UNIVERSIDADE DE BRASÍLIA INSTITUTO DE FÍSICA Tese de Doutorado

❯◆■❱❊❘❙■❉❆❉❊ ❉❊ ❇❘❆❙❮▲■❆

■◆❙❚■❚❯❚❖ ❉❊ ❋❮❙■❈❆

❚❡s❡ ❞❡ ❉♦✉t♦r❛❞♦

Pr♦♣r✐❡❞❛❞❡s ❡❧étr✐❝❛s ❡ ♠❛❣♥ét✐❝❛s ❞❡ ♠♦❧é❝✉❧❛s

❛rt✐✜❝✐❛✐s s❡♠✐❝♦♥❞✉t♦r❛s

❋➪❇■❖ ❱■❊■❘❆ ▼❖❯❘❆

❖r✐❡♥t❛❞♦r✿Pr♦❢✳ ❉r✳ ❘✐❝❛r❞♦ ●❛r❣❛♥♦

❈♦✲♦r✐❡♥t❛❞♦r✿Pr♦❢✳ ❉r✳ ❋❛♥②❛♦ ◗✉

✏Pr♦♣r✐❡❞❛❞❡s ❡❧étr✐❝❛s ❡ ♠❛❣♥ét✐❝❛s ❞❡ ♠♦❧é❝✉❧❛s ❛rt✐✜❝✐❛✐s

s❡♠✐❝♦♥❞✉t♦r❛s✑

P♦r

❋á❜✐♦ ❱✐❡✐r❛ ▼♦✉r❛

❚❡s❡ s✉❜♠❡t✐❞❛ ❛♦ ■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí❧✐❛ ❝♦♠♦

♣❛rt❡ ❞♦s r❡q✉❡s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ❉♦✉t♦r ❡♠ ❋ís✐❝❛✳

❆♣r♦✈❛❞❛ ♣♦r✿

Pr♦❢✳ ❉r✳ ❘✐❝❛r❞♦ ●❛r❣❛♥♦

✭❖r✐❡♥t❛❞♦r✮ ■❋✴❯♥❇

Pr♦❢✳ ❉r✳ ●❡r❛❧❞♦ ▼❛❣❡❧❛ ❡ ❙✐❧✈❛

■❋✴❯♥❇

Pr♦❢✳ ❉r✳ P❡❞r♦ ❍❡♥r✐q✉❡ ❞❡ ❖❧✐✈❡✐r❛ ◆❡t♦ ■❋✴❯♥❇

Pr♦❢✳ ❉r✳ ❍❡✐❜❜❡ ❈ ❇❡♥❡❞✐t♦ ❞❡ ❖❧✐✈❡✐r❛

■◗✲❯♥❇

Pr♦❢✳ ❉r✳ ❈❛✐♦ ❍❡♥r✐q✉❡ ▲❡✇❡♥❦♦♣❢

❯❋❋✲ ❘❏

✏✳✳✳✳❖s ❤♦♠❡♥s ♣❡r❞❡♠ ❛ s❛ú❞❡ ♣❛r❛ ❥✉♥t❛r ❞✐♥❤❡✐r♦✱ ❞❡♣♦✐s ♣❡r❞❡♠ ♦ ❞✐♥❤❡✐r♦ ♣❛r❛ r❡❝✉♣❡r❛r ❛ s❛ú❞❡✳ ❊ ♣♦r ♣❡♥s❛r❡♠ ❛♥s✐♦s❛♠❡♥t❡ ♥♦ ❢✉t✉r♦ ❡sq✉❡❝❡♠ ❞♦ ♣r❡s❡♥t❡ ❞❡ ❢♦r♠❛ q✉❡ ❛❝❛❜❛♠ ♣♦r ♥ã♦ ✈✐✈❡r ♥❡♠ ♥♦ ♣r❡s❡♥t❡ ♥❡♠ ♥♦ ❢✉t✉r♦✳ ❊ ✈✐✈❡♠ ❝♦♠♦ s❡ ♥✉♥❝❛ ❢♦ss❡♠ ♠♦rr❡r✳✳✳ ❡ ♠♦rr❡♠ ❝♦♠♦ s❡ ♥✉♥❝❛ t✐✈❡ss❡♠ ✈✐✈✐❞♦✳ ✑

