Quantized Conductance in Metallic Nanocontacts.

Abstract

When the contact size becomes comparable to electron Fermi wavelength, the electron transport through such a small point contact shows various quantum phenomena. Quantization of conductance is a marked example of such quantum effects. In the case of metal contacts, one has to fabricate atom-sized contacts for observing the quantized conductance. However, thanks to recent developments in nanotechnology, it is now possible to investigate experimentally some properties of quantized conductance in various metallic nanocontacts. In this article, I will give a brief survey of previous studies of quantized conductance in metal nanocontacts. Since this field is relatively new, many aspects of quantized conductance still remain to be identified. 1.-Ê Žq‰»ƒR ƒ" ƒ_ ƒNƒ^ ƒ" ƒX‚É ‚ ‚¢ ‚Ä •@ ‹à '®‚Ì 'ï •R ‚Í,"` "± "d Žq‚ª ƒt ƒI ƒmƒ"‚â •s •ƒ •¨ •EOE‹•»-± ŠE‚È ‚Ç ‚É ‚ae ‚èŽU-•‚³ ‚ê ‚é ‚± ‚AE‚É ‚ae ‚Á‚Ä• ¶ ‚ ¶ ‚é •B "` "± "d Žq ‚ª 'S ‚-ŽU-•‚³ ‚ê ‚È ‚¢-•'z "I ‚È ‹à '®‚ª ‚ ‚é ‚AE ‚· ‚é ‚AE,‚» ‚Ì 'ï •R ‚Í ƒ[ ƒ• ‚É‚È ‚è,ƒR ƒ"ƒ_ ƒNƒ^ ƒ" ƒX‚Í-³ OEÀ 'å ‚É‚È ‚é •B ‚à ‚¿ ‚ë ‚ñ OE»ŽÀ‚Ì ‹à '®‚Å ‚Í "d Žq ‚Í •â ‚¦ ŠÔ‚È ‚-ŽU-•‚ð Žó ‚¯ ‚Ä‚¨ ‚è,ŽU-•‚Ì • ‡ ŠÔ‚É"d Žq‚ª •i ‚Þ ‹-£‚Í ‚½‚©‚¾‚©•" •m‚Å ‚ ‚é •B ‚µ ‚© ‚µ‹t ‚É•l ‚¦ ‚é ‚AE,10nm'ö "x ˆÈ ‰º‚Ì ‹à '®ƒi ƒm ƒ• ƒCƒ" •[ ‚ð •ì •» ‚µ ‚Ä‚» ‚̈ê‚̈ê '[ ‚© ‚ç"d Žq‚ð '• "ü ‚· ‚é ‚AE,"d Žq‚Í "r ' † ‚Å‚Í ŽU-•‚³ ‚ê ‚¸‚É‚¸‚É'¼'[ ‚É 'B ‚· ‚é(ƒo ƒŠƒXƒe ƒBƒb ƒN"` "±)‚Ì ‚Å,ƒi ƒmƒ• ƒCƒ" •[ ‚Ì ƒRƒ" ƒ_ ƒNƒ^ ƒ" ƒX‚Í-³ OEÀ 'å ‚É‚È ‚é ‚AE-\'z ‚³ ‚ê ‚é •B ‚AE‚± ‚ë ‚ÅŽÀ•Û‚É 'ª 'è ‚³ ‚ê ‚é ƒRƒ"ƒ_ ƒNƒ^ ƒ"ƒX‚Í,OEµ-§ ‚É ‚Í ƒi ƒmƒ• ƒCƒ" •[ ‚Ì ƒRƒ"ƒ_ ƒNƒ^ ƒ" ƒX‚Å ‚Í ‚È ‚-,‚» ‚Ì-¼ '[ ‚É •Ú'± ‚µ ‚½"d ‹É ŠÔ‚Ì ƒRƒ"ƒ_ ƒNƒ^ ƒ" ƒX‚Å ‚ ‚é •B ƒi ƒmƒ• ƒCƒ" •[ "à ‚Ì ŽU-•‚ª ‚È ‚-"d ‹É ‚Ì •Ú•G'ï •R ‚ª ƒ[ ƒ• ‚Å ‚ ‚é-•'z "I ‚È •ê • ‡ ‚É ‚à,Šï-‚È ‚± ‚AE‚É'ª 'è ‚³ ‚ê ‚é ƒR ƒ"ƒ_ ƒNƒ^ ƒ" ƒX‚Í-³ OEÀ 'å ‚É ‚Í ‚È ‚ç ‚È ‚¢ •B ‚» ‚Ì-•-R ‚Í,"d ‹É ‚© ‚çƒi ƒmƒ• ƒCƒ" •[ ‚É'• "ü ‚Å ‚« ‚é "d Žq ‚Ì-¬ '© ‚É•ã OEÀ ‚ª ‚ ‚é ‚½‚ß ‚Å‚ ‚é •B ‚± ‚Ì-¬ '© ‚Ì • § OEÀ ‚ÍPauliOE´-‚ÍPauliOE´-•‚É Šî ‚à ‚-Ê Žq OEø‰Ê ‚Å ‚ ‚è,‚± ‚Ì OEø‰Ê ‚É ‚ae ‚é •u•Ú•G 'ï •R •v ‚Íh/4e2‚É 'Š "-‚· ‚é(e‚Í "d Žq"d ‰×,h‚ÍPlanck'è •")•B ‚± ‚Ì •u •Ú •G'ï •R •v ‚Ì ‚½‚ß ‚É,'ª 'è ‚³ ‚ê ‚é ƒi ƒmƒ• ƒC ƒ" •[ ‚Ì ƒRƒ" ƒ_ ƒN ƒ^ ƒ" ƒX‚Í2e2/h‚AE ‚¢ ‚¤-L OEÀ 'l ‚ð ‚AE‚é ‚± ‚AE‚É ‚È ‚é •B •@ ŽU-•‚Ì ‚È ‚¢ ƒi ƒmƒ• ƒCƒ"•[ ‚É'• "ü ‚³ ‚ê ‚½"d Žq ‚Í,‚» ‚Ì •‰ Šú•ó 'Ô‚ð •Û ‚Á‚½‚Ü‚Ü,'¼ ‚Ì •ó 'Ô ‚É'J ˆÚ‚· ‚é ‚± ‚AE‚È ‚-,ƒi ƒmƒ• ƒCƒ" •[ ‚ð 'Ê ‚è "² ‚¯ ‚é •B ‚µ ‚½‚ª ‚Á‚ăi ƒmƒ• ƒCƒ" •[ ' † ‚É ' ¶ •Ý‚· ‚é '¼OEð‚· ‚é "d Žq•ó 'Ô‚Í,"AE-§ ‚É "d Žq-A '-‚É Šñ-^ ‚· ‚é ‚± ‚AE‚É ‚È ‚é •B ‚± ‚Ì ‚ae ‚¤ ‚È"d Žq•ó 'Ô‚Í •u ƒ` ƒƒ ƒl ƒ‹ •v ‚AEOEÄ ‚Î ‚ê ‚Ä‚¢ ‚é •B •ae ‚Ì ‹c˜_‹c˜_ ‚ð Še ƒ` ƒƒ ƒl ƒ‹ ‚É "K-p ‚· ‚é ‚AE,ƒ` ƒƒ ƒl ƒ‹ ‚ªNOE ‚ ‚é ƒi ƒmƒ• ƒCƒ" •[ ‚Ì ƒRƒ" ƒ_ ƒNƒ^ ƒ" ƒX‚Í,ŽŸ ‚ÌLandauerOEö Ž®‚Å-^‚¦ ‚ç ‚ê ‚é ‚± ‚AE‚ª ‚í ‚© ‚é •B G=(2e2/h)N(1) ‚± ‚Ì Ž®‚Í,ƒR ƒ" ƒ_ ƒNƒ^ ƒ" ƒX‚ª2ƒAE2/h‚ð 'P ˆÊ ‚AE‚µ ‚Ä-Ê Žq ‰»‚³ ‚ê ‚Ä‚¨‚è‚Ä‚¨‚è,ƒR ƒ" ƒ_ ƒNƒ^ ƒ" ƒX‚Í2e2/h‚Ì •® •" "{ ‚Å•Ï ‰» ‚· ‚é ‚± ‚AE‚𠎦 ‚µ ‚Ä‚¢ ‚é •B ‚± ‚Ì OE»•Û‚ª ƒRƒ" ƒ_ ƒNƒ^ ƒ" ƒX‚Ì-Ê Žq‰» ‚Å‚ ‚è,G0•ß2e2/h‚Í-Ê Žq‰» ƒRƒ" ƒ_ ƒNƒ^ ƒ" ƒX‚AEOEÄ ‚Î ‚ê ‚Ä ‚¢ ‚é •B1/G0‚Í-ñ13kƒ ¶ ‚AE"Žè • ‚È"'ï •R 'l ‚Å‚ ‚è,-Ê Žqƒz •[ ƒ‹ 'ï •R(h/e2)‚Ì ‚¿ ‚å ‚¤ ‚Ç"¼•ª ‚Å‚ ‚é •B •@ ƒi ƒmƒ• ƒCƒ" •[ ' † ‚Å"d ŽqŽU-•‚ª ‚ ‚é •ê • ‡ ‚É ‚Í,'• "ü ‚³ ‚ê