{"id":25386,"date":"2016-09-05T00:38:38","date_gmt":"2016-09-04T16:38:38","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=25386"},"modified":"2018-08-03T15:13:46","modified_gmt":"2018-08-03T07:13:46","slug":"%e3%80%90%e7%89%a9%e7%90%86%e4%b8%96%e7%95%8c%e3%80%91%e9%87%8f%e5%ad%90%e9%9c%8d%e7%88%be%e6%95%88%e6%87%89%ef%bc%88%e4%b8%89%ef%bc%89%ef%bc%9a%e8%a4%87%e5%90%88%e8%b2%bb%e7%b1%b3%e5%ad%90","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=25386","title":{"rendered":"\u3010\u7269\u7406\u4e16\u754c\u3011\u91cf\u5b50\u970d\u723e\u6548\u61c9\uff08\u4e09\uff09\uff1a\u8907\u5408\u8cbb\u7c73\u5b50"},"content":{"rendered":"

\u25a0\u5728 Laughlin \u6ce2\u51fd\u6578\u5f8c\uff0cJ. Jain \u63d0\u51fa\u4e86\u8907\u5408\u8cbb\u7c73\u5b50\u7684\u6982\u5ff5\uff0c\u5c07\u6574\u6578\u91cf\u5b50\u970d\u723e\u6548\u61c9\u8207\u5206\u6578\u91cf\u5b50\u970d\u723e\u6548\u61c9\u7d50\u5408\u5728\u4e00\u500b\u6846\u67b6\u4e0b\uff0c\u4e26\u6210\u70ba\u7814\u7a76\u91cf\u5b50\u970d\u723e\u6548\u61c9\u7684\u4e00\u500b\u5178\u7bc4\u3002<\/strong><\/span><\/p>\n

\"\u672c\u5716\u5f15\u81ea1990\u5e746\u670822\u300a\u79d1\u5b78\u300b\u96dc\u8a8c\u5c01\u9762\uff0ccourtesy
\u672c\u5716\u5f15\u81ea1990\u5e746\u670822\u300a\u79d1\u5b78\u300b\u96dc\u8a8c\u5c01\u9762\uff0ccourtesy of illustration T. S. Duff and T. Kovacs, AT&T Bell Laboratories<\/figcaption><\/figure>\n

\u64b0\u6587\uff5c<\/strong>\u856d\u7dad\u7ff0<\/p>\n

\u5118\u7ba1 Laughlin \u6ce2\u51fd\u6578\u5f9e\u5b9a\u91cf\u7684\u89d2\u5ea6\u63d0\u4f9b\u4e86\u7576\u6642\u4eba\u5011\u4e86\u89e3\u67d0\u4e9b\u5206\u6578\u970d\u723e\u614b\u7684\u51fa\u767c\u9ede\uff0c\u5b83\u4e26\u4e0d\u7a31\u5f97\u4e0a\u662f\u4e00\u500b\u5b8c\u6574\u7684\u300c\u6545\u4e8b\u300d\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5b83\u7684\u6210\u529f\u4e5f\u591a\u4fb7\u9650\u65bc1\/3. 1\/5 \u7b49\u5206\u6578\uff0c\u800c\u4e0d\u6db5\u84cb\u5176\u4ed6\u59822\/5, 3\/7 \u7b49\u4e5f\u5728\u5be6\u9a57\u4e2d\u88ab\u767c\u73fe\u7684\u72c0\u614b\u3002<\/p>\n

