ff5\u56f3<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-content-justification-center is-nowrap is-layout-flex wp-container-core-group-is-layout-9 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"531\" height=\"427\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u306a\u975e\u5c40\u5728\u72b6\u614b\u306e\u5bfe\u6d88\u6ec5.png\" alt=\"\" class=\"wp-image-42\" style=\"width:405px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u306a\u975e\u5c40\u5728\u72b6\u614b\u306e\u5bfe\u6d88\u6ec5.png 531w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u306a\u975e\u5c40\u5728\u72b6\u614b\u306e\u5bfe\u6d88\u6ec5-300x241.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><figcaption class=\"wp-element-caption\">\u91cf\u5b50\u30b9\u30d4\u30f3Hall\u7cfb\u306b\u304a\u3051\u308b\u4f4d\u76f8\u5e7e\u4f55\u5b66\u7684\u306b\u975e\u81ea\u660e\u306a\u975e\u5c40\u5728\u72b6\u614b\u306e\u5bfe\u6d88\u6ec5<\/figcaption><\/figure>\n<\/div>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"http:\/\/dx.doi.org\/10.1103\/PhysRevB.72.081301\" data-type=\"link\" data-id=\"http:\/\/dx.doi.org\/10.1103\/PhysRevB.72.081301\">&#8220;Role of relaxation in the spin Hall effect&#8221;<br>Masaru Onoda and Naoto Nagaosa<br>Physical Review B 72 (8) 081301-1 &#8211; 081301-4 (2005)<\/a><\/p>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"http:\/\/dx.doi.org\/10.1103\/PhysRevLett.95.106601\" data-type=\"link\" data-id=\"http:\/\/dx.doi.org\/10.1103\/PhysRevLett.95.106601\">&#8220;Spin Current and Accumulation Generated by the Spin Hall Insulator&#8221;<br>Masaru Onoda and Naoto Nagaosa<br>Physical Review Letters 95 (10) 106610-1 &#8211; 106610-4 (2005)<\/a><\/p>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"http:\/\/dx.doi.org\/10.1103\/PhysRevLett.98.076802\" data-type=\"link\" data-id=\"http:\/\/dx.doi.org\/10.1103\/PhysRevLett.98.076802\">&#8220;Localization in a Quantum Spin Hall System&#8221;<br>Masaru Onoda, Yshai Avishai, and Naoto Nagaosa<br>Physical Review Letters 98 (7) 076802-1 &#8211; 076802-4 (2007)<\/a><\/p>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<h4 class=\"wp-block-heading\">\u5149\u306e\u5e7e\u4f55\u5b66\u7684Hall\u52b9\u679c\u3068\u5149\u30ab\u30a4\u30e9\u30eb\u30a8\u30c3\u30b8\u30e2\u30fc\u30c9<\/h4>\n\n\n\n<p>\u3000\u96fb\u5b50\u7cfb\u306b\u304a\u3051\u308b\u5185\u56e0\u7684\u6a5f\u69cb\u306b\u3088\u308b\u7570\u5e38Hall\u52b9\u679c\u3084\u30b9\u30d4\u30f3Hall\u52b9\u679c\u306e\u672c\u8cea\u306f\u3001\u91cf\u5b50\u3067\u3042\u308b\u96fb\u5b50\u304c\u6301\u3064\u6ce2\u52d5\u6027\u306b\u4f34\u3046\u5e7e\u4f55\u5b66\u7684\u4f4d\u76f8\u306b\u3042\u308a\u307e\u3057\u305f\u3002\u3053\u306e\u4f4d\u76f8\u304c\u73fe\u308c\u308b\u6761\u4ef6\u306e\u4e00\u3064\u3068\u3057\u3066\u3001\u30b9\u30d4\u30f3\u3068\u8ecc\u9053\u904b\u52d5\u306e\u7d50\u5408\u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002\u5149\u5b50\u306e\u96c6\u307e\u308a\u3067\u3042\u308b\u96fb\u78c1\u6ce2\u304c\u6301\u3064\u504f\u5149\u306e\u81ea\u7531\u5ea6\u306f\u5149\u5b50\u306e\u30b9\u30d4\u30f3\u81ea\u7531\u5ea6\u3068\u5bfe\u5fdc\u3057\u3066\u304a\u308a\u3001\u307e\u305f\u3001\u5149\u5b50\u306f\u8cea\u91cf\u3092\u6301\u305f\u306a\u3044\u76f8\u5bfe\u8ad6\u7684\u306a\u7c92\u5b50\u306e\u305f\u3081\u3001\u30b9\u30d4\u30f3\u3068\u8ecc\u9053\u904b\u52d5\u304c\u5f37\u304f\u7d50\u5408\u3057\u3066\u3044\u307e\u3059\u3002\u305d\u3053\u3067\u96fb\u5b50\u7cfb\u306b\u304a\u3051\u308b\u77e5\u898b\u3092\u3082\u3068\u306b\u3001\u53e4\