❆❣r❛❞❡❝✐♠❡♥t♦s

❆♦s ♠❡✉s ♣❛✐s✱ ❊s♠❡r❛❧❞♦ P❡r❡✐r❛ ▼♦✉r❛ ❡ ❈é❧✐❛ ❱✐❡✐r❛ ▼♦✉r❛✱ ♣❡❧♦ ❝❛r✐♥❤♦ ❡ ❝♦♠♣r❡❡♥sã♦ ❞✉r❛♥t❡ t♦❞♦s ❡ss❡s ❛♥♦s✳

❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r ❘✐❝❛r❞♦ ●❛r❣❛♥♦✱ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛✱ ❝♦♥✜❛♥ç❛✱ ❛♣♦✐♦ ❡ ✐♥✲ ❝❡♥t✐✈♦ ❢✉♥❞❛♠❡♥t❛✐s ♥❛ r❡❛❧✐③❛çã♦ ❞❡ss❡ tr❛❜❛❧❤♦✳ ❆♦ ♠❡✉ ❝♦✲♦r✐❡♥t❛❞♦r ❋❛♥②❛♦ ◗✉ ♣❡❧❛ r✐❝❛ ❝♦♥tr✐❜✉✐çã♦ ❡ ❡①♣❡r✐❡♥❝✐❛ ❛ ♠✐♠ tr❛♥s♠✐t✐❞❛ ❞✉r❛♥t❡ t♦❞♦s ❡ss❡s ❛♥♦s✳ ❆❣r❛❞❡ç♦✲♦ ❛✐♥❞❛✱ ♣❡❧❛ ❣❡♥❡r♦s❛ ❝♦♥tr✐❜✉✐çã♦ ♣❛r❛ ❝♦♠ ♠❡✉ ❛♠❛❞✉r❡❝✐♠❡♥t♦ ♣r♦✲ ✜ss✐♦♥❛❧✳

❆♦s ♣r♦❢❡ss♦r❡s ❱✐❝t♦r ❉♦❞♦♥♦✈✱ ❆♥tô♥✐♦ ❈❛r❧♦s P❡❞r♦③❛ ❡ ❆❞❡♠✐r ❊✉❣ê♥✐♦ ❞❡ ❙❛♥t❛♥❛ ♣♦r ♠✐♥❤❛ ❢♦r♠❛çã♦ ❝✐❡♥tí✜❝❛✳

❆♦s ♣r♦❢❡ss♦r❡s ❞❛ ♣ós✲❣r❛❞✉❛çã♦ q✉❡ ❝♦♠ ❛ r❡❛❧✐③❛çã♦ ❞❡ s❡✉s tr❛❜❛❧❤♦s ❝♦♥tr✐❜✉❡♠ ♣❛r❛ ♦ s✉❝❡ss♦ ❞♦s ❛❧✉♥♦s✳

❆♦ ♣r♦❢❡ss♦r ●❡r❛❧❞♦ ▼❛❣❡❧❛✱ ♣❡❧♦ s❡✉ tr❛t♦ ❝♦r❞✐❛❧ ❡ ♣❡❧❛ s✉❛ ✈❛st❛ s❛❜❡✲ ❞♦r✐❛ tr❛♥s♠✐t✐❞❛ ❡♠ ❝♦♥✈❡rs❛s ✐♥❢♦r♠❛✐s ♥♦ ✐♥st✐t✉t♦✳

❆♦s ♠❡✉s ❛♠✐❣♦s P❡❞r♦ ❍❡♥r✐q✉❡ ❞❡ ❖❧✐✈❡✐r❛ ◆❡t♦✱ ❲✐❧✐❛♠ ❋❡rr❡✐r❛ ❞❛ ❈✉♥❤❛✱ q✉❡ ♠❡ ❛❝♦♠♣❛♥❤❛r❛♠ ♥❡ss❛ ❥♦r♥❛❞❛✳

➚ ❋❛❜✐❛♥❛ ♣❡❧❛ ❝♦♠♣r❡❡♥sã♦✱ ❛♣♦✐♦ ❡✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡✱ ♣❡❧♦ ❝❛r✐♥❤♦✳