Jain \u57281989 \u5e74\u63d0\u51fa\u6240\u8b02\u8907\u5408\u8cbb\u7c73\u5b50\uff08composite fermion\uff09\u7684\u6982\u5ff5 [\u53c31]\uff0c\u5e0c\u671b\u4ee5\u5b83\u4f86\u63d0\u4f9b\u6574\u6578\u91cf\u5b50\u970d\u723e\u6548\u61c9\u8207\u5206\u6578\u91cf\u5b50\u970d\u723e\u6548\u61c9\u4e00\u500b\u7d71\u4e00\u7684\u5716\u50cf\u3002\u9867\u540d\u601d\u7fa9\uff0c\u76f8\u5c0d\u65bc\u96fb\u5b50\u9019\u7a2e\u300c\u57fa\u672c\u7c92\u5b50\u300d\uff0c\u8907\u5408\u8cbb\u7c73\u5b50\u53ef\u4ee5\u88ab\u7406\u89e3\u6210\u662f\u96fb\u5b50\u7d81\u4e0a\u5176\u4ed6\u5143\u7d20\uff0c\u5728\u66f4\u65e9\u7684\u6838\u5b50\u7269\u7406\u4e2d\uff0c\u4e00\u500b\u6838\u5b50\u4e5f\u53ef\u8996\u70ba\u8907\u5408\u7c92\u5b50\uff08composite particle\uff09\uff08\u5118\u7ba1\u4e0d\u4e00\u5b9a\u662f\u8cbb\u7c73\u5b50\uff09\u90a3\u6642\u5176\u4ed6\u5143\u7d20\u53ef\u80fd\u662f\u8cea\u5b50\u3001\u6216\u4e2d\u5b50\uff0c\u800c\u5728\u91cf\u5b50\u970d\u723e\u6548\u61c9\u4e2d\uff0c\u9019\u500b\u5143\u7d20\u62bd\u8c61\u7684\u591a\uff1a\u6211\u5011\u8981\u5c07\u96fb\u5b50\u548c\u78c1\u901a\u91cf[1]<\/a>\u7d81\u5728\u4e00\u8d77\uff01<\/p>\n

\u9019\u500b\u4e3b\u610f\u80cc\u5f8c\u7684\u52d5\u6a5f\u6216\u8005\u53ef\u4ee5\u9019\u9ebc\u7406\u89e3\uff1a\u5728\u524d\u9762\u5169\u7bc7\u6587\u7ae0\u4e2d\u6211\u5011\u90fd\u8ac7\u5230\u4e86\u4f4f\u516c\u5bd3\u9019\u500b\u6bd4\u55bb\uff0c\u8981\u628a\u516c\u5bd3\u8ddf\u7cfb\u7d71\u4e2d\u727d\u6d89\u7684\u7269\u7406\u91cf\u7d50\u5408\uff0c\u78c1\u5834\u9019\u500b\u5c40\u57df\u7684\u91cf\u4e26\u4e0d\u5408\u9069\uff0c\u76f8\u5c0d\u800c\u8a00\uff0c\u7e3d\u78c1\u901a\u91cf\u8207\u6574\u500b\u7cfb\u7d71\u5927\u5c0f\uff08\u5373\u516c\u5bd3\u623f\u9593\u6578\u76ee\uff09\u6210\u6b63\u6bd4\uff0c\u662f\u4e00\u500b\u6bd4\u8f03\u597d\u5c0d\u61c9\u7684\u91cf\u3002\u5e73\u5747\u4f86\u8aaa\u6211\u5011\u53ef\u4ee5\u60f3\u50cf\u6bcf\u500b\u623f\u9593\u90fd\u53ef\u4ee5\u6709\u4e00\u500b\u671d\u4e0a\u7684\u5c0f\u7bad\u982d\u4f86\u4ee3\u8868\uff0c\u9019\u500b\u7bad\u982d\u5e36\u6709\u4e00\u500b\u78c1\u901a\u91cf\u7684\u55ae\u5143[2]<\/a>\uff0c\u7d93\u904e\u8a08\u7b97\u5b83\u7684\u5927\u5c0f\u662f hc\/e\uff0c\u5176\u4e2d h, c, e \u5206\u5225\u662f\u666e\u6717\u514b\u5e38\u6578\u3001\u5149\u901f\u8207\u96fb\u5b50\u96fb\u91cf\u3002<\/p>\n

Jain \u6240\u8b02\u7684\u8907\u5408\u8cbb\u7c73\u5b50\u5c31\u662f\u5c07\u4e00\u500b\u96fb\u5b50\u7d81\u4e0a 2, 4, 6, \u2026\u7b49\u5076\u6578\u500b\u78c1\u901a\u91cf\u7bad\u982d\u5f62\u6210\u7684\u65b0\u8cbb\u7c73\u5b50[3]<\/a>\u3002<\/p>\n