u304f\u304b\u3089\u77e5\u3089\u308c\u3066\u3044\u305f\u5149\u7dda\u306e\u53cd\u5c04\u30fb\u5c48\u6298\u306b\u304a\u3051\u308b\u6a2a\u30ba\u30ec\u304c\u3001\u5185\u56e0\u7684\u6a5f\u69cb\u306b\u3088\u308b\u5149\u306e\u30b9\u30d4\u30f3Hall\u52b9\u679c\u3068\u3057\u3066\u7406\u89e3\u3067\u304d\u308b\u3053\u3068\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3057\u305f\u3002\u3055\u3089\u306b\u3001\u5c48\u6298\u7387\u304c\u5468\u671f\u7684\u306b\u5909\u8abf\u3057\u305f\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u7d50\u6676\u3068\u547c\u3070\u308c\u308b\u4eba\u5de5\u7d50\u6676\u4e2d\u3092\u4f1d\u642c\u3059\u308b\u96fb\u78c1\u6ce2\u306b\u5bfe\u3059\u308b\u540c\u69d8\u306e\u52b9\u679c\u3092\u7406\u8ad6\u7684\u306b\u793a\u3057\u307e\u3057\u305f\u3002<br>\u3000\u524d\u8ff0\u306e\u3053\u3068\u306f\u3001\u30b9\u30d4\u30f3\u89d2\u904b\u52d5\u91cf\u306b\u4ee3\u308f\u308b\u5185\u90e8\u8ecc\u9053\u89d2\u904b\u52d5\u91cf\u3092\u6301\u3063\u305f\u96fb\u78c1\u6ce2\u3092\u5468\u671f\u69cb\u9020\u3092\u7528\u3044\u3066\u751f\u6210\u3067\u304d\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u3055\u3089\u306b\u3001\u3053\u306e\u3088\u3046\u306a\u96fb\u78c1\u6ce2\u304c\u4f4d\u76f8\u5e7e\u4f55\u5b66\u7684\u306b\u975e\u81ea\u660e\u306a\u5e7e\u4f55\u5b66\u7684\u4f4d\u76f8\u3092\u6301\u3061\u5f97\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u96fb\u5b50\u7cfb\u306e\u91cf\u5b50Hall\u52b9\u679c\u306b\u73fe\u308c\u308b\u30ab\u30a4\u30e9\u30eb\u30a8\u30c3\u30b8\u72b6\u614b\u306e\u5149\u5b50\u7cfb\u7248\u3092\u78c1\u6027\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u7d50\u6676\u306b\u304a\u3044\u3066\u5b9f\u73fe\u3067\u304d\u308b\u3053\u3068\u304c\u3001\u6d77\u5916\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u3088\u308a\u793a\u3055\u308c\u307e\u3057\u305f\u3002\u3053\u306e\u3053\u3068\u3092\u53d7\u3051\u3001\u7406\u8ad6\u6a21\u578b\u3092\u7528\u3044\u3066\u5149\u30ab\u30a4\u30e9\u30eb\u30a8\u30c3\u30b8\u30e2\u30fc\u30c9\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8abf\u3079\u3001\u8a66\u6599\u306e\u30a8\u30c3\u30b8\u306b\u6cbf\u3063\u3066\u9589\u3058\u8fbc\u3081\u3089\u308c\u305f\u672c\u7269\u306e\u5149\u30ab\u30a4\u30e9\u30eb\u30a8\u30c3\u30b8\u30e2\u30fc\u30c9\u4ee5\u5916\u306b\u3082\u3001\u5149\u5b50\u7cfb\u306b\u7279\u6709\u306e\u5916\u90e8\u3078\u306e\u6f0f\u308c\u3092\u4f34\u3046\u5171\u9cf4\u7684\u306a\u5149\u30ab\u30a4\u30e9\u30eb\u30a8\u30c3\u30b8\u30e2\u30fc\u30c9\u3082\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3057\u305f\u3002\u307e\u305f\u3001\u3053\u308c\u3089\u306e\u30e2\u30fc\u30c9\u3092\u3046\u307e\u304f\u3064\u306a\u3052\u308b\u3053\u3068\u3067\u5f8c\u8005\u3092\u901a\u3058\u3066\u5916\u90e8\u304b\u3089\u524d\u8005\u3092\u52b1\u8d77\u3067\u304d\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<div class=\"wp-block-group is-content-justification-center is-nowrap is-layout-flex wp-container-core-group-is-layout-11 wp-block-group-is-layout-flex\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-1 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"272\" height=\"283\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5149\u30b9\u30d4\u30f3Hall\u52b9\u679c.png\" alt=\"\" class=\"wp-image-43\" style=\"width:187px;height:auto\"\/><figcaption class=\"wp-element-caption\">\u5149\u30b9\u30d4\u30f3Hall\u52b9\u679c\u306e\u6982\u5ff5\u56f3<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"297\" height=\"300\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u30d0\u30f3\u30c9\u306eBerry\u66f2\u7387.png\" alt=\"\" class=\"wp-image-45\" style=\"width:196px;height:auto\"\/><figcaption