➚ t♦❞♦s ♦s ❛♠✐❣♦s✱ s❡♠ ♦s q✉❛✐s ❡✉ ♥ã♦ s❡r✐❛ ♦ ♠❡s♠♦✳ ❊♠ ❡s♣❡❝✐❛❧✱ ❛♦ ➱r✐❝♦ ❡ ❛♦ ❊✈❛♥❞r♦✱ q✉❡ ❛❧é♠ ❞❛ ❛♠✐③❛❞❡ ❢♦r❛♠ r❡s♣♦♥sá✈❡✐s ❞✐r❡t❛ ❡ ✐♥❞✐r❡t❛♠❡♥t❡ ♣❡❧❛ ❝♦♥❝r❡t✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳

❘❡s✉♠♦

◆❛ ♣r✐♠❡✐r❛ ♣❛rt❡ ❞❡st❛ ❚❡s❡✱ r❡❛❧✐③❛♠♦s ✉♠ ❝á❧❝✉❧♦ ❞❡ ❞✐❛❣♦♥❛❧✐③❛çã♦ ❡①❛t❛ ♣❛r❛ ❛ ❡str✉t✉r❛ ❡❧❡trô♥✐❝❛ ❞❡ ❉◗❉s ✭❞♦ ✐♥❣❧ês ❉♦✉❜❧❡ ◗✉❛♥t✉♠ ❉♦ts✮ ❛❝♦♣❧❛❞♦s ✈❡rt✐❝❛❧♠❡♥t❡✱ ✉s❛♥❞♦ ♦ ♠ét♦❞♦ ▲❈❆❖ ✭❞♦ ✐♥❣❧ês ▲✐♥❡❛r ❈♦♠❜✐♥❛t✐♦♥ ♦❢ ❆t♦♠✐❝ ❖r❜✐t❛❧s✮✳ ❆❝❤❛♠♦s q✉❡ ♣❛r❛ ❛t✐♥❣✐r ✉♠❛ ❜♦❛ ♣r❡❝✐sã♦ ❡ ♦❜t❡r ✉♠❛ rá♣✐❞❛ ❝♦♥✈❡r✲ ❣ê♥❝✐❛ ❞♦s ❝á❧❝✉❧♦s✱ ✉♠❛ ❡s♣❡❝✐❛❧ ❛t❡♥çã♦ ❞❡✈❡ s❡r ❞❛❞❛ ♥❛ ❡s❝♦❧❤❛ ❞❛s ❢✉♥çõ❡s ❞❡ ❜❛s❡✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❛r❛ ♣♦♥t♦s q✉â♥t✐❝♦s ♣❡q✉❡♥♦s✳ ❉❡♠♦♥str❛♠♦s q✉❡ ❛s ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ❞♦s ♣♦♥t♦s q✉â♥t✐❝♦s s❡r✈❡♠ ❝♦♠♦ ❢✉♥çõ❡s ❞❡ ❜❛s❡ ✐❞❡❛✐s ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞❡ ♦r❜✐t❛✐s ♠♦❧❡❝✉❧❛r❡s ❞❡ ❉◗❉s ❡♠ ♥♦ss♦ ❝á❧❝✉❧♦ ❞❡ ❞✐❛❣♦♥❛❧✐③❛çã♦ ❡①❛t❛✳ ❆❝❤❛✲ ♠♦s t❛♠❜é♠ ❛ ♥❛t✉r❡③❛ ❞♦s ❡st❛❞♦s ❡❧❡trô♥✐❝♦s ❞♦s ❉◗❉s q✉❡ ❡✈♦❧✉❡♠ ❞♦s ♦r❜✐t❛✐s ❛tô♠✐❝♦s ♦ ❞♦ t✐♣♦ ♠♦❧❡❝✉❧❛r ✭❧✐❣❛❞♦ ❡ ♥ã♦✲❧✐❣❛❞♦✮ q✉❛♥❞♦ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ♦s ♣♦♥✲ t♦s q✉â♥t✐❝♦s ❞✐♠✐♥✉✐✳ ❆ ❡str✉t✉r❛ ❡❧❡trô♥✐❝❛ ❞♦s ❉◗❉s ♣♦❞❡ s❡r ♣r♦❥❡t❛❞❛ ❛tr❛✈és ❞❡ ✉♠ ❞❡s❡♥❤♦ ❞❡ ✉♠ ❉◗❉✳ ■st♦ ❡stá ❡♠ ♥ít✐❞♦ ❝♦♥tr❛st❡ ❝♦♠ ❛s ♠♦❧é❝✉❧❛s r❡❛✐s ❡♠ q✉❡ ❛s ♣♦s✐çõ❡s ❣❡♦♠étr✐❝❛s ❞♦s át♦♠♦s ♥ã♦ sã♦ ✈❛r✐❛❞❛s✳ ◆❛ s❡❣✉♥❞❛ ♣❛rt❡✱ ❛♣r❡s❡♥t❛♠♦s ❛ ♥♦ss❛ t❡♦r✐❛ s♦❜r❡ ♦ ❝♦♥tr♦❧❡ ó♣t✐❝♦ ❞❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛p₋d❡♥tr❡