\u9019\u6a23\u505a\u6703\u7372\u5f97\u4ec0\u9ebc\u7d50\u679c\u5462\uff1f\u9996\u5148\u6211\u5011\u8003\u616e1\/3\u586b\u6eff\u7684\u5206\u6578\u970d\u723e\u614b\uff0c\u5f9e\u5b9a\u7fa9\u4e0a\u77e5\u9053\uff0c\u9019\u500b\u614b\u4e2d\u82e5\u6709N\u500b\u96fb\u5b50\uff0c\u5c31\u6703\u67093N\u500b\u623f\u9593\uff08\u5c0f\u7bad\u982d\uff09\uff0c\u5982\u679c\u5c07\u6bcf\u500b\u96fb\u5b50\u90fd\u7d81\u4e0a2\u500b\u78c1\u901a\u91cf\u5c0f\u7bad\u982d\u5f62\u6210\u4e00\u500b\u8907\u5408\u8cbb\u7c73\u5b50\uff08\u7c21\u7a31CF2\uff09\uff0c\u6574\u500b\u7cfb\u7d71\u5c31\u6703\u5269\u4e0bN\u500b\u8907\u5408\u8cbb\u7c73\u5b50\u8207N\u500b\u78c1\u901a\u91cf\u5c0f\u7bad\u982d\uff0c\u9019\u4e0d\u662f\u5225\u7684\uff0c\u5c31\u662f\u6574\u6578\u91cf\u5b50\u970d\u723e\u6548\u61c9\u4e2d\u586b\u6eff\u7b2c\u4e00\u5c64\u862d\u9053\u968e\u7684\u72c0\u614b\uff01\uff08\u898b\u5716\u4e00\uff09<\/p>\n

\"fig1\"<\/p>\n

\u66f4\u9032\u4e00\u6b65\u4f86\u8aaa\uff0c\u6211\u5011\u7528CF2\u7d44\u6210\u4e00\u500b\u586b\u6effn\u5c64\u862d\u9053\u968e\u7684\u6574\u6578\u91cf\u5b50\u970d\u723e\u614b\uff0c\u5373\u7cfb\u7d71\u4e2d\u6703\u6709N\u500b\u671d\u4e0a\u7bad\u982d\u4ee5\u53canN\u500bCF2\u3002\u63a5\u8457\u5c07\u6bcf\u500bCF2\u62c6\u89e3\u6210\u4e00\u500b\u96fb\u5b50\u8ddf2\u500b\u5c0f\u7bad\u982d\uff0c\u5247\u6574\u500b\u7cfb\u7d71\u8b8a\u6210\u6709nN\u500b\u96fb\u5b50\u8207(2n+1)N\u500b\u5c0f\u7bad\u982d\uff0c\u5c0d\u61c9\u5230\u7684\u5c31\u662fn\/(2n+1)=1\/3, 2\/5, 3\/7,\u2026\u7684\u5206\u6578\u970d\u723e\u6548\u61c9\u614b\u3002\u540c\u6a23\u7684\u904a\u6232\u4e5f\u53ef\u4ee5\u9019\u9ebc\u73a9\uff1a\u7528CF2\u7d44\u6210\u4e00\u500b\u586b\u6effn+1\u5c64\u862d\u9053\u968e\u7684\u6574\u6578\u91cf\u5b50\u970d\u723e\u614b\uff0c\u4f46\u5c07\u78c1\u5834\u7684\u65b9\u5411\u53cd\u904e\u4f86\uff0c\u7cfb\u7d71\u4e2d\u6703\u6709N\u500b\u300c\u671d\u4e0b\u5c0f\u7bad\u982d\u300d\u4ee5\u53ca(n+1)N\u500bCF2\uff0c\u5c07\u8907\u5408\u8cbb\u7c73\u5b50\u62c6\u89e3\u56de\u96fb\u5b50\u548c\u671d\u4e0a\u5c0f\u7bad\u982d\u5f8c\uff0c\u9019\u500b\u7cfb\u7d71\u6703\u5c0d\u61c9\u5230(n+1)\/(2n+1)=1, 2\/3, 3\/5, 4\/7,\u2026\u7b49\u614b\u3002 \uff08\u898b\u5716\u4e8c\uff09<\/p>\n

\"fig2\"<\/p>\n

\u9019\u5169\u500b\u5e8f\u5217\u7a31\u70baJain \u5e8f\u5217 \uff0c\u900f\u904e\u8907\u5408\u8cbb\u7c73\u5b50\u7684\u5716\u50cf\uff0cJain\u4e0d\u50c5\u5c07\u6574\u6578\u8207\u5206\u6578\u91cf\u5b50\u970d\u723e\u6548\u61c9\u7d0d\u9032\u540c\u4e00\u500b\u6846\u67b6\uff0c\u6307\u51fa\u300c\u96fb\u5b50\u7684\u5206\u6578\u970d\u723e\u6548\u61c9\u5373\u8907\u5408\u8cbb\u7c73\u5b50\u7684\u6574\u6578\u970d\u723e\u6548\u61c9\u3002\u300d\u4e5f\u6bd4\u55ae\u7d14\u7684 Laughlin \u6ce2\u51fd\u6578\u89e3\u91cb\u4e86\u66f4\u591a\u5be6\u9a57\u4e0a\u767c\u73fe\u7684\u5206\u6578\u3002<\/p>\n