class=\"wp-element-caption\">\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u30d0\u30f3\u30c9\u306eBerry\u66f2\u7387<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"277\" height=\"550\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u7d50\u6676\u306e\u6a21\u578b\u3068\u305d\u306e\u30d0\u30f3\u30c9\u56f3.png\" alt=\"\" class=\"wp-image-44\" style=\"width:220px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u7d50\u6676\u306e\u6a21\u578b\u3068\u305d\u306e\u30d0\u30f3\u30c9\u56f3.png 277w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u7d50\u6676\u306e\u6a21\u578b\u3068\u305d\u306e\u30d0\u30f3\u30c9\u56f3-151x300.png 151w\" sizes=\"(max-width: 277px) 100vw, 277px\" \/><figcaption class=\"wp-element-caption\">\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u7d50\u6676\u3068\u305d\u306e\u30d0\u30f3\u30c9\u69cb\u9020<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-content-justification-center is-nowrap is-layout-flex wp-container-core-group-is-layout-12 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"383\" height=\"252\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u78c1\u6027\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u7d50\u6676\u306e\u30d0\u30f3\u30c9\u56f3.png\" alt=\"\" class=\"wp-image-46\" style=\"width:270px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u78c1\u6027\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u7d50\u6676\u306e\u30d0\u30f3\u30c9\u56f3.png 383w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u78c1\u6027\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u7d50\u6676\u306e\u30d0\u30f3\u30c9\u56f3-300x197.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><figcaption class=\"wp-element-caption\">\u78c1\u6027\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u7d50\u6676\u306e\u30d0\u30f3\u30c9\u69cb\u9020<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"383\" height=\"314\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5149\u30ab\u30a4\u30e9\u30eb\u30a8\u30c3\u30b8\u72b6\u614b.png\" alt=\"\" class=\"wp-image-47\" style=\"width:215px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5149\u30ab\u30a4\u30e9\u30eb\u30a8\u30c3\u30b8\u72b6\u614b.png 383w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5149\u30ab\u30a4\u30e9\u30eb\u30a8\u30c3\u30b8\u72b6\u614b-300x246.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><figcaption class=\"wp-element-caption\">\u5149\u30ab\u30a4\u30e9\u30eb\u30a8\u30c3\u30b8\u30e2\u30fc\u30c9<\/figcaption><\/figure>\n<\/div>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"http:\/\/dx.doi.org\/10.1103\/PhysRevLett.93.083901\" data-type=\"link\" data-id=\"http:\/\/dx.doi.org\/10.1103\/PhysRevLett.93.083901\">&#8220;Hall Effect of Light&#8221;<br>Masaru Onoda, Shuichi Murakami, and Naoto Nagaosa<br>Physical Review Letters 93 (8) 083901-1 &#8211; 083901-4 (2004)<\/a><\/p>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"http:\/\/dx.doi.org\/10.1103\/PhysRevE.74.066610\" data-type=\"link\" data-id=\"http:\/\/dx.doi.org\/10.1103\/PhysRevE.74.066610\">&#8220;Geometrical aspects in optical wave-packet dynamics&#8221;<br>Masaru Onoda, Shuichi Murakami, and Naoto Nagaosa<br>Physical Review E 74 (6) 066610-1 &#8211; 066610-29 (2006)<\/a><\/p>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"http:\/\/dx.doi.org\/10.1103\/PhysRevLett.103.033903\" data-type=\"link\" data-id=\"http:\/\/dx.doi.org\/10.1103\/PhysRevLett.103.033903\">&#8220;Designing