Bài viết nghiên cứu ảnh hưởng của điện trường lên tính chất điện tử của BLG thuần khiết và H-BLG với bốn kiểu hydro hóa khác nhau. Mời các bạn cùng tham khảo bài viết để nắm chi tiết hơn nội dung nghiên cứu.
▼❾❚ ✣❐ ❚❘❸◆● ❚❍⑩■ ✣■➏◆ ❚Û ❚❘❖◆● ●❘❆P❍❊◆❊ ❍❆■ ▲❰P ❇➚ ❍❨❉❘❖ ❍➶❆ ❉×❰■ ❷◆❍ ❍×Ð◆● ❈Õ❆ ✣■➏◆ ❚❘×❮◆● ❑❍➷◆● ✣✃■ ❇Ị■ ✣➐◆❍ ❍Đ■1 ✱ ✣➱ ▲■◆❍ ❚❍➁◆●1 P❍❆◆ ❱❿◆ t ỵ rữớ ữ ✣↕✐ ❤å❝ ❍✉➳ ❱✐➺♥ ◆❣❤✐➯♥ ❝ù✉ ✈➔ P❤→t tr✐➸♥ ❈ỉ♥❣ ♥❣❤➺ ❝❛♦✱ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❉✉② ❚➙♥ ❚â♠ t➢t✿ ❚r♦♥❣ ❝ỉ♥❣ tr➻♥❤ ♥➔②✱ ❝❤ó♥❣ tỉ✐ ❦❤↔♦ s→t ♠➟t ✤ë tr↕♥❣ t❤→✐ ✤✐➺♥ tû ✭❉❖❙✮ tr♦♥❣ ❣r❛♣❤❡♥❡ ❤❛✐ ❧ỵ♣ ❜à ❤②❞r♦ ❤â❛ ✭❍✲❇▲●✮ ✤➦t tr♦♥❣ ✤✐➺♥ tr÷í♥❣ ❦❤ỉ♥❣ ✤ê✐ ✈✉ỉ♥❣ ❣â❝✳ ❇è♥ ❦✐➸✉ ❤②❞r♦ ❤â❛ ❦❤→❝ ♥❤❛✉ ✤÷đ❝ ①❡♠ ①➨t ✤â ❧➔✿ ❦✐➸✉ ❜➔♥ ✭❚▲✕ ❍✲❇▲●✮✱ ❦✐➸✉ ❣❤➳ tü❛ ✭❈▲✕❍✲❇▲●✮✱ ❦✐➸✉ ❜➔♥ t❤✉ ❣å♥ ✭r❚▲✕❍✲❇▲●✮ ✈➔ ❦✐➸✉ ❣❤➳ tü❛ t❤✉ ❣å♥ ✭r❈▲✕❍✲❇▲●✮✳ ❇✐➸✉ t❤ù❝ ❝õ❛ ❉❖❙ ✤÷đ❝ t❤✉ ♥❤➟♥ t❤ỉ♥❣ q✉❛ ♠è✐ ❧✐➯♥ ❤➺ ✈ỵ✐ ❤➔♠ ●r❡❡♥✱ sû ❞ư♥❣ ❍❛♠✐❧t♦♥✐❛♥ tr♦♥❣ ❣➛♥ ✤ó♥❣ ❧✐➯♥ ❦➳t ♠↕♥❤✳ ❈→❝ ❦➳t q✉↔ t➼♥❤ t r r r ợ t t ữ ❜à ❤②❞r♦ ❤â❛✮ ❧➔ ❜→♥ ❦✐♠ ❧♦↕✐✱ tr♦♥❣ ❦❤✐ ✤â ❈▲✕❍✲❇▲● ✈➔ ❚▲✕❍✲❇▲● ❧➔ ❝→❝ ❜→♥ ❞➝♥✳ ❇➯♥ ❝↕♥❤ ✤â✱ ✤✐➺♥ tr÷í♥❣ ♥❣♦➔✐ ↔♥❤ ❤÷ð♥❣ ♠↕♥❤ ❧➯♥ ❉❖❙✳ ❚r♦♥❣ t➜t ❝↔ ❝→❝ ❝➜✉ tró❝✱ ❉❖❙ t↕✐ ✈à tr➼ ♠ù❝ ♥➠♥❣ ❧÷đ♥❣ ❋❡r♠✐ t➠♥❣ ❦❤✐ ❝÷í♥❣ ✤ë ✤✐➺♥ tr÷í♥❣ t➠♥❣✳ ◆❣♦➔✐ r❛✱ ✤ë rë♥❣ ✈ị♥❣ ❝➜♠ tr♦♥❣ ❝→❝ ❝➜✉ tró❝ ❈▲✕❍✲❇▲● ✈➔ ❚▲✕❍✲❇▲● ❣✐↔♠ t❤❡♦ ❝÷í♥❣ ✤ë ✤✐➺♥ tr÷í♥❣✳ ❈→❝ ✤➦❝ ✤✐➸♠ tr➯♥ ❧➔ ❝ì sð ❝❤♦ ✈✐➺❝ sû ❞ư♥❣ ✤✐➺♥ tr÷í♥❣ ✤➸ ✤✐➲✉ ❝❤➾♥❤ t➼♥❤ ❝❤➜t ✤✐➺♥ tû ❝õ❛ ❍✲❇▲● s❛♦ ❝❤♦ ♣❤ị ❤đ♣ ✈ỵ✐ ❝→❝ ù♥❣ ❞ư♥❣ tr♦♥❣ ❝→❝ t❤✐➳t ❜à q✉❛♥❣✲✤✐➺♥ tû ♥❛♥♦✳ ❚ø ❦❤â❛✿ ❣r❛♣❤❡♥❡ ❤❛✐ ❧ỵ♣❀ ❤②❞r♦ ❤â❛❀ ♠➟t ✤ë tr↕♥❣ t❤→✐❀ ♠æ ❤➻♥❤ ❧✐➯♥ ❦➳t ♠↕♥❤✳ ✶ ●■❰■ ❚❍■➏❯ ❱ỵ✐ ❝➜✉ tró❝ ✤ì♥ ❧ỵ♣ ❞↕♥❣ ❧ö❝ ❣✐→❝ ❝õ❛ ❝→❝ ♥❣✉②➯♥ tû ❝❛r❜♦♥✱ ❣r❛♣❤❡♥❡ ❧➔ ✈➟t õ trú t t t ỵ ❜✐➺t ♥❤➜t ❤✐➺♥ ♥❛②✳ ❚✉② ♥❤✐➯♥✱ ❣r❛♣❤❡♥❡ t❤✉➛♥ ❦❤✐➳t ❝â ♥❤÷đ❝ ✤✐➸♠ ❧➔ ✤ë rë♥❣ ✈ị♥❣ ❝➜♠ ❜➡♥❣ ❦❤ỉ♥❣✱ ♥➯♥ ❦❤ỉ♥❣ t❤➸ →♣ ❞ư♥❣ tr♦♥❣ ❝→❝ t❤✐➳t ❜à ✤â♥❣✲♠ð ✭❝❤➥♥❣ ❤↕♥ ♥❤÷ tr❛♥s✐t♦r ❤✐➺✉ ù♥❣ tr÷í♥❣✮✱ ❝→❝ t❤✐➳t ❜à q✉❛♥❣ ✤✐➺♥ tû ❬✶❪✳ ✣➸ ❦❤➢❝ ♣❤ư❝ ♥❤÷đ❝ ✤✐➸♠ ✤â✱ ❝→❝ ♥❤➔ ❦❤♦❛ ❤å❝ ✤➣ ✈➔ ✤❛♥❣ t➻♠ r❛ ❝→❝ ♣❤÷ì♥❣ ♣❤→♣ ✤➸ t↕♦ r❛ ✈➔ ✤✐➲✉ ❝❤➾♥❤ ✤ë rë♥❣ ✈ò♥❣ ❝➜♠ ❝õ❛ ❣r❛♣❤❡♥❡ ♠➔ ✈➝♥ ❞✉② tr➻ ✤÷đ❝ ❝→❝ t➼♥❤ ♥➠♥❣ ÷✉ ✈✐➺t ❝õ❛ ♥â✳ ❈â t❤➸ ❦➸ ✤➳♥ ♠ët sè ❝→❝❤ ♥❤÷✿ ✤➦t t➜♠ ❣r❛♣❤❡♥❡ ❧➯♥ ✤➳ ♣❤➙♥ ❝ü❝ trữớ r ợ ✺❪✱ ❣➙② ❜✐➳♥ ❞↕♥❣ ✤ì♥ trư❝ ❬✻✱ ✼❪✱ ❝➢t t➜♠ ❣r❛♣❤❡♥❡ t❤➔♥❤ ❝→❝ ❞↔✐ ♥❛♥♦ ✭♥❛♥♦r✐❜❜♦♥✮ ❬✽✱ ✾❪✱ t→❝ ✤ë♥❣ ❤â❛ ❤å❝ ❬✶✵❪✳ ▼ư❝ ✤➼❝❤ ❝õ❛ ❝→❝ ♣❤÷ì♥❣ ♣❤→♣ tr➯♥ ❧➔ ♣❤→ ✈ï t➼♥❤ ✤è✐ ①ù♥❣ ✤✐➺♥ tû✲❧é trè♥❣ tr♦♥❣ ❝➜✉ tró❝ ✈ị♥❣ ♥➠♥❣ ❧÷đ♥❣ ❝õ❛ ❣r❛♣❤❡♥❡ ✈➔ t↕♦ ❚↕♣ ❝❤➼ ❑❤♦❛ ❤å❝✱ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❙÷ ♣❤↕♠✱ ✣↕✐ ❤å❝ ❍✉➳ ■❙❙◆ ✶✽✺✾✲✶✻✶✷✱ ❙è ✸✭✺✺✮✴✷✵✷✵✿ tr✳✸✵✲✸✾ ◆❣➔② ♥❤➟♥ ❜➔✐✿ ✵✶✴✵✼✴✷✵✶✾❀ ❍♦➔♥ t❤➔♥❤ ♣❤↔♥ ❜✐➺♥✿✷✺✴✵✼✴✷✵✶✾❀ ◆❣➔② ♥❤➟♥ ✤➠♥❣✿ ✸✵✴✵✼✴✷✵✶✾ ✸✶ ▼❾❚ ✣❐ ❚❘❸◆● ❚❍⑩■ ✣■➏◆ ❚Û ❚❘❖◆● ●❘❆P❍❊◆❊ ✳✳✳ r❛ ✈ò♥❣ ổ ụ ữ ỵ r ữỡ õ ỵ õ ổ ♣❤→ ✈ï ❝➜✉ tró❝ ❝õ❛ ❣r❛♣❤❡♥❡ ✈➔ ✈➝♥ ❣✐ú ✤÷đ❝ ❝→❝ ✤➦❝ t➼♥❤ ❝ì ❜↔♥ ❝õ❛ ♥â✳ ❍✐➺♥ ♥❛②✱ ✈➟t ❧✐➺✉ ❝❛r❜♦♥ ❤②❞r♦ ❤â❛ t❤ü❝ sü ❤➜♣ ❞➝♥ ❝→❝ ♥❤➔ ♥❤✐➯♥ ❝ù✉ ❞♦ ❝→❝ t➼♥❤ ❝❤➜t ♠ỵ✐ ♠➫✱ ❤ù❛ ❤➭♥ ♥❤✐➲✉ ù♥❣ ❞ö♥❣ ✤➡♥❣ s❛✉ ♥â✳ ●r❛♣❤❡♥❡ ❜à ❤②❞r♦ ❤â❛ sð ❤ú✉ ♠ët sè ✤➦❝ t➼♥❤ ✤✐➺♥ tû ♠ỵ✐ s♦ ✈ỵ✐ ❣r❛♣❤❡♥❡ t❤✉➛♥ ❦❤✐➳t✱ ❧➔♠ ❝❤♦ ✈➟t ❧✐➺✉ ♥➔② trð t❤➔♥❤ ù♥❣ ✈✐➯♥ t✐➲♠ ♥➠♥❣ tr♦♥❣ ❝→❝ t❤✐➳t ❜à ❧♦❣✐❝ ❝â ✈ị♥❣ ❝➜♠ ❦❤→❝ ✵✱ ✤÷đ❝ q✉❛♥ t➙♠ ❝↔ ✈➲ t ỵ tt tỹ ởt tr♦♥❣ ♥❤ú♥❣ ②➳✉ tè q✉❛♥ trå♥❣ q✉②➳t ✤à♥❤ ✤➳♥ t➼♥❤ ❝❤➜t ✤✐➺♥ tû ❝õ❛ ❣r❛♣❤❡♥❡ ❜à ❤②❞r♦ ❤â❛ ❧➔ ❦✐➸✉ ❤②❞r♦ ❤â❛✳ ❍②❞r♦ ❤â❛ ❤♦➔♥ t♦➔♥ ❣r❛♣❤❡♥❡ ❝❤♦ t❛ ❝→❝ t➼♥❤ ❝❤➜t ❦❤→❝ ✈ỵ✐ ❤②❞r♦ ❤â❛ ♠ët ♥û❛✳ ▼ư❝ t✐➯✉ ❝❤➼♥❤ ❝õ❛ q✉→ tr➻♥❤ ♥➔② ❧➔ ♣❤→ ✈ï ❧❛✐ ❤â❛ sp2 ✤➸ t↕♦ t❤➔♥❤ ❝→❝ ❧❛✐ ❤â❛ sp3 t÷ì♥❣ tü ❧❛✐ ❤â❛ ❝õ❛ ❦✐♠ ❝÷ì♥❣✳ ❇➯♥ ❝↕♥❤ ✤â✱ ✈✐➺❝ ✤✐➲✉ ❝❤➾♥❤ ✤ë rë♥❣ ✈ò♥❣ ❝➜♠ ✈➔ ❝→❝ t➼♥❤ ❝❤➜t ✤✐➺♥ tû tr♦♥❣ ❣r❛♣❤❡♥❡ ❤❛✐ ❧ỵ♣ ❞➵ ❞➔♥❣ ❤ì♥ ❣r❛♣❤❡♥❡ ✤ì♥ ❧ỵ♣ ❬✶✹❪✳ ❈→❝ ♥❤➔ ♥❣❤✐➯♥ ❝ù✉ ✤➣ ❝❤➾ r❛ r➡♥❣ ❝→❝ t➼♥❤ ❝❤➜t ❝õ❛ ❣r❛♣❤❡♥❡ ♥❤✐➲✉ ❧ỵ♣ ❜à ❤②❞r♦ ❤â❛ tở số ợ ỗ ❝→❝ ❧ỵ♣ ❝ơ♥❣ r➜t q✉❛♥ trå♥❣✳ ❍❛✐ ❧ỵ♣ ❣r❛♣❤❡♥❡ ❝â ỗ ỗ ỗ ỗ t ỗ ❞↕♥❣ ①♦➢♥ ✭t✇✐st❡❞✮ ❬✶✻✱ ✶✼❪✳ ❚r♦♥❣ ❝ỉ♥❣ tr➻♥❤ ♥➔②✱ ❝❤ó♥❣ tỉ✐ ♥❣❤✐➯♥ ❝ù✉ ↔♥❤ ❤÷ð♥❣ ❝õ❛ ♠ët ✤✐➺♥ tr÷í♥❣ ✈✉ỉ♥❣ ❣â❝ ❧➯♥ t➼♥❤ ❝❤➜t ✤✐➺♥ tû ❝õ❛ ❍✲❇▲●✳ ✣↕✐ ❧÷đ♥❣ ✤➦❝ tr÷♥❣ ❝❤♦ t➼♥❤ ❝❤➜t ✤✐➺♥ tû ❧➔ ♠➟t ✤ë tr↕♥❣ t❤→✐ ✤✐➺♥ tû ✭❉❖❙✮ ✤÷đ❝ t➼♥❤ t♦→♥ ❜➡♥❣ ♣❤÷ì♥❣ ♣❤→♣ ❤➔♠ ●r❡❡♥ sû ❞ư♥❣ ❍❛♠✐❧t♦♥✐❛♥ tr♦♥❣ ❣➛♥ ✤ó♥❣ ❧✐➯♥ t ú tổ q t ỗ ❆❆ ❝õ❛ ❣r❛♣❤❡♥❡ ❤❛✐ ❧ỵ♣ ✈➻ ♥❤ú♥❣ ♥❣❤✐➯♥ ❝ù✉ ✈➲ ❝➜✉ tró❝ ♥➔② ✈➝♥ ❝á♥ ❦❤→ ➼t✳ ❚r♦♥❣ tr÷í♥❣ ❤đ♣ ỗ tỷ r tr ợ tự ♥❤➜t ♥➡♠ t❤➥♥❣ ❣â❝ ✈ỵ✐ ❝→❝ ♥❣✉②➯♥ tû ❝❛r❜♦♥ ✭tr♦♥❣ ũ ợ tự ữủ ❝➜✉ tró❝ ♥❤÷ s❛✉✳ ❚r♦♥❣ ♠ư❝ ✷✱ ❝❤ó♥❣ tỉ✐ tr➻♥❤ ❜➔② ♠ỉ ❤➻♥❤ t➼♥❤ t♦→♥ ✈➔ ❝→❝ ❝ỉ♥❣ t❤ù❝ ❝ì ❜↔♥✳ ▼ư❝ ✸ ❣✐ỵ✐ t❤✐➺✉ ❝→❝ ❦➳t q✉↔ t➼♥❤ t♦→♥ sè ✈➔ t❤↔♦ ❧✉➟♥✳ ▼ët sè ❦➳t ❧✉➟♥ q✉❛♥ trå♥❣ ✈➲ ❦➳t q✉↔ ♥❣❤✐➯♥ ❝ù✉ s➩ ✤÷đ❝ tr➻♥❤ ❜➔② ð ♠ö❝ ✹✳ ✷ ▼➷ ❍➐◆❍ ❚➑◆❍ ❚❖⑩◆ ❱⑨ ❈⑩❈ ❈➷◆● t trú ỗ ❆❆✳ ❚ò② t❤❡♦ ❝→❝❤ s➢♣ ①➳♣ ❝õ❛ ❝→❝ ♥❣✉②➯♥ tû ❍ tr♦♥❣ ♠↕♥❣ ❣r❛♣❤❡♥❡ ❤❛✐ ❧ỵ♣✱ ❝❤ó♥❣ tỉ✐ ①➨t ❜è♥ ❦✐➸✉ ❤②❞r♦ ❤â❛ ❦❤→❝ ♥❤❛✉✱ ✤÷đ❝ ❝❤➾ r❛ tr➯♥ ❍➻♥❤ ✶✿ ❦✐➸✉ ❜➔♥ ✭❚▲✕❍✲❇▲●✮✱ ❦✐➸✉ ❣❤➳ tü❛ ✭❈▲✕❍✲❇▲●✮✱ ❦✐➸✉ ❜➔♥ t❤✉ ❣å♥ ✭r❚▲✕❍✲ ❇▲●✮ ✈➔ ❦✐➸✉ ❣❤➳ tü❛ t❤✉ ❣å♥ r t ởt trữớ ổ ổ õ ợ ♠➦t ♣❤➥♥❣ ❝õ❛ t➜♠ ❍✲❇▲●✱ tr↕♥❣ t❤→✐ ❝õ❛ ❝→❝ ❢❡r♠✐♦♥ ❉✐r❛❝ ❝â t❤➸ ✤÷đ❝ ♠ỉ t↔ ❜ð✐ ❍❛♠✐❧t♦♥✐❛♥ tr♦♥❣ ❣➛♥ ✤ó♥❣ ❧✐➯♥ ❦➳t ♠↕♥❤ ♥❤÷ s❛✉✿ ˆ ˆA B H ˆA A H ˆA B H ˆA H H ˆA H HA1 A1 H 1 2 1 H ˆB A H ˆB B H ˆB A H ˆB B H ˆB H H ˆB H 1 2 1 2 1 H ˆA A H ˆA B H ˆA A H ˆA B H ˆA H H ˆA H 2 2 2 2 ˆ HBLG = H ✭✶✮ , ˆ ˆ ˆ ˆ ˆ ˆ HB2 A1 HB2 B1 HB2 A2 HB2 B2 HB2 H1 HB2 H2 ˆH A H ˆH B H ˆH A H ˆH B H ˆH H H ˆH H H 1 1 2 1 ˆ ˆ ˆ ˆ ˆ ˆH H HH A HH B HH A HH B HH H H 2 2 2 2 ✸✷ ❇Ò■ ✣➐◆❍ ❍Ñ■✱ ✣➱ ▲■◆❍ ❚❍➁◆●✱ P❍❆◆ ❱❿◆ ◆❍❹▼ ❍➻♥❤ ✶✿ r ợ ỗ t ❦❤✐➳t❀ ✭❜✮ ❤②❞r♦ ❤â❛ ❦✐➸✉ ❜➔♥ ✭❚▲✕❍✲❇▲●✮❀ ✭❝✮ ❤②❞r♦ ❤â❛ ❦✐➸✉ ❣❤➳ tü❛ ✭❈▲✕❍✲❇▲●✮❀ ✭❞✮ ❤②❞r♦ ❤â❛ ❦✐➸✉ ❜➔♥ t❤✉ ❣å♥ ✭r❚▲✕❍✲❇▲●✮❀ ✭❡✮ ❤②❞r♦ ❤â❛ ❦✐➸✉ ❣❤➳ tü❛ t❤✉ ❣å♥ ✭r❈▲✕❍✲❇▲●✮✳ ❤♦➦❝ ❝â t❤➸ ✈✐➳t ❣å♥ ♥❤÷ s❛✉✿ ˆ 11 (k) H ˆ 12 (k) H ˆ 13 (k) H ˆ HBLG (k) = ˆ † (k) H ˆ 22 (k) H ˆ 23 (k) H , H 12 † † ˆ ˆ ˆ H13 (k) H23 (k) H33 (k) ✭✷✮ ˆ 11 (k) ✈➔ H ˆ 22 (k) ❧➔ ❍❛♠✐❧t♦♥✐❛♥ ♠æ t↔ ❧✐➯♥ ❦➳t ❝õ❛ ❝→❝ ♥❣✉②➯♥ tû tr♦♥❣ ✤â✱ t❤➔♥❤ ♣❤➛♥ H ❈ tr♦♥❣ ♠é✐ ợ ữủ 11 (k) = H A A H 1 ˆB A H 1 ˆA B H 1 ˆB B H 1 = −V ε0 g(k) , ∗ ε0 g(k) −V ✭✸✮ ˆ 22 (k) = H ˆA A H 2 ˆB A H 2 ˆA B H 2 ˆB B H 2 = V ε0 g(k) ∗ ε0 g(k) V ✭✹✮ √ ˚ ✈➔ V ❧➔ t❤➳ ♥➠♥❣ Ð ✤➙②✱ g(k) = cos( 23 kx a)e−iky a/2 + eiky a ✈➔ ε0 ≈ ❡❱ ✈➔ a = 1, 42 A ˆ 12 (k) ❧➔ ❍❛♠✐❧t♦♥✐❛♥ ♠ỉ t↔ ❧✐➯♥ ❦➳t ❝õ❛ ✤✐➺♥ tû tr♦♥❣ ✤✐➺♥ tr÷í♥❣ ♥❣♦➔✐✳ ❚❤➔♥❤ ♣❤➛♥ H ❝õ❛ ❝→❝ ♥❣✉②➯♥ tû ❈ ❣✐ú❛ ợ ữủ 12 (k) = H ˆA A H ˆ HB1 A2 ˆA B H ˆ HB1 B2 = γ1 0 γ1 , ✭✺✮ ✸✸ ▼❾❚ ✣❐ ❚❘❸◆● ❚❍⑩■ ✣■➏◆ ❚Û ❚❘❖◆● ●❘❆P❍❊◆❊ ✳✳✳ ✈ỵ✐ γ1 ≈ 0, ❡❱✳ ❈→❝ ❤➡♥❣ sè tr♦♥❣ ❝ỉ♥❣ tr➻♥❤ ♥➔② ✤÷đ❝ ❝❤♦ ❜ð✐ ❝→❝ ❝æ♥❣ tr➻♥❤ ❬✶✽✱ ✶✾✱ ✷✵❪✳ ˆ 13 (k) ✈➔ H ˆ 23 (k) ❧➔ ❍❛♠✐❧t♦♥✐❛♥ ♠ỉ t↔ t÷ì♥❣ t→❝ ❣✐ú❛ ❝→❝ ♥❣✉②➯♥ tû ❍ ✈➔ ❈ ❚❤➔♥❤ ♣❤➛♥ H ✈➔ ♣❤ö t❤✉ë❝ ♠↕♥❤ ✈➔♦ ❧♦↕✐ ❤②❞r♦ ❤â❛✿ TL ˆ 13 H = −t1 TL ˆ 23 ;H = −t1 0 t2 t2 CL ˆ 13 H = −t1 CL ˆ 23 ;H = t1 0 t2 −t2 ˆ rT L = H 13 0 ˆ rT L = ;H 23 0 t2 t2 rCL ˆ 13 H = 0 rCL ˆ 23 ;H = 0 t2 −t2 ; ; ✭✻✮ ; ; ✈ỵ✐ t1 = t2 = 5.72 ❡❱✳ ˆ 33 (k) ❧➔ ❍❛♠✐❧t♦♥✐❛♥ ❝❤♦ t÷ì♥❣ t→❝ ❣✐ú❛ ❝→❝ ♥❣✉②➯♥ tû ❍✿ ❈✉è✐ ❝ò♥❣ H ˆ 33 (k) = H ˆH H H 1 ˆH H H ˆH H H ˆH H H 2 = tp ✭✼✮ ✈ỵ✐ = −2, ❡❱✳ ❚ø ❜✐➸✉ t❤ù❝ ❝õ❛ ❍❛♠✐❧t♦♥✐❛♥ ✭✷✮✱ t❛ ❝â t❤➸ ✈✐➳t r❛ ♠❛ tr➟♥ ❤➔♠ ●r❡❡♥ q✉❛ ♠è✐ ❧✐➯♥ ❤➺ ❬✷✶❪✿ ˆ k, iωn ) = , ✭✽✮ G( ˆ ˆ iωn I − HHBLG (k) tr♦♥❣ ✤â✱ Iˆ ❧➔ ♠❛ tr➟♥ ✤ì♥ ✈à✱ iωn → E + i0+ ❧➔ t➛♥ sè ▼❛ts✉❜❛r❛✱ ✈ỵ✐ 0+ ❧➔ sè t❤ü❝ ❞÷ì♥❣ r➜t ♥❤ä ♠❛♥❣ t❤ù ♥❣✉②➯♥ ♥➠♥❣ ❧÷đ♥❣✳ ❚ø ✤â✱ ❝â t❤➸ t❤✉ ✤÷đ❝ ❜✐➸✉ t❤ù❝ ❝❤♦ ❉❖❙✿ D(E) = − 2πNa Nc Gµµ (k, E), ✭✾✮ k µ=1 tr♦♥❣ ✤â✱ Na ✈➔ Nc ❧➛♥ ❧÷đt ❧➔ sè ♥❣✉②➯♥ tû tr♦♥❣ ♠ët ỉ ✤ì♥ ✈à ✈➔ sè ỉ ✤ì♥ ✈à✳ ❚r♦♥❣ ❝ỉ♥❣ t❤ù❝ tr➯♥✱ tê♥❣ t❤❡♦ k ✤÷đ❝ ❧➜② tr♦♥❣ ✈ị♥❣ ❇r✐❧❧♦✉✐♥ t❤ù ♥❤➜t ✭❋❇❩✮ tr♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ♠↕♥❣ ✤↔♦✳ ❚r♦♥❣ ♠ư❝ t✐➳♣ t❤❡♦✱ ❝❤ó♥❣ tỉ✐ s➩ tr➻♥❤ ❜➔② ❝→❝ ❦➳t q✉↔ t➼♥❤ sè ✤è✐ ✈ỵ✐ ❜✐➸✉ t❤ù❝ ❣✐↔✐ t➼❝❤ ❝õ❛ ❉❖❙ ❝❤♦ ❜ð✐ ❝æ♥❣ t❤ù❝ ✭✾✮✳ ✸ ❑➌❚ ◗❯❷ ❚➑◆❍ ❙➮ ❱⑨ ❚❍❷❖ ▲❯❾◆ ❚r♦♥❣ ♠ư❝ ♥➔②✱ ❝❤ó♥❣ tỉ✐ s➩ ❦❤↔♦ s→t ❝❤✐ t✐➳t ❉❖❙ ♥❤÷ ❧➔ ♠ët ❤➔♠ ❝õ❛ ♥➠♥❣ ❧÷đ♥❣ ✤✐➺♥ tû tr♦♥❣ ❍✲❇▲● ✈ỵ✐ ❝→❝ ❦✐➸✉ ❤②❞r♦ ❤â❛ ❦❤→❝ ♥❤❛✉ tr♦♥❣ ❤❛✐ tr÷í♥❣ ❤đ♣✿ ❦❤ỉ♥❣ ❝â ✈➔ ❝â ♠➦t ♠ët ✤✐➺♥ tr÷í♥❣ ♥❣♦➔✐ ❦❤ỉ♥❣ ✤ê✐✳ ✣➸ t❤✉➟♥ t✐➺♥✱ ❝❤ó♥❣ tỉ✐ sû ❞ư♥❣ t ❧➔ ✤ì♥ ✈à ✤♦ ❝õ❛ ♥➠♥❣ ❧÷đ♥❣ tr♦♥❣ ❝→❝ t➼♥❤ t♦→♥ sè✳ ✸✹ ❇Ị■ ✣➐◆❍ ❍Đ■✱ ✣➱ P rữợ t t q t ữủ t ỵ ❝õ❛ ❉❖❙✳ ❉❖❙ ❝❤♦ t❛ t❤æ♥❣ t✐♥ ✈➲ sü ♣❤➙♥ ❜è ❝→❝ tr↕♥❣ t❤→✐ ❝õ❛ ❝→❝ ❤↕t t↔✐ ✭❡❧❡❝tr♦♥ ✈➔ ❧é trè♥❣✮ tr♦♥❣ ♠ët ❤➺✳ ❈ö t❤➸✱ ❉❖❙ ❝❤♦ t❛ ❜✐➳t sè tr↕♥❣ t❤→✐ tr➯♥ ♠é✐ ✤ì♥ ✈à ♥➠♥❣ ❧÷đ♥❣✱ ❝❤➥♥❣ ❤↕♥ ♠é✐ ❡❱✱ tr♦♥❣ tø♥❣ ✈ị♥❣ ♥➠♥❣ ❧÷đ♥❣✳ ❚❤❡♦ ✤â✱ sü ①✉➜t ❤✐➺♥ ❝→❝ tr↕♥❣ t❤→✐ s✉② ❜✐➳♥ ♣❤ö t❤✉ë❝ ✈➔♦ ❝→❝ ✤➾♥❤ ❝ü❝ ✤↕✐ tr♦♥❣ ✤÷í♥❣ ❝♦♥❣ ❜✐➸✉ ữ ỵ r sỹ t ỳ ❝→❝ ♠ù❝ ♥➠♥❣ ❧÷đ♥❣ ❧➜♣ ✤➛② ✈➔ ❝→❝ ♠ù❝ ❝❤÷❛ ❧➜♣ ✤➛② ✤â ❧➔ ❝→❝ ✤➾♥❤ ❝ü❝ ✤↕✐ ❉❖❙ ❝➔♥❣ ❝❛♦ t❤➻ sè ❝→❝ ♠ù❝ ❧➜♣ ✤➛② ❝➔♥❣ ♥❤✐➲✉ ✈➔ ♥❣÷đ❝ ❧↕✐✳ ✸✳✶✳ ❉❖❙ ❝õ❛ ❇▲● ✈➔ ❍✲❇▲● ❦❤✐ ❦❤ỉ♥❣ ❝â ✤✐➺♥ tr÷í♥❣ ❍➻♥❤ ✷✿ ❉❖❙ tr♦♥❣ ❇▲● t❤✉➛♥ ❦❤✐➳t ✈➔ ❍✲❇▲● ✈ỵ✐ ❝→❝ ❦✐➸✉ ❤②❞r♦ ❤â❛ ❦❤→❝ ♥❤❛✉ ❦❤✐ ❦❤ỉ♥❣ ❝â ✤✐➺♥ tr÷í♥❣ ♥❣♦➔✐✳ ❍➻♥❤ ✷ ♠ỉ t↔ sü ♣❤ư t❤✉ë❝ ❝õ❛ ❉❖❙ ✈➔♦ t❤❛♠ sè ❦❤ỉ♥❣ t❤ù ♥❣✉②➯♥ E/t ✤è✐ ✈ỵ✐ ❝→❝ ❝➜✉ tró❝ ❣r❛♣❤❡♥❡ ❤❛✐ ❧ỵ♣ ❦❤→❝ ♥❤❛✉✿ ❇▲● t❤✉➛♥ ❦❤✐➳t ✭✤÷í♥❣ ♠➔✉ ✤❡♥✮✱ ❚▲✕❍✲❇▲● ✭✤÷í♥❣ ♠➔✉ ỗ ữớ ọ r ữớ ❝➙②✮ ✈➔ r❈▲✕ ❍✲❇▲● ✭✤÷í♥❣ ♠➔✉ ①❛♥❤ ✤➟♠✮ ❦❤✐ ❦❤ỉ♥❣ ❝â ♠➦t ✤✐➺♥ tr÷í♥❣ ❦❤ỉ♥❣ ✤ê✐ ✭V = 0✮✳ ❚ø ❤➻♥❤ ✈➩ t❛ ❝â t❤➸ t❤➜② r➡♥❣ ❉❖❙ ✤è✐ ✈ỵ✐ ❇▲● t❤✉➛♥ ❦❤✐➳t ♣❤ị ❤đ♣ tèt ✈ỵ✐ ❣✐→ trà t❤✉ ✤÷đ❝ tr♦♥❣ ❝ỉ♥❣ tr➻♥❤ ❬✷✷❪✳ ✣✐➲✉ ✤â ❝❤♦ t❤➜② sü ✤ó♥❣ ✤➢♥ ✈➔ ✤ë t✐♥ ❝➟② ❝õ❛ ♣❤÷ì♥❣ ♣❤→♣ ♠➔ ❝❤ó♥❣ tỉ✐ sû ❞ư♥❣ ✤➸ t➼♥❤ t♦→♥ ❉❖❙ ✈➔ ❧➔ ❝ì sð ✤➸ ❝❤ó♥❣ tỉ✐ t✐➳♣ tư❝ ♣❤➙♥ t➼❝❤ ❝→❝ ✤➦❝ tr÷♥❣ ❝õ❛ ❉❖❙ tr♦♥❣ ❝→❝ ❝➜✉ tró❝ ❍✲❇▲● ❦❤→❝ ♥❤❛✉✳ ❚ø ❤➻♥❤ ✈➩ t❛ ❝ô♥❣ t❤➜② r➡♥❣ ❉❖❙ tr♦♥❣ ❝→❝ ❝➜✉ tró❝ ❍✲❇▲● t❤❛② ✤ê✐ ♠↕♥❤ s♦ ✈ỵ✐ ❇▲● t❤✉➛♥ ❦❤✐➳t✳ ❳✉➜t ❤✐➺♥ ❝→❝ ✈ò♥❣ ❝➜♠ ❝â ✤ë rë♥❣ ❦❤♦↔♥❣ 2, 2t ✈➔ 3, 1t t÷ì♥❣ ù♥❣ tr♦♥❣ ❈▲✕❍✲❇▲● ✈➔ ❚▲✕❍✲❇▲●✳ ❈→❝ ❣✐→ trà ♥➔② ❝❤♦ t❤➜② ❈▲✕❍✲❇▲● ✈➔ ữ ữợ t ❝õ❛ ❤②❞r♦ ❤â❛✱ ✤➣ ❝â sü ❝❤✉②➸♥ ♣❤❛ tr♦♥❣ ❣r❛♣❤❡♥❡ ❤❛✐ ❧ỵ♣ tø ❜→♥ ❦✐♠ ❧♦↕✐ s❛♥❣ ❜→♥ ❞➝♥✳ ❇➯♥ ❝↕♥❤ ✤â✱ ✈ỵ✐ ❝→❝ ❝➜✉ tró❝ r❚▲✕❍✲❇▲● ✈➔ r❈▲✕❍✲❇▲●✱ ❉❖❙ ❝ô♥❣ t❤❛② ✤ê✐ ♠↕♥❤✱ ❣✐→ trà ❝õ❛ ❉❖❙ t➠♥❣ ♠↕♥❤ t↕✐ ♠ët sè ❣✐→ trà ❝õ❛ ♥➠♥❣ ❧÷đ♥❣ E/t ✈➔ ①✉➜t ❤✐➺♥ ♥❤✐➲✉ ❦ý ❞à ✈❛♥ ❍♦✈❡ ❤ì♥ s♦ ✈ỵ✐ r ợ t t ữủ t ❧➔ ❞♦ ❦❤✐ ❜à ❤②❞r♦ ❤â❛✱ sü ❝â ♠➦t ❝õ❛ ❝→❝ ✤✐➺♥ tû tr♦♥❣ ❝→❝ ♥❣✉②➯♥ tû ❤②❞r♦ ❧➔♠ t➠♥❣ sè ❧÷đ♥❣ ✤✐➺♥ tû ❝õ❛ ❤➺ ✈➔ ❞♦ ✈➟② sè tr↕♥❣ t❤→✐ ✤✐➺♥ tû ❝ô♥❣ ♣❤↔✐ t➠♥❣ ❧➯♥✱ ❞➝♥ ✤➳♥ ❉❖❙ t➠♥❣✳ ▼❾❚ ✣❐ ❚❘❸◆● ❚❍⑩■ ✣■➏◆ ❚Û ❚❘❖◆● ●❘❆P❍❊◆❊ ✳✳✳ ✸✺ ✸✳✷✳ ❷♥❤ ❤÷ð♥❣ ❝õ❛ ✤✐➺♥ tr÷í♥❣ ❧➯♥ ❉❖❙ ❝õ❛ ❍✲❇▲● ❷♥❤ ❤÷ð♥❣ ❝õ❛ ✤✐➺♥ tr÷í♥❣ ❧➯♥ ❉❖❙ ✤÷đ❝ t❤➸ ❤✐➺♥ tr♦♥❣ ❝→❝ ♣❤÷ì♥❣ tr➻♥❤ ✭✸✮ ✈➔ ✭✹✮ ❝❤♦ ❍❛♠✐❧t♦♥✐❛♥✳ ❇➙② ❣✐í ❝❤ó♥❣ tỉ✐ s➩ ❧➔♠ rã ↔♥❤ ❤÷ð♥❣ ❝õ❛ ✤✐➺♥ tr÷í♥❣ ❧➯♥ ❝→❝ ✤➦❝ tr÷♥❣ ❝õ❛ ❉❖❙ tr♦♥❣ ❝→❝ ❝➜✉ tró❝ ♥â✐ tr➯♥✳ ✣➸ t❤✉➟♥ t✐➺♥ ❝❤ó♥❣ tỉ✐ ❝❤å♥ ✤ì♥ ✈à ❝õ❛ t❤➳ ♥➠♥❣ t➽♥❤ ✤✐➺♥ ✭❡❱✮ ❧➔♠ ✤ì♥ ✈à ✤♦ ❝õ❛ ✤✐➺♥ tr÷í♥❣ t÷ì♥❣ ù♥❣✳ ❍➻♥❤ ✸✿ ❉❖❙ tr♦♥❣ ❇▲● t❤✉➛♥ ❦❤✐➳t t↕✐ ♠ët sè ❣✐→ trà ❦❤→❝ ♥❤❛✉ ❝õ❛ ✤✐➺♥ tr÷í♥❣✳ ❍➻♥❤ ✹✿ ❉❖❙ t❤❡♦ ♥➠♥❣ ❧÷đ♥❣ tr♦♥❣ ❚▲✕❍✲❇▲● ✭❛✮✱ ❈▲✕❍✲❇▲● ✭❜✮✱ r❚▲✕❍✲❇▲● ✭❝✮ ✈➔ r❈▲✕❍✲❇▲● t↕✐ ♠ët sè ❣✐→ trà ❦❤→❝ ♥❤❛✉ ❝õ❛ ✤✐➺♥ tr÷í♥❣ V rữợ t ú tổ t ữ ✤✐➺♥ tr÷í♥❣ ❧➯♥ ❉❖❙ tr♦♥❣ ❇▲● t❤✉➛♥ ❦❤✐➳t✱ ✤÷đ❝ ❝❤➾ r❛ tr➯♥ ❍➻♥❤ ✸✳ ❍➻♥❤ ✈➩ ❝❤♦ t❤➜② ❦❤✐ t➠♥❣ ❣✐→ trà ❝õ❛ ✤✐➺♥ tr÷í♥❣ t❤➻ sè ❧÷đ♥❣ ❝→❝ ❦ý ✸✻ ❇Ị■ ✣➐◆❍ ❍Đ■✱ ✣➱ ▲■◆❍ ❚❍➁◆●✱ P❍❆◆ ❱❿◆ ◆❍❹▼ ❍➻♥❤ ✺✿ ❙ü ♣❤ö t❤✉ë❝ ❝õ❛ ❉❖❙ t↕✐ ♠ù❝ ♥➠♥❣ ❧÷đ♥❣ ❋❡r♠✐ ✈➔♦ ✤✐➺♥ tr÷í♥❣ tr♦♥❣ ❝→❝ ❝➜✉ tró❝ ❣r❛♣❤❡♥❡ ❤❛✐ ❧ỵ♣ ❦❤→❝ ♥❤❛✉✳ ❍➻♥❤ ✻✿ ❙ü ♣❤ư t❤✉ë❝ ❝õ❛ ✤ë rë♥❣ ✈ị♥❣ ❝➜♠ ✈➔♦ ✤✐➺♥ tr÷í♥❣ tr♦♥❣ ❚▲✕❍✲❇▲● ✭❝→❝ ❝❤➜♠ trá♥✮ ✈➔ ❈▲✕❍✲❇▲● ✭❝→❝ ❝❤➜♠ ✈✉æ♥❣✮✳ ▼❾❚ ✣❐ ❚❘❸◆● ❚❍⑩■ ✣■➏◆ ❚Û ❚❘❖◆● ●❘❆P❍❊◆❊ ✳✳✳ ✸✼ ❞à ✈❛♥ ❍♦✈❡ tr♦♥❣ ❉❖❙ ❦❤æ♥❣ t❤❛② ✤ê✐✱ tù❝ ❧➔ ❦❤æ♥❣ ❧➔♠ ①✉➜t ❤✐➺♥ t❤➯♠ ❝→❝ tr↕♥❣ t❤→✐ s✉② ❜✐➳♥✳ ◆❣♦➔✐ r❛✱ ❦❤✐ ✤✐➺♥ tr÷í♥❣ t➠♥❣ ❧➯♥ t❤➻ ✤ë rë♥❣ ❝õ❛ ❝→❝ ❦ý ❞à ✈❛♥ ❍♦✈❡ ♠ð rë♥❣ r❛ ✈➔ ✤ë ❝❛♦ ❝→❝ ✤➾♥❤ ❦ý ❞à ❣✐↔♠ ①✉è♥❣✳ ✣✐➲✉ ♥➔② ❤♦➔♥ t♦➔♥ ♣❤ò ủ t t ỵ tỹ t sỹ ❝â ♠➦t ❝õ❛ ✤✐➺♥ tr÷í♥❣ ❦❤ỉ♥❣ ❧➔♠ t❤❛② ✤ê✐ sè ✤✐➺♥ tû t♦➔♥ ♣❤➛♥ tr♦♥❣ ❝→❝ ✈ị♥❣ ♥➠♥❣ ❧÷đ♥❣ ✭sè ✤✐➺♥ tû ❜↔♦ t♦➔♥✮✱ ❝â ♥❣❤➽❛ ❧➔ ✈➲ ♠➦t ❤➻♥❤ t ợ ữớ ❜✐➸✉ ❞✐➵♥ ❉❖❙ ✈➔ trư❝ ♥➠♥❣ ❧÷đ♥❣ E/t ♣❤↔✐ ❜↔♦ t♦➔♥ ❦❤✐ ✤✐➺♥ tr÷í♥❣ t❤❛② ✤ê✐✳ ❇➯♥ ❝↕♥❤ ✤â✱ ❣✐→ trà ❝õ❛ ❉❖❙ t↕✐ ✈à tr➼ ♠ù❝ ❋❡r♠✐ ✭D(0)✮ t➠♥❣ ❧➯♥ ❦❤✐ t➠♥❣ ✤✐➺♥ tr÷í♥❣ t➠♥❣✱ ❞➝♥ ✤➳♥ ①✉➜t ❤✐➺♥ ♣❤❛ ❜→♥ ❦✐♠ ❧♦↕✐ q✉→ ✤ë✳ ❚÷ì♥❣ tü✱ ❝❤ó♥❣ tỉ✐ t✐➳♣ tư❝ ♣❤➙♥ t➼❝❤ ↔♥❤ ❤÷ð♥❣ ❝õ❛ ✤✐➺♥ tr÷í♥❣ ❧➯♥ ❉❖❙ tr♦♥❣ ❍✲❇▲● ✈ỵ✐ ❝→❝ ❦✐➸✉ ❤②❞r♦ ❤â❛ ❦❤→❝ ♥❤❛✉✳ ❍➻♥❤ ✹ ♠æ t↔ ❉❖❙ tr♦♥❣ ❍✲❇▲● t↕✐ ♠ët sè ❣✐→ trà ❦❤→❝ ♥❤❛✉ ❝õ❛ ✤✐➺♥ tr÷í♥❣✳ ◆❤➻♥ ❝❤✉♥❣✱ ❉❖❙ tr♦♥❣ t➜t ❝↔ ❝→❝ ❝➜✉ tró❝ ❍✲❇▲● ♣❤ư t❤✉ë❝ rã r➺t ✈➔♦ ✤✐➺♥ tr÷í♥❣✳ ❙ü t❤❛② ✤ê✐ ❝õ❛ D(0) t❤❡♦ ✤✐➺♥ tr÷í♥❣ tr♦♥❣ ❇▲● t❤✉➛♥ ❦❤✐➳t ❝ơ♥❣ ♥❤÷ tr♦♥❣ ❝→❝ ❝➜✉ tró❝ ❍✲❇▲● ❦❤→❝ ♥❤❛✉ ✤÷đ❝ ❝❤➾ r❛ tr➯♥ ❍➻♥❤ ✺✳ ◆❣♦➔✐ r❛✱ tø ❍➻♥❤ ✹ t❛ ❝ô♥❣ t❤➜② r➡♥❣ ❦❤✐ ✤✐➺♥ tr÷í♥❣ t➠♥❣ t❤➻ ❜➲ rë♥❣ ✈ị♥❣ ❝➜♠ tr♦♥❣ ❚▲✕❍✲❇▲● ✈➔ ❈▲✕❍✲❇▲● ❜à t❤✉ ❤➭♣✳ ✣✐➲✉ ♥➔② ❝â t❤➸ ❣✐↔✐ t➼❝❤ ❧➔ ❞♦ t→❝ ❞ư♥❣ ❝õ❛ ✤✐➺♥ tr÷í♥❣ ✤➣ ❧➔♠ ❝❤♦ ✤✐➺♥ tû ð ✈ò♥❣ ❞➝♥ ✈➔ ❧é trè♥❣ ð ✈ò♥❣ ❤â❛ trà ❞à❝❤ ❝❤✉②➸♥ ❧↕✐ ❣➛♥ ♥❤❛✉✱ tù❝ ❧➔ ✤➾♥❤ ❝õ❛ ✈ò♥❣ ❤â❛ trà ✈➔ ✤→② ❝õ❛ ✈ò♥❣ ❞➝♥ ❝➔♥❣ ❣➛♥ ♥❤❛✉ ❦❤✐ ✤✐➺♥ tr÷í♥❣ ❝➔♥❣ t➠♥❣✱ ❞➝♥ ✤➳♥ ✤ë rë♥❣ ✈ị♥❣ ❝➛♠ ❣✐↔♠ t❤❡♦ ✤✐➺♥ tr÷í♥❣✳ ❙ü ♣❤ư t❤✉ë❝ ❝õ❛ ✤ë rë♥❣ ✈ị♥❣ ❝➜♠ tr♦♥❣ ❚▲✕❍✲❇▲● ✈➔ ❈▲✕❍✲❇▲● ✈➔♦ ✤✐➺♥ tr÷í♥❣ ♥❣♦➔✐ ✤÷đ❝ ❝❤➾ r❛ tr➯♥ ❍➻♥❤ ✻✳ ❙ü ♣❤ư t❤✉ë❝ ❝õ❛ ❉❖❙ ✈➔♦ ✤✐➺♥ tr÷í♥❣ ❧➔ ❝ì sð ❝õ❛ ❦➽ t❤✉➟t t❤❛② ✤ê✐ ❜➲ rë♥❣ ✈ị♥❣ ❝➜♠ ❝õ❛ ✈➟t ❧✐➺✉ ❍✲❇▲● ❜➡♥❣ ✤✐➺♥ tr÷í♥❣✳ ❚❛ ❝â t❤➸ t❤✉ ✤÷đ❝ ✈➟t ❧✐➺✉ ❝â ✤ë rë♥❣ ✈ị♥❣ ❝➜♠ ữ ỵ ố tr trữớ t❤➼❝❤ ❤đ♣✳ ✹ ❑➌❚ ▲❯❾◆ ❈❤ó♥❣ tỉ✐ ✤➣ ♥❣❤✐➯♥ ❝ù✉ ↔♥❤ ❤÷ð♥❣ ❝õ❛ ✤✐➺♥ tr÷í♥❣ ♥❣♦➔✐ ❧➯♥ t➼♥❤ ❝❤➜t ✤✐➺♥ tû ❝õ❛ ❇▲● t❤✉➛♥ ❦❤✐➳t ✈➔ ❍✲❇▲● ✈ỵ✐ ❜è♥ ❦✐➸✉ ❤②❞r♦ ❤â❛ ❦❤→❝ ♥❤❛✉✳ ●✐→ trà ❝õ❛ ❉❖❙ t❤✉ ✤÷đ❝ ỵ tt r sỷ t t ♠↕♥❤ tr♦♥❣ ❇▲● t❤✉➛♥ ❦❤✐➳t ♣❤ị ❤đ♣ tèt ✈ỵ✐ ❝→❝ ❦➳t q✉↔ t❤✉ ✤÷đ❝ ❜ð✐ ❝→❝ t→❝ ❣✐↔ ❦❤→❝✳ ◆❤➻♥ ❝❤✉♥❣✱ ❉❖❙ t↕✐ ✈à tr➼ ♠ù❝ ❋❡r♠✐ t➠♥❣ ❦❤✐ ❝÷í♥❣ ✤ë ✤✐➺♥ tr÷í♥❣ t➠♥❣ tr♦♥❣ t➜t ❝↔ ❝→❝ ❝➜✉ tró❝✳ ✣➦❝ ❜✐➺t✱ ✤ë rë♥❣ ✈ò♥❣ ❝➜♠ tr♦♥❣ ❚▲✕❍✲❇▲● ✈➔ ❈▲✕❍✲❇▲● t❤❛② ✤ê✐ ✤→♥❣ ❦➸ ❦❤✐ ✤✐➺♥ tr÷í♥❣ t❤❛② ✤ê✐✳ ✣➦❝ ✤✐➸♠ ♥➔② ❧➔ ❝ì sð ❝❤♦ ❝→❝ ù♥❣ ❞ư♥❣ ❝õ❛ ✤✐➺♥ tr÷í♥❣ tr♦♥❣ ✈✐➺❝ ✤✐➲✉ ❝❤➾♥❤ ✤ë rë♥❣ ✈ị♥❣ ❝➜♠ ❝ơ♥❣ ♥❤÷ ❝→❝ t➼♥❤ ❝❤➜t q✉❛♥❣ ✤✐➺♥ ❧✐➯♥ q✉❛♥ tr♦♥❣ ❝→❝ t❤✐➳t ❜à q✉❛♥❣ ✤✐➺♥ tû ♥❛♥♦✱ ♣❤ị ❤đ♣ ✈ỵ✐ tø♥❣ ù♥❣ ❞ư♥❣ ❝ư t❤➸✳ ▲í✐ ❝↔♠ ì♥ ◆❣❤✐➯♥ ❝ù✉ ♥➔② ✤÷đ❝ t➔✐ trđ ❜ð✐ ◗✉ÿ P❤→t tr✐➸♥ ❦❤♦❛ ❤å❝ ✈➔ ❝æ♥❣ ♥❣❤➺ ◗✉è❝ ❣✐❛ ✭◆❆❋❖❙✲ ❚❊❉✮ tr♦♥❣ ✤➲ t➔✐ ♠➣ sè ✶✵✸✳✵✶✲✷✵✶✼✳✸✻✶✳ ✸✽ ❇Ị■ ✣➐◆❍ ❍Đ■✱ ✣➱ ▲■◆❍ ❚❍➁◆●✱ P❍❆◆ ❱❿◆ ◆❍❹▼ ❚⑨■ ▲■➏❯ ❚❍❆▼ ❑❍❷❖ ❬✶❪ ❳✐❛ ❋✳✱ ❋❛r♠❡r ❉✳❇✳✱ ▲✐♥ ❚✳▼✳✱ ❆✈♦✉r✐s P✳ ✭✷✵✶✵✮✱ ◆❛♥♦ ▲❡tt✳✱ ✶✵✱ ♣♣✳ ✼✶✺✲✼✶✽✳ ❬✷❪ ●✐♦✈❛♥♥❡tt✐ ●✳✱ ❑❤♦♠②❛❦♦✈ P✳❆✳✱ ❇r♦❝❦s ●✳✱ ❑❡❧❧② P✳❏✳✱ ✈❛♥ ❞❡♥ ❇r✐♥❦ ❏✳ ✭✷✵✵✼✮✱ P❤②s✳ ❘❡✈✳ ❇✱ ✼✻✱ ♣✳ ✵✼✸✶✵✸✳ ❬✸❪ ❈❤❡♥ ❳✳❋✳✱ ▲✐❛♥ ❏✳❙✳✱ ❏✐❛♥❣ ◗✳ ✭✷✵✶✷✮✱ P❤②s✳ ❘❡✈✳ ❇✱ ✽✻✱ ♣✳ ✶✷✺✹✸✼✳ ◆❛t✉r❡✱ ✹✺✾✱ ♣♣✳ ✽✷✵✲✽✷✸✳ ❈❛str♦ ❊✳❱✳✱ ❡t ❛❧✳ ✭✷✵✵✼✮✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳✱ ✾✾✱ ♣✳ ✷✶✻✽✵✷✳ ●✉✐ ●✳✱ ▲✐ ❏✳✱ ❩❤♦♥❣ ❏✳ ✭✷✵✵✽✮✱ P❤②s✳ ❘❡✈✳ ❇ ✼✽✱ ✵✼✺✹✸✺✳ ❬✹❪ ❩❤❛♥❣ ❨✳✱ ❡t ❛❧✳ ✭✷✵✵✾✮✱ ❬✺❪ ❬✻❪ ❬✼❪ ❙✉♥ ▲✳✱ ▲✐ ◗✳✱ ❘❡♥ ❍✳✱ ❙✉ ❍✳✱ ❙❤✐ ◗✳❲✳✱ ❨❛♥❣ ❏✳ ✭✷✵✵✽✮✱ ✵✼✹✼✵✹✳ ❏✳ ❈❤❡♠✳ P❤②s✳✱ ✶✷✾✱ ♣✳ ❏✳ P❤②s✳ ❈❤❡♠✳ ❈✱ ✶✶✼✱ ♣♣✳ ✹✼✾✶✲✹✼✾✾✳ ❉❛✐ ◗✳◗✳✱ ❩❤✉ ❨✳❋✳✱ ❏✐❛♥❣ ◗✳ ✭✷✵✶✹✮✱ P❤②s✳ ❈❤❡♠✳ ❈❤❡♠✳ P❤②s✳✱ ✶✻✱ ♣♣✳ ✶✵✻✵✼✲✶✵✻✶✸✳ ▲✐ ▲✳✱ ❡t ❛❧✳ ✭✷✵✶✶✮✱ ❆❈❙ ◆❛♥♦✱ ✺✱ ♣♣✳ ✷✻✵✶✲✷✻✶✵✳ ❊❧✐❛s ❉✳❈✳✱ ❡t ❛❧✳ ✭✷✵✵✾✮✱ ❙❝✐❡♥❝❡✱ ✸✷✸✱ ♣♣✳ ✻✶✵✲✻✶✸✳ ❩❤♦✉ ❏✳✱ ❲❛♥❣ ◗✳✱ ❙✉♥ ◗✳✱ ❈❤❡♥ ❳✳❙✳✱ ❑❛✇❛③♦❡ ❨✳✱❏❡♥❛ P✳ ✭✷✵✵✾✮✱ ◆❛♥♦ ▲❡tt✳✱ ✾✱ ♣♣✳ ❬✽❪ ❉❛✐ ◗✳◗✳✱ ❩❤✉ ❨✳✱ ❏✐❛♥❣ ◗✳ ✭✷✵✶✸✮✱ ❬✾❪ ❬✶✵❪ ❬✶✶❪ ❬✶✷❪ ✸✽✻✼✲✸✽✼✵✳ ◆❛♥♦ ▲❡tt✳✱ ✶✵✱ ♣♣✳ ✸✸✻✵✲✸✸✻✻✳ ❈❤♦✐ ❙✳✲▼✳✱ ❏❤✐ ❙✳✲❍✳✱ ❙♦♥ ❨✳✲❲✳ ✭✷✵✶✵✮✱ ◆❛♥♦ ▲❡tt✳✱ ✶✵✱ ♣♣✳ ✸✹✽✻✲✸✹✽✾✳ ❬✶✸❪ ❍❛❜❡r❡r ❉✳✱ ❡t ❛❧✳ ✭✷✵✶✵✮✱ ❬✶✹❪ ❬✶✺❪ ▲✉♦ ❩✳✱ ❨✉ ❚✳✱ ❑✐♠ ❑✳✱ ◆✐ ❩✳✱ ❨♦✉ ❨✳✱ ▲✐♠ ❙✳✱ ❙❤❡♥ ❩✳✱ ❲❛♥❣ ❙✳✱ ▲✐♥ ❏✳ ✭✷✵✵✾✮✱ ◆❛♥♦✱ ✸✱ ♣♣✳ ✶✼✽✶✲✶✼✽✽✳ ❆❈❙ P❤②s✳ ❘❡✈✳ ▲❡tt✳✱ ✶✵✼✱ ♣✳ ✵✽✻✽✵✶✳ ▲♦♣❡s ❞♦s ❙❛♥t♦s ❏✳▼✳❇✳✱ P❡r❡s ◆✳▼✳❘✳✱ ❈❛str♦ ◆❡t♦ ❆✳❍✳ ✭✷✵✵✼✮✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳✱ ❬✶✻❪ ❑✐❧❧✐ ▼✳✱ ❲✉ ❙✳✱ P❛r❛♠❡❦❛♥t✐ ❆✳ ✭✷✵✶✶✮✱ ❬✶✼❪ ✾✾✱ ♣✳ ✷✺✻✽✵✷✳ ❬✶✽❪ ❙❛✐t♦ ❘✳✱ ❉r❡ss❡❧❤❛✉s ●✳✱ ❉r❡ss❡❧❤❛✉s ▼✳❙✳ ✭✶✾✾✽✮✱ ◆❛♥♦t✉❜❡s✱ ■♠♣❡r✐❛❧ ❈♦❧❧❡❣❡ Pr❡ss✱ ▲♦♥❞♦♥✳ ✷❉ ▼❛t❡r✳✱ ✶✱ ♣✳ ✵✶✶✵✵✺✳ ●r❛ss✐ ❘✳✱ ▲♦✇ ❚✳✱ ▲✉♥❞str♦♠ ▼✳ ✭✷✵✶✶✮✱ ◆❛♥♦ ▲❡tt✳✱ ✶✶✱ ♣♣✳ ✹✺✼✹✲✹✺✼✽✳ ▼❛❤❛♥ ●✳❉✳ ✭✶✾✾✸✮✱ ▼❛♥② P❛rt✐❝❧❡ P❤②s✐❝s✱ P❧❡♥✉♠ Pr❡ss✱ ◆❡✇ ❨♦r❦✳ ❚❛❜❡rt ❈✳❏✳✱ ◆✐❝♦❧ ❊✳❏✳ ✭✷✵✶✷✮✱ P❤②s✳ ❘❡✈✳ ❇✱ ✽✻✱ ♣✳ ✵✼✺✹✸✾✳ ❬✶✾❪ ❩♦❧②♦♠✐ ❱✳✱ ❲❛❧❧❜❛♥❦ ❏✳❘✳✱ ❋❛❧❦♦ ❱✳■✳ ✭✷✵✶✹✮✱ ❬✷✵❪ ❬✷✶❪ ❬✷✷❪ P❤②s✐❝❛❧ Pr♦♣❡rt✐❡s ♦❢ ❈❛r❜♦♥ ▼❾❚ ✣❐ ❚❘❸◆● ❚❍⑩■ ✣■➏◆ ❚Û ❚❘❖◆● ●❘❆P❍❊◆❊ ✳✳✳ ✸✾ ❚✐t❧❡✿ ❊▲❊❈❚❘❖◆■❈ ❉❊◆❙■❚❨ ❖❋ ❙❚❆❚❊❙ ■◆ ❍❨❉❘❖●❊◆❆❚❊❉ ❇■▲❆❨❊❘ ●❘❆P❍❊◆❊ ❯◆❉❊❘ ❚❍❊ ■◆❋▲❯❊◆❈❊ ❖❋ ❆ ❉❈ ❊▲❊❈❚❘■❈ ❋■❊▲❉ ❆❜str❛❝t✿ ■♥ t❤✐s ✇♦r❦✱ ✇❡ ✐♥✈❡st✐❣❛t❡ t❤❡ ❡❧❡❝tr♦♥✐❝ ❞❡♥s✐t② ♦❢ st❛t❡s ✭❉❖❙✮ ✐♥ ❤②❞r♦✲ ❣❡♥❛t❡❞ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡ ✭❍✲❇▲●✮ s✉❜❥❡❝t❡❞ ✐♥ ❛ ❞❝ ❡❧❡❝tr✐❝ ❢✐❡❧❞✳ ❋♦✉r ❞✐❢❢❡r❡♥t t②♣❡s ♦❢ ❤②❞r♦❣❡♥❛t✐♦♥ ❛r❡ ❝♦♥s✐❞❡r❡❞✿ t❛❜❧❡✲❧✐❦❡ ❍✲❇▲● ✭❚▲✕❍✲❇▲●✮✱ ❝❤❛✐r✲❧✐❦❡ ❍✲❇▲● ✭❈▲✕❍✲ ❇▲●✮✱ r❡❞✉❝❡❞ t❛❜❧❡✲❧✐❦❡ ❍✲❇▲● ✭r❚▲✕❍✲❇▲●✮ ❛♥❞ r❡❞✉❝❡❞ ❝❤❛✐r✲❧✐❦❡ ❍✲❇▲● ✭r❈▲✕❍✲ ❇▲●✮✳ ❚❤❡ ❡①♣r❡ss✐♦♥ ♦❢ t❤❡ ❉❖❙ ✐s ♦❜t❛✐♥❡❞ ❜② ✐ts r❡❧❛t✐♦♥ t♦ t❤❡ ●r❡❡♥ ❢✉♥❝t✐♦♥✱ ✉s✐♥❣ ❍❛♠✐❧t♦♥✐❛♥ ✐♥ t❤❡ t✐❣❤t✲❜✐♥❞✐♥❣ ❛♣♣r♦①✐♠❛t✐♦♥✳ ◆✉♠❡r✐❝❛❧ r❡s✉❧ts s❤♦✇ t❤❛t ♣r✐st✐♥❡ ❜✐✲ ❧❛②❡r ❣r❛♣❤❡♥❡ ✐s ❛ s❡♠✐♠❡t❛❧✱ ✇❤✐❧❡ t❤❡ ❈▲✕❍✲❇▲● ❛♥❞ ❚▲✕❍✲❇▲● ❛r❡ s❡♠✐❝♦♥❞✉❝t♦rs✳ ❇❡s✐❞❡s✱ t❤❡ ❡①t❡r♥❛❧ ❡❧❡❝tr✐❝ ❢✐❡❧❞ ❤❛s ❛ str♦♥❣ ✐♥❢❧✉❡♥❝❡ ♦♥ t❤❡ ❉❖❙✳ ■♥ ❛❧❧ str✉❝t✉r❡s✱ t❤❡ ❉❖❙ ❛t t❤❡ ❋❡r♠✐ ❡♥❡r❣② ❧❡✈❡❧ ✐♥❝r❡❛s❡s ✇✐t❤ ✐♥❝r❡❛s✐♥❣ t❤❡ ❡❧❡❝tr✐❝ ❢✐❡❧❞ str❡♥❣t❤✳ ■♥ ❛❞❞✐t✐♦♥✱ t❤❡ ❜❛♥❞ ❣❛♣ ✐♥ ❈▲✕❍✲❇▲● ❛♥❞ ❚▲✕❍✲❇▲● str✉❝t✉r❡s ❞❡❝r❡❛s❡s ✇✐t❤ t❤❡ ❡❧❡❝tr✐❝ ❢✐❡❧❞ str❡♥❣t❤✳ ❚❤❡ ❛❜♦✈❡ ❝❤❛r❛❝t❡r✐st✐❝s ❛r❡ t❤❡ ❜❛s✐s ❢♦r t❤❡ ✉s❡ ♦❢ ❛♥ ❡❧❡❝tr✐❝ ❢✐❡❧❞ t♦ ❛❞❥✉st t❤❡ ❡❧❡❝tr♦♥✐❝ ♣r♦♣❡rt✐❡s ♦❢ ❍✲❇▲● s♦ t❤❛t ✐t ✐s s✉✐t❛❜❧❡ ❢♦r ❛♣♣❧✐❝❛t✐♦♥s ✐♥ ♥❛♥♦✲♦♣t♦❡❧❡❝tr♦♥✐❝ ❞❡✈✐❝❡s✳ ❑❡②✇♦r❞s✿ ❜✐❧❛②❡r ❣r❛♣❤❡♥❡✱ ❤②❞r♦❣❡♥❛t✐♦♥✱ ❞❡♥s✐t② ♦❢ st❛t❡s✱ t✐❣❤t✲❜✐♥❞✐♥❣ ♠♦❞❡❧✳