\u7136\u800c\uff0c\u9019\u500b\u7406\u8ad6\u4f9d\u820a\u4e0d\u662f\u5f88\u5b8c\u5099\u3002\u5176\u4e2d\u4e00\u500b\u5f88\u986f\u7136\u7684\u7f3a\u9677\u662f\uff0c\u5728\u970d\u723e\u6548\u61c9\u7684\u554f\u984c\u4e2d\uff0c\u539f\u5247\u4e0a\u5728\u78c1\u5834\u5920\u5927\u7684\u60c5\u6cc1\u4e0b\uff0c\u6240\u6709\u7684\u7269\u7406\u61c9\u8a72\u53ea\u8ddf\u6700\u4f4e\u5c64\u7684\u862d\u9053\u968e\u6709\u95dc\uff0c\u4f46\u5c07\u554f\u984c\u8b8a\u6210\u8907\u5408\u8cbb\u7c73\u5b50\u7684\u6574\u6578\u970d\u723e\u6548\u61c9\u6642\uff0c\u4e0d\u53ef\u907f\u514d\u5730\u6703\u4f7f\u7528\u5230\u9ad8\u5c64\u862d\u9053\u968e\uff0c\u56e0\u800c\u5728\u9032\u884c\u8a08\u7b97\u6642\u6211\u5011\u5fc5\u9808\u624b\u52d5\u5730\u53bb\u5c07\u9ad8\u5c64\u862d\u9053\u968e\u6210\u4efd\u53bb\u9664\u3002\u4e5f\u56e0\u6b64\u6709\u5176\u4ed6\u5b78\u8005\u5617\u8a66\u5f9e\u5176\u4ed6\u89d2\u5ea6\uff0c\u53bb\u5efa\u69cb\u6709\u6548\u7406\u8ad6\u6216\u6ce2\u51fd\u6578 [\u53c32, 3]\u3002<\/p>\n

\u53e6\u5916\u4e00\u500b\u7269\u7406\u5b78\u5bb6\u611f\u8208\u8da3\u7684\u9ede\u662f\uff0cJain \u5e8f\u5217\u5728\u00a0 n \u5728\u7121\u7aae\u5927\u7684\u6975\u9650\u662f 1\/2\uff0c\u5982\u679c\u5957\u7528\u4e0a\u9762\u8cbc\u9644\u78c1\u901a\u91cf\u7684\u8ad6\u8ff0\uff0c\u7cfb\u7d71\u4e2d\u6709 2N \u500b\u671d\u4e0a\u5c0f\u7bad\u982d\u8207 N \u500b\u96fb\u5b50\uff0c\u5728\u8f49\u63db\u6210 CF2 \u5f8c\uff0c\u6703\u8b8a\u6210 N\u500bCF2\u4f46\u300c\u6c92\u6709\u78c1\u5834\u300d\u3002B. Halperin\u3001P. Lee \u548c N. Read \u9996\u5148\u57281993\u5e74\u63d0\u51fa\u73fe\u4eca\u4eba\u7a31\u7684 HLR \u7406\u8ad6\u4f86\u63cf\u8ff0\u9019\u500b 1\/2 \u586b\u6eff\u7684\u614b [\u53c34]\uff0c\u4f46\u76f4\u81f3 20 \u5e74\u5f8c\uff0c\u70ba\u4e86\u91d0\u6e05\u554f\u984c\u4e2d\u4e0d\u53ef\u6216\u7f3a\u7684\u5c0d\u7a31\u6027\uff0c\u4e00\u500b\u65b0\u7684\u767c\u60f3\u518d\u4e00\u6b21\u5730\u9019\u500b 1\/2 \u586b\u6eff\u7684\u614b\u767c\u51fa\u885d\u64ca\u3002<\/p>\n

 <\/p>\n

\u53c3\u8003\u8cc7\u6599\uff1a
\n<\/strong>1. K. Jain, Phys. Rev. Lett. 63<\/strong>, 199 (1989).
\n2. N. Ginocchio, and W. C. Haxton, Phys. Rev. Lett. 77<\/strong>, 1568 (1996).
\n3. H. Hansson, M. Hermanns, S. H. Simon, and S. F. Viefers, arXiv: 1601.01697 (2016).
\n4. I. Halperin, P. A. Lee and N. Read, Phys. Rev. B 47<\/strong>,7312 (1993) .<\/p>\n