♦s s♣✐♥s ❞♦ ❜✉r❛❝♦ ❞♦ ♠❛t❡r✐❛❧ ❞❡ ●❛❆s ❞♦♣❛❞♦ ❝♦♠ ✉♠ ú♥✐❝♦ ♠❛♥❣❛♥ês ▼♥2+ _❡ ✐rr❛❞✐❛❞♦ ♣♦r ✉♠ ❝❛♠♣♦ ❞❡ ❧❛s❡r ♣✉❧s❛❞♦ ✭❈▲P✮ ♣♦❧❛r✐③❛❞♦ ❧✐♥❡❛r♠❡♥t❡ ❡ ♠♦♥♦❝r♦✲ ♠át✐❝♦ s♦❜ ❝♦♥❞✐çõ❡s ❞❡ ♥ã♦✲r❡ss♦♥â♥❝✐❛ ❜❛s❡❛❞♦ ❡♠ ✉♠❛ t❡♦r✐❛ ♥ã♦✲♣❡rt✉r❜❛t✐✈❛ ✉t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ ▲❈❆❖✳ ❆❝❤❛♠♦s q✉❡ ❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛p₋d❧❡✈❛ ❛ ❢♦r♠❛çã♦

❞❡ ✉♠ ♣ó❧❛r♦♥ ♠❛❣♥ét✐❝♦ ✭P▼✮✱ ❡♥q✉❛♥t♦ ♦ ❈▲P ✐♥❞✉③ ✉♠ ♣♦t❡♥❝✐❛❧ ❞❡ ❈♦✉❧♦♠❜ q✉❡ r❡✈❡st❡ ♦ ❛❝❡✐t❛❞♦r✱ q✉❡ tr❛♥s❢♦r♠❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ✉♠ ú♥✐❝♦ ❝❡♥tr♦ ❡♠ ✉♠ ♦✉tr♦ ❝♦♠ ❞♦✐s ❝❡♥tr♦s ✈✐rt✉❛✐s ❝❛rr❡❣❛❞♦s ♣♦s✐t✐✈❛♠❡♥t❡ ❛ss❡♠❡❧❤❛♥❞♦ ❛♦ í♦♥ ♠♦❧❡❝✉❧❛r ❍+

2✳ ❆ ❞✐❝♦t♦♠✐❛ ❞❛s ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ❞♦ ❜✉r❛❝♦ ❞❡♣❡♥❞❡ ❢♦rt❡♠❡♥t❡ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦ ❝❛♠♣♦ ❞❡ ❧❛s❡r✱ q✉❡ ❛❢❡t❛ ❞r❛st✐❝❛♠❡♥t❡ ❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛p₋d ❜❡♠ ❝♦♠♦ ❛