Spinning Bloch States in 2D Photonic Crystals for Stirring Nanoparticles&#8221;<br>Masaru Onoda and Tetsuyuki Ochiai<br>Physical Review Letters 103 (3) 033903-1 &#8211; 033903-4 (2009)<\/a><\/p>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"http:\/\/dx.doi.org\/10.1103\/PhysRevB.80.155103\" data-type=\"link\" data-id=\"http:\/\/dx.doi.org\/10.1103\/PhysRevB.80.155103\">&#8220;Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states&#8221;<br>Tetsuyuki Ochiai and Masaru Onoda<br>Physical Review B 80 (15) 155103-1 &#8211; 155103-9 (2009)<\/a><\/p>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<h4 class=\"wp-block-heading\">\u74b0\u72b6\u6e26\u69cb\u9020\u3092\u3082\u3064\u30c8\u30ed\u30a4\u30c0\u30eb\u5149\u6ce2\u675f\u306e\u4f1d\u642c\u7279\u6027<\/h4>\n\n\n\n<p>\u3000\u96fb\u78c1\u6ce2\u306e\u3082\u3064\u504f\u5149\u306e\u81ea\u7531\u5ea6\u306f\u5149\u5b50\u306e\u30b9\u30d4\u30f3\u89d2\u904b\u52d5\u91cf\u306b\u7531\u6765\u3057\u3066\u304a\u308a\u3001\u53e4\u5178\u7684\u306a\u901a\u4fe1\u306b\u304a\u3051\u308b\u591a\u91cd\u5316\u3084\u91cf\u5b50\u60c5\u5831\u901a\u4fe1\u306b\u304a\u3051\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u5b9f\u88c5\u306b\u5229\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6210\u529f\u4f8b\u306b\u304a\u3044\u3066\u5171\u901a\u3059\u308b\u306e\u306f\u3001\u72ed\u3044\u5468\u6ce2\u6570\u5e2f\u306b\u304a\u3051\u308b\u8907\u6570\u306e\u307b\u307c\u76f4\u4ea4\u3059\u308b\u30e2\u30fc\u30c9\u306e\u5229\u7528\u3067\u3059\u3002\u4e00\u65b9\u3001\u96fb\u78c1\u6ce2\u306f\u8ecc\u9053\u89d2\u904b\u52d5\u91cf\u3092\u3082\u3064\u3053\u3068\u3082\u3067\u304d\u3001\u30b9\u30d4\u30f3\u89d2\u904b\u52d5\u91cf\u306e\u81ea\u7531\u5ea6\u3092\u88dc\u5b8c\u3059\u308b\u3082\u306e\u3068\u3057\u3066\u671f\u5f85\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u540c\u69d8\u306e\u8003\u3048\u65b9\u306e\u3055\u3089\u306a\u308b\u62e1\u5f35\u3092\u63a2\u6c42\u3059\u308b\u3053\u3068\u306f\u610f\u7fa9\u6df1\u3044\u3068\u8003\u3048\u307e\u3059\u3002<br>\u3000\u307e\u305f\u3001\u5fae\u7d30\u52a0\u5de5\u6280\u8853\u306e\u9032\u6b69\u306b\u3088\u308a\u3001\u96fb\u78c1\u30e2\u30fc\u30c9\u306e\u4f4d\u76f8\u5e7e\u4f55\u5b66\u7684\u7279\u6027\u3092\u5229\u7528\u3057\u305f\u65b0\u3057\u3044\u30bf\u30a4\u30d7\u306e\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u6750\u6599\u306e\u8a2d\u8a08\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u30d5\u30a9\u30c8\u30cb\u30c3\u30af\u7d50\u6676\u306b\u304a\u3051\u308b\u5149\u5b50\u7cfb\u7248\u306e\u5e7e\u4f55\u5b66\u7684\u30db\u30fc\u30eb\u52b9\u679c\u3084\u91cf\u5b50\u30db\u30fc\u30eb\u52b9\u679c\u3001\u7d50\u6676\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u7d76\u7e01\u4f53\u306a\u3069\u304c\u63d0\u6848\u3055\u308c\u3001\u305d\u306e\u3044\u304f\u3064\u304b\u306f\u5b9f\u73fe\u3055\u308c\u3066\u3044\u307e\u3059\u3002<br>\u3000\u4ee5\u4e0a\u306e\u9032\u5c55\u306b\u7740\u60f3\u3092\u5f97\u3066\u3001\u8ecc\u9053\u89d2\u904b\u52d5\u91cf\u306b\u95a2\u9023\u3057\u305f\u7dda\u72b6\u306e\u6e26\u3060\u3051\u3067\u306a\u304f\u3001\u74b0\u72b6\u306e\u6e26\u3092\u6301\u3064\u65b0\u3057\u3044\u30c8\u30ed\u30a4\u30c0\u30eb\u5149\u6ce2\u675f\u306e\u53ef\u80fd\u6027\u3092\u63d0\u6848\u3057\u307e\u3057\u305f\u3002\u751f\u6210\u65b9\u6cd5\u306e\u4e00\u3064\u306e\u6848\u3068\u3057\u3066\u3001\u5149\u5b50\u7cfb\u7248\u7d50\u6676\