\u8a3b\u91cb\uff1a
\n<\/strong>[1]<\/a> \u570b\u4e2d\u7406\u5316\u6211\u5011\u6703\u5b78\u5230\u78c1\u901a\u91cf\u7684\u8b8a\u5316\u6703\u7522\u751f\u96fb\u52d5\u52e2\uff08\u96fb\u58d3\u5dee\uff09\uff0c\u9019\u662f\u767c\u96fb\u6a5f\u7684\u57fa\u672c\u539f\u7406\uff0c\u8ddf\u9019\u908a\u8b1b\u7684\u78c1\u901a\u91cf\u662f\u4e00\u6a23\u7684\u6771\u897f\uff0c\u7d04\u7565\u800c\u8a00\u5373\u78c1\u5834\u4e58\u4e0a\u9762\u7a4d\u3002
\n[2]<\/a> \u4e5f\u5c31\u662f\u78c1\u5834\u4e58\u4e0a\u9762\u7a4d\u9664\u4ee5\u6bcf\u500b\u862d\u9053\u968e\u7684\u623f\u9593\u6578\u76ee\u3002
\n[3]<\/a> \u975e\u5f97\u662f\u5076\u6578\u500b\u78c1\u901a\u91cf\u55ae\u5143\u662f\u6709\u91cd\u8981\u7406\u7531\u7684\uff0c\u4f46\u8981\u8b1b\u8ff0\u9019\u500b\u5927\u6982\u53c8\u5f97\u53e6\u5916\u5beb\u4e00\u7bc7\u6587\u7ae0\uff0c\u5728\u91cf\u5b50\u7269\u7406\u4e2d\u6709\u4e00\u500b\u6240\u8b02Aharonov-Bohm\u6548\u61c9\uff0c\u6307\u51fa\u5728\u6e96\u4e8c\u7dad\u7cfb\u7d71\u4e2d\uff0c\u4e00\u500b\u7c92\u5b50\u7684\u6ce2\u51fd\u6578\u7e5e\u904e\u4e00\u500b\u78c1\u901a\u91cf\u6642\u6703\u4e58\u4e0a\u4e00\u500b\u5927\u5c0f\u70ba1\u7684\u8907\u6578\u3002\u7c21\u55ae\u5730\u8aaa\uff0c\u8cbb\u7c73\u5b50\u8981\u9ecf\u4e0a\u5076\u6578\u500b\u78c1\u901a\u91cf\u55ae\u5143hc\/e\uff0c\u624d\u80fd\u9084\u662f\u4e00\u500b\u8cbb\u7c73\u5b50\u3002<\/p>\n

--
\n\u4f5c\u8005\uff1a\u856d\u7dad\u7ff0\uff0c\u81fa\u5927\u7269\u7406\u7cfb\u7562\u696d\u5f8c\u9003\u5230\u829d\u52a0\u54e5\uff0c\u5439\u98a8\u5439\u96ea\u4e4b\u9918\uff0c\u505a\u7814\u7a76\u8b80\u535a\u58eb\u73ed\u3002\u53ef\u60dc\u96e2\u958b\u81fa\u7063\u5f8c\u7121\u6d77\u53ef\u770b\uff0c\u53ea\u80fd\u5728\u5bc6\u897f\u6839\u6e56\u65c1\u63c0\u4e00\u65b9\u5824\u5cb8\uff0c\u507d\u88dd\u6210\u770b\u6d77\u7684\u4eba\u3002\u79d1\u6559\u4e2d\u5fc3\u7279\u7d04\u5beb\u624b\uff0c\u5f9e\u4e8b\u79d1\u666e\u6587\u7ae0\u5beb\u4f5c\u3002<\/span><\/strong><\/p>\n

 <\/p>\n

\"\u52a0\u5165\u597d\u53cb\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

\u25a0\u5728 Laughlin \u6ce2\u51fd\u6578\u5f8c\uff0cJ. <\/p>\n","protected":false},"author":20,"featured_media":25420,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3293,39],"tags":[2794,2793,313,2653],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2015\/09\/\u672a\u547d\u540d.png","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/25386"}],"collection":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=25386"}],"version-history":[{"count":5,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/25386\/revisions"}],"predecessor-version":[{"id":32650,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/25386\/revisions\/32650"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/25420"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25386"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25386"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25386"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}