❡♥❡r❣✐❛ ❞❡ ❧✐❣❛çã♦ ❞♦ ♣ó❧❛r♦♥ ♠❛❣♥ét✐❝♦✳ ❈♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦ ❧❛s❡r

r❡❞✉③✲s❡ t❛♥t♦ ♦ ♣ó❧❛r♦♥ ♠❛❣♥ét✐❝♦ ❝♦♠♦ ❛ ❡♥❡r❣✐❛ ❞❡ ❧✐❣❛çã♦✳ P❛r❛ ✉♠❛ ✐♥t❡♥s✐✲ ❞❛❞❡ ❞❡ ❡①❝✐t❛çã♦ ❣r❛♥❞❡✱ ♦ ♣ó❧❛r♦♥ ♣♦❞❡ s❡r ❝♦♠♣❧❡t❛♠❡♥t❡ ❞✐ss♦❧✈✐❞♦✳ ◆❛ t❡r❝❡✐r❛ ♣❛rt❡✱ ❡st❡♥❞❡♠♦s ♦ ♠♦❞❡❧♦ ▲❈❆❖ ♣❛r❛ ♦ ♠♦❞❡❧♦ ▲❈❆❖ ✈❛r✐❛❝✐♦♥❛❧ ♦♥❞❡ ❛s ❢✉♥çõ❡s ❞❡ ❜❛s❡ sã♦ ♦t✐♠✐③❛❞❛s ✈❛r✐❛❝✐♦♥❛❧♠❡♥t❡✳ ❆❧é♠ ❞✐ss♦✱ ❢♦❝❛♠♦s ♥♦ss❛ ❛t❡♥çã♦ ♥♦s ❡❢❡✐t♦s ✐♥❞✐✈✐❞✉❛✐s ❞❛ ❛tr❛çã♦ ❞❡ ❈♦✉❧♦♠❜ ❡ ❞❡ tr♦❝❛ s♣✐♥✲s♣✐♥ ❛♥t✐✲❢❡rr♦♠❛❣♥ét✐❝♦ ❡ ♥❛ ✐♥st❛❜✐❧✐❞❛❞❡ ❞♦ P▼ ❡ ✐♦♥✐③❛çã♦ ❞♦ ❛❝❡✐t❛❞♦r ▼♥ ✐♥❞✉③✐❞♦ ♣❡❧♦ ❈▲P✳ ❈♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦ ❈▲P✱ ❡♥❝♦♥tr❛♠♦s ♣r✐♠❡✐r❛♠❡♥t❡ q✉❡ ♦ P▼ t♦r♥❛✲s❡ ✐♥stá✈❡❧ ❡✱ ❡♠ s❡❣✉✐❞❛✱ ❡❧❡ é s✉♣r✐♠✐❞♦ ❞❡✈✐❞♦ ❛ ❡♥❡r❣✐❛ ❞❡ tr♦❝❛ s❡r ③❡r♦✳ ❆✉♠❡♥✲ t❛♥❞♦ ❛✐♥❞❛ ♠❛✐s ❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦ ❧❛s❡r✱ ❛ ✐♦♥✐③❛çã♦ ❞♦ ❛❝❡✐t❛❞♦r ▼♥ ♦❝♦rr❡ ❞❡✈✐❞♦ ❛♦ ❞❡s❛♣❛r❡❝✐♠❡♥t♦ ❞❛ ❡♥❡r❣✐❛ ❞❡ ❧✐❣❛çã♦✳ ❋✐♥❛❧♠❡♥t❡✱ ♥❛ ú❧t✐♠❛ ♣❛rt❡ ❞❡st❡ tr❛✲ ❜❛❧❤♦✱ ♥ós ❞❡s❡♥✈♦❧✈❡♠♦s ✉♠ ♠ét♦❞♦✱ ❛tr❛✈és ❞♦ ✉s♦ ❞❡ ❢✉♥çõ❡s ❞❡ ❜❛s❡ ❣❛✉ss✐❛♥❛s ♦t✐♠✐③❛❞❛s ❝♦♠♦ ❜❛s❡ ♥♦ ♠ét♦❞♦ ▲❈❆❖✱ ♣❛r❛ tr❛t❛r ❡❢❡✐t♦s ❞❡ ♠✉✐t♦s ❝♦r♣♦s ❡♠ ♠♦❧é❝✉❧❛s ❛rt✐✜❝✐❛✐s✳