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u7d76\u7e01\u4f53\u306e\u8868\u9762\u306e\u5229\u7528\u304c\u8003\u3048\u3089\u308c\u307e\u3059\u304c\u3001\u307e\u3060\u5341\u5206\u306a\u691c\u8a3c\u306f\u3067\u304d\u3066\u3044\u307e\u305b\u3093\u3002\u3053\u3053\u3067\u306f\u307e\u305a\u305d\u306e\u4f1d\u642c\u7279\u6027\u3092\u6570\u5024\u7684\u306b\u8abf\u3079\u308b\u305f\u3081\u306b\u3001\u8907\u6570\u306e\u7a2e\u985e\u306e\u6e26\u3092\u6301\u3064Maxwell\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u69cb\u7bc9\u3059\u308b\u305f\u3081\u306e\u7c21\u5358\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u793a\u3057\u307e\u3057\u305f\u3002\u3055\u3089\u306b\u3001\u5747\u8cea\u306a\u8a98\u96fb\u4f53\u9593\u306e\u754c\u9762\u306b\u304a\u3051\u308b\u53cd\u5c04\u3068\u5c48\u6298\u306b\u5bfe\u3059\u308b\u305d\u306e\u3088\u3046\u306a\u6ce2\u675f\u306e\u5b89\u5b9a\u6027\u3084\u3001\u6e26\u306e\u69cb\u9020\u306b\u898b\u3089\u308c\u308b\u4f4d\u76f8\u5e7e\u4f55\u5b66\u7684\u306a\u7279\u6027\u304c\u3001\u53cd\u5c04\u3084\u5c48\u6298\u3092\u901a\u3058\u3066\u3069\u306e\u3088\u3046\u306b\u5909\u63db\u3059\u308b\u306e\u304b\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<div class=\"wp-block-group is-content-justification-center is-nowrap is-layout-flex wp-container-core-group-is-layout-14 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"781\" height=\"310\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u96fb\u5b50\u7cfb\u30d8\u30ea\u30ab\u30eb\u8868\u9762\u72b6\u614b\u3068\u5149\u5b50\u7cfb\u30d8\u30ea\u30ab\u30eb\u8868\u9762\u30e2\u30fc\u30c9.png\" alt=\"\" class=\"wp-image-48\" style=\"width:437px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u96fb\u5b50\u7cfb\u30d8\u30ea\u30ab\u30eb\u8868\u9762\u72b6\u614b\u3068\u5149\u5b50\u7cfb\u30d8\u30ea\u30ab\u30eb\u8868\u9762\u30e2\u30fc\u30c9.png 781w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u96fb\u5b50\u7cfb\u30d8\u30ea\u30ab\u30eb\u8868\u9762\u72b6\u614b\u3068\u5149\u5b50\u7cfb\u30d8\u30ea\u30ab\u30eb\u8868\u9762\u30e2\u30fc\u30c9-300x119.png 300w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u96fb\u5b50\u7cfb\u30d8\u30ea\u30ab\u30eb\u8868\u9762\u72b6\u614b\u3068\u5149\u5b50\u7cfb\u30d8\u30ea\u30ab\u30eb\u8868\u9762\u30e2\u30fc\u30c9-768x305.png 768w\" sizes=\"(max-width: 781px) 100vw, 781px\" \/><figcaption class=\"wp-element-caption\">\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u7d76\u7e01\u4f53\u30d8\u30ea\u30ab\u30eb\u8868\u9762\u72b6\u614b\uff08\u5de6\uff09\u3068\u305d\u306e\u5149\u5b50\u7cfb\u7248\uff08\u53f3\uff09\u306e\u6982\u5ff5\u56f3<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-content-justification-center is-nowrap is-layout-flex wp-container-core-group-is-layout-15 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"804\" height=\"227\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u74b0\u72b6\u6e26\u69cb\u9020\u3092\u3082\u3064\u30c8\u30ed\u30a4\u30c0\u30eb\u578b\u5149\u6ce2\u675f.png\" alt=\"\" class=\"wp-image-49\" style=\"width:480px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u74b0\u72b6\u6e26\u69cb\u9020\u3092\u3082\u3064\u30c8\u30ed\u30a4\u30c0\u30eb\u578b\u5149\u6ce2\u675f.png 804w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u74b0\u72b6\u6e26\u69cb\u9020\u3092\u3082\u3064\u30c8\u30ed\u30a4\u30c0\u30eb\u578b\u5149\u6ce2\u675f-300x85.png 300w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u74b0\u72b6\u6e26\u69cb\u9020\u3092\u3082\u3064\u30c8\u30ed\u30a4\u30c0\u30eb\u578b\u5149\u6ce2\u675f-768x217.png 768w\" sizes=\"(max-width: 804px) 100vw, 804px\" \/><figcaption class=\"wp-element-caption\">\u74b0\u72b6\u6e26\u69cb\u9020\u3092\u3082\u3064\u30c8\u30ed\u30a4\u30c0\u30eb\u5149\u6ce2\u675f\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u5bc6\u5ea6\uff08\u8272\uff09\u3068\u30a8\u30cd\u30eb\u30ae\u30fc\u6d41\uff08\u77e2\u5370\uff09<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-content-justification-center is-nowrap is-layout-flex wp-container-core-group-is-layout-16 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"927\" height=\"160\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5e73\u5766\u306a\u754c\u9762\u306b\u304a\u3051\u308b\u53cd\u5c04.png\" alt=\"\" class=\"wp-image-50\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5e73\u5766\u306a\u754c\u9762\u306b\u304a\u3051\u308b\u53cd\u5c04.png 927w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5e73\u5766\u306a\u754c\u9762\u306b\u304a\u3051\u308b\u53cd\u5c04-300x52.png 300w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5e73\u5766\u306a\u754c\u9762\u306b\u304a\u3051\u308b\u53cd\u5c04-768x133.png 768w\" sizes=\"(max-width: 927px) 100vw, 927px\" \/><figcaption class=\"wp-element-caption\">\u5e73\u5766\u306a\u754c\u9762\u306b\u304a\u3051\u308b\u53cd\u5c04\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-content-justification-center is-nowrap is-layout-flex wp-container-core-group-is-layout-17 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"924\" height=\"160\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5e73\u5766\u306a\u754c\u9762\u306b\u304a\u3051\u308b\u5c48\u6298.png\" alt=\"\" class=\"wp-image-51\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5e73\u5766\u306a\u754c\u9762\u306b\u304a\u3051\u308b\u5c48\u6298.png 924w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5e73\u5766\u306a\u754c\u9762\u306b\u304a\u3051\u308b\u5c48\u6298-300x52.png 300w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5e73\u5766\u306a\u754c\u9762\u306b\u304a\u3051\u308b\u5c48\u6298-768x133.png 768w\" sizes=\"(max-width: 924px) 100vw, 924px\" \/><figcaption class=\"wp-element-caption\">\u5e73\u5766\u306a\u754c\u9762\u306b\u304a\u3051\u308b\u5c48\u6298\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/figcaption><\/figure>\n<\/div>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"http:\/\/dx.doi.org\/10.3390\/app9071468\" data-type=\"link\" data-id=\"http:\/\/dx.doi.org\/10.3390\/app9071468\">&#8220;Topological Photonic Media and the Possibility of Toroidal Electromagnetic Wavepackets&#8221;<br>Masaru Onoda<br>Applied Sciences 9 (7) 1468-01 &#8211; 1468-19 (2019)<\/a><\/p>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<h4 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decoding=\"async\" width=\"499\" height=\"268\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u96fb\u8377\u3068\u30b9\u30d4\u30f3\u306e\u5206\u5e03.png\" alt=\"\" class=\"wp-image-53\" style=\"width:334px;height:auto\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u96fb\u8377\u3068\u30b9\u30d4\u30f3\u306e\u5206\u5e03.png 499w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u96fb\u8377\u3068\u30b9\u30d4\u30f3\u306e\u5206\u5e03-300x161.