❆❜str❛❝t

■♥ t❤❡ ✜rst ♣❛rt ♦❢ t❤✐s ✇♦r❦✱ ✇❡ ❤❛✈❡ ♣❡r❢♦r♠❡❞ ❛♥ ❡①❛❝t ❞✐❛❣♦♥❛❧✐③❛t✐♦♥ ❝❛❧❝✉❧❛t✐♦♥ ✭❊❉✮ ❢♦r ❡❧❡❝tr♦♥✐❝ str✉❝t✉r❡ ♦❢ ✈❡rt✐❝❛❧❧② ❝♦✉♣❧❡❞ ❞♦✉❜❧❡ q✉❛♥t✉♠ ❞♦ts ✭❉◗❉s✮✱ ✉s✐♥❣ ❧✐♥❡❛r ❝♦♠❜✐♥❛t✐♦♥s ♦❢ ❛t♦♠✐❝ ♦r❜✐t❛❧s ✭▲❈❆❖✮✳ ❲❡ ✜♥❞ t❤❛t t♦ r❡❛❝❤ ❤✐❣❤ ❞❡❣r❡❡ ♦❢ ❛❝❝✉r❛❝② ❛♥❞ ❣❡t ❛ q✉✐❝❦ ❝♦♥✈❡r❣❡♥❝❡✱ ❛ s♣❡❝✐❛❧ ❛tt❡♥t✐♦♥ ✐♥ ❝❤♦✐❝❡ ♦❢ ❜❛s✐s ❢✉♥❝t✐♦♥s ❤❛s t♦ ❜❡ ♣❛✐❞✱ s♣❡❝✐❛❧❧② ❢♦r s♠❛❧❧ q✉❛♥t✉♠ ❞♦ts✳ ❲❡ ❞❡♠♦♥str❛t❡ t❤❛t t❤❡ ✇❛✈❡ ❢✉♥❝t✐♦♥s ♦❢ ✐♥❞✐✈✐❞✉❛❧ q✉❛♥t✉♠ ❞♦ts s❡r✈❡ ❛s ✐❞❡❛❧ ❜❛s✐s ❢✉♥❝t✐♦♥s ❢♦r ❝♦♥str✉❝t✐♦♥ ♦❢ ♠♦❧❡❝✉❧❛r ♦r❜✐t❛❧s ♦❢ t❤❡ ❉◗❉s ✐♥ ♦✉r ❊❉ ❝❛❧❝✉❧❛t✐♦♥✳ ❲❡ ❛❧s♦ ✜♥❞ t❤❡ ♥❛t✉r❡ ♦❢ ❡❧❡❝tr♦♥✐❝ st❛t❡s ♦❢ t❤❡ ❉◗❉s ❡✈♦❧✈❡s ❢r♦♠ ❛t♦♠✐❝ t♦ ♠♦❧❡❝✉❧❛r✲ ❧✐❦❡ ♦r❜✐t❛❧s ✭❜♦♥❞✐♥❣ ❛♥❞ ❛♥t✐✲❜♦♥❞✐♥❣✮ ❛s ✐♥t❡r❞♦t ❞✐st❛♥❝❡ ❞❡❝r❡❛s❡s✳ ■♥ ❛❞❞✐t✐♦♥✱ t❤❡ ❡❧❡❝tr♦♥✐❝ str✉❝t✉r❡ ♦❢ ❉◗❉s ❝❛♥ ❜❡ ❡♥❣✐♥❡❡r❡❞ t❤r♦✉❣❤ ♣r♦♣❡r❧② ❉◗❉ ❞❡s✐❣♥✳ ❚❤✐s ✐s ✐♥ s❤❛r♣ ❝♦♥tr❛st t♦ t❤❡ ♥❛t✉r❛❧ ♠♦❧❡❝✉❧❡s ✐♥ ✇❤✐❝❤ t❤❡ ❣❡♦♠❡tr✐❝ ♣♦s✐t✐♦♥s ♦❢ ❝♦♠♣♦s❡❞ ❛t♦♠s ❛r❡ ♥♦t ❝❤❛♥❣❡❛❜❧❡✳ ■♥ t❤❡ s❡❝♦♥❞ ♣❛rt✱ ✇❡ r❡♣♦rt ♦✉r ❝♦♠✲ ♣r❡❤❡♥s✐✈❡ t❤❡♦r② ❛❜♦✉t ♦♣t✐❝❛❧ ❝♦♥tr♦❧ ♦❢ ♣✲❞ ❡①❝❤❛♥❣❡ ✐♥t❡r❛❝t✐♦♥ ❜❡t✇❡❡♥ s♣✐♥s ♦❢ ❤♦❧❡ ❛♥❞ ▼♥2+ _{✐♥ s✐♥❣❧❡✲♠❛♥❣❛♥❡s❡ ❞♦♣❡❞ ●❛❆s ♠❛t❡r✐❛❧ ✐rr❛❞✐❛t❡❞ ❜② ❛ ♠♦✲} ♥♦❝❤r♦♠❛t✐❝✱ ❧✐♥❡❛r❧② ♣♦❧❛r✐③❡❞✱ ✐♥t❡♥s❡ ♣✉❧s❡❞ ❧❛s❡r ✜❡❧❞ ✭P▲❋✮ ✉♥❞❡r ♥♦♥r❡s♦♥❛♥t ❝♦♥❞✐t✐♦♥s✱ ❜❛s❡❞ ♦♥ ♥♦♥♣❡rt✉r❜❛t✐♦♥ t❤❡♦r② ♣❧✉s st❛♥❞❛r❞ ▲❈❆❖✳ ❲❡ ✜♥❞ t❤❛t t❤❡ ♣✲❞ ❡①❝❤❛♥❣❡ ✐♥t❡r❛❝t✐♦♥ ❧❡❛❞s t♦ ❢♦r♠❛t✐♦♥ ♦❢ ♠❛❣♥❡t✐❝ ♣♦❧❛r♦♥ ✭▼P✮✳ ❲❤✐❧❡ t❤❡ P▲❋ ✐♥❞✉❝❡s ❛ ❞r❡ss❡❞ ❛❝❝❡♣t♦r ❈♦✉❧♦♠❜ ♣♦t❡♥t✐❛❧✱ ✇❤✐❝❤ tr❛♥s❢♦r♠s s✐♥❣❧❡ ❝❡♥t❡r ♣r♦❜❧❡♠ ✐♥t♦ t❤❡ ♦♥❡ ✇✐t❤ t✇♦ ✈✐rt✉❛❧ ♣♦s✐t✐✈❡❧② ❝❤❛r❣❡❞ ❝❡♥t❡rs✱ r❡s❡♠❜❧✐♥❣ ❤②❞r♦✲ ❣❡♥ ♠♦❧❡❝✉❧❡ ✐♦♥ ❍+