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><figcaption class=\"wp-element-caption\">\u96fb\u8377\u3068\u30b9\u30d4\u30f3\u306b\u95a2\u3059\u308b\u89e3\u6790\u89e3\uff08\u8d64\uff09\u3068\u6570\u5024\u89e3\uff08\u9ed2\uff09\u306e\u6bd4\u8f03<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-nowrap is-layout-flex wp-container-core-group-is-layout-20 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"483\" height=\"237\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5f37\u3044\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u7d76\u7e01\u4f53.png\" alt=\"\" class=\"wp-image-56\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5f37\u3044\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u7d76\u7e01\u4f53.png 483w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5f37\u3044\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u7d76\u7e01\u4f53-300x147.png 300w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><figcaption class=\"wp-element-caption\">\u5f37\u3044\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u7d76\u7e01\u4f53(100)\u9762(111)\u9762\u306e\u30d0\u30f3\u30c9\u56f3<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"499\" height=\"245\" src=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5f31\u3044\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u7d76\u7e01\u4f53.png\" alt=\"\" class=\"wp-image-57\" srcset=\"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5f31\u3044\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u7d76\u7e01\u4f53.png 499w, http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-content\/uploads\/2024\/06\/\u5f31\u3044\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u7d76\u7e01\u4f53-300x147.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><figcaption class=\"wp-element-caption\">\u5f31\u3044\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u7d76\u7e01\u4f53(100)\u9762(111)\u9762\u306e\u30d0\u30f3\u30c9\u56f3<\/figcaption><\/figure>\n<\/div>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"http:\/\/dx.doi.org\/10.1103\/PhysRevB.106.245409\" data-type=\"link\" data-id=\"http:\/\/dx.doi.org\/10.1103\/PhysRevB.106.245409\">&#8220;Analytical solutions of topological surface states in a series of lattice models&#8221;<br>Masaru Onoda<br>Physical Review B 106 (24) 2454091-1 &#8211; 245409-6 (2022)<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u7814\u7a76\u80cc\u666f \u3000\u96fb\u5b50\u304c\u91cf\u5b50\u529b\u5b66\u7684\u306a\u7c92\u5b50\uff08\u91cf\u5b50\uff09\u3067\u3042\u308b\u3053\u3068\u306e\u7279\u5fb4\u306e\u4e00\u3064\u3068\u3057\u3066\u3001\u56fa\u4f53\u7d50\u6676\u306a\u3069\u306e\u5468\u671f\u69cb\u9020\u4e2d\u306b\u73fe\u308c\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u5206\u5e03\u306e\u30d0\u30f3\u30c9\u69cb\u9020\uff08\u30a8\u30cd\u30eb\u30ae\u30fc\u30b9\u30da\u30af\u30c8\u30eb\u306b\u304a\u3051\u308b\u7981\u5236\u5e2f\u306e\u5b58\u5728\uff09\u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u30d0\u30f3\u30c9\u69cb\u9020\u306f\u3001\u96fb\u5b50\u306e\u5b58\u5728\u78ba [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"_links":{"self":[{"href":"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-json\/wp\/v2\/pages\/11"}],"collection":[{"href":"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-json\/wp\/v2\/comments?post=11"}],"version-history":[{"count":26,"href":"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-json\/wp\/v2\/pages\/11\/revisions"}],"predecessor-version":[{"id":87,"href":"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-json\/wp\/v2\/pages\/11\/revisions\/87"}],"wp:attachment":[{"href":"http:\/\/www.math.akita-u.ac.jp\/onoda\/wp-json\/wp\/v2\/media?parent=11"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}