2 ✳ ❚❤❡ ❞✐❝❤♦t♦♠② ♦❢ ❤♦❧❡ ✇❛✈❡ ❢✉♥❝t✐♦♥s ❞❡♣❡♥❞ str♦♥❣❧② ♦♥ t❤❡ ❧❛s❡r✲✐♥t❡♥s✐t②✱ ✇❤✐❝❤ ❛✛❡❝ts ❞r❛♠❛t✐❝❛❧❧② t❤❡ ♣✲❞ ❡①❝❤❛♥❣❡ ✐♥t❡r❛❝t✐♦♥ ❛s ✇❡❧❧ ❛s ❜✐♥❞✐♥❣ ❡♥❡r❣② ♦❢ ♠❛❣♥❡t✐❝ ♣♦❧❛r♦♥✳ ■♥❝r❡❛s✐♥❣ t❤❡ ❧❛s❡r ✐♥t❡♥s✐t② r❡❞✉❝❡s t❤❡ ♠❛❣♥❡t✐❝ ♣♦❧❛r♦♥ ❛♥❞ ❜✐♥❞✐♥❣ ❡♥❡r❣②✳ ❆t ❧❛r❣❡r ❡①❝✐t❛t✐♦♥ ✐♥t❡♥s✐t②✱ t❤❡ ♠❛❣♥❡✲ t✐❝ ♣♦❧❛r♦♥ ❝❛♥ ❜❡ ❝♦♠♣❧❡t❡❧② ❞✐ss♦❧✈❡❞✳ ■♥ t❤❡ t❤✐r❞ ♣❛rt✱ ✇❡ ❤❛✈❡ ❡①t❡♥❞❡❞ ♦✉r

st❛♥❞❛r❞ ▲❈❆❖ t♦ ✈❛r✐❛t✐♦♥❛❧ ▲❈❆❖ ❜② ✈❛r✐❛t✐♦♥❛❧❧② ♦♣t✐♠✐③❡ t❤❡ ❜❛s✐s ❢✉♥❝t✐♦♥s✳ ■♥ ❛❞❞✐t✐♦♥✱ ✇❡ ❢♦❝✉s ♦✉r ❛tt❡♥t✐♦♥ ♦♥ t❤❡ ✐♥❞✐✈✐❞✉❛❧ ❡✛❡❝ts ♦❢ ❛♥t✐✲❢❡rr♦♠❛❣♥❡t✐❝ s♣✐♥✲s♣✐♥ ❡①❝❤❛♥❣❡✲ ❛♥❞ ❝❤❛r❣❡ ❈♦✉❧♦♠❜ ❛ttr❛❝t✐♦♥ ♦♥ ❛♥ ✐♥st❛❜✐❧✐t② ♦❢ ▼P ❛♥❞ ✐♦♥✐③❛t✐♦♥ ♦❢ ▼♥✲❛❝❝❡♣t♦r ✐♥❞✉❝❡❞ ❜② t❤❡ P▲❋✳ ■t ✐s ❢♦✉♥❞ t❤❛t ✇✐t❤ ❛♥ ✐♥❝r❡❛s❡ ♦❢ P▲❋ ✐♥t❡♥s✐t②✱ ▼P ✜rst❧② ❜❡❝♦♠❡s ✐♥st❛❜❧❡✳ ❆♥❞ t❤❡♥ ✐t ✐s s✉♣♣r❡ss❡❞ ❞✉❡ t♦ ③❡r♦✲❡①❝❤❛♥❣❡ ❡♥❡r❣②✳ ❲✐t❤ ❛ ❢✉rt❤❡r ✐♥❝r❡❛s❡s ❧❛s❡r ✐♥t❡♥s✐t②✱ t❤❡ ✐♦♥✐③❛t✐♦♥ ♦❢ ▼♥✲ ❛❝❝❡♣t♦r ♦❝❝✉rs ❞✉❡ t♦ ✈❛♥✐s❤✐♥❣ ❜✐♥❞✐♥❣ ❡♥❡r❣②✳ ■♥ t❤❡ ❧❛st ♣❛rt ♦❢ t❤✐s ✇♦r❦✱ ✇❡ ❤❛✈❡ ❞❡✈❡❧♦♣❡❞ ❛ ✈❡r② ❡✣❝✐❡♥t ♠❡t❤♦❞✱ ✉s✐♥❣ ♦♣t✐♠✐③❡❞ ●❛✉ss✐❛♥ ❢✉♥❝t✐♦♥s ❛s ❜❛s✐s ✐♥ t❤❡ ▲❈❆❖✱ t♦ t❛❝❦❧❡ t❤❡ ♠❛♥②✲❜♦❞② ❡✛❡❝ts ✐♥ ❛rt✐✜❝✐❛❧ ♠♦❧❡❝✉❧❡s✳

❙✉♠ár✐♦

✶ ■♥tr♦❞✉çã♦ ✶

✷ ❊st✉❞♦ ❞❡ ❉♦✐s P♦♥t♦s ◗✉â♥t✐❝♦s ✼

✷✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷ ▼♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✸ ❘❡s✉❧t❛❞♦s ❡ ❉✐s❝✉ssõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✹ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾

✸ ❊❢❡✐t♦s ❞❡ ❝❛♠♣♦s ✐♥t❡♥s♦s ❞❡ ❧❛s❡r s♦❜r❡ ❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛ p₋d

❡♠ ●❛❆s ❞♦♣❛❞♦ ❝♦♠ ✉♠ ú♥✐❝♦ ▼❛♥❣❛♥ês✿ ▼♦❞❡❧♦ ▲❈❆❖ ✷✵ ✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✷ ■♥t❡r❛çã♦ ❞❡ tr♦❝❛ ❞❡ p₋d ❡♠ ●❛❆s ❞♦♣❛❞♦ ❝♦♠ ✉♠ ú♥✐❝♦ ♠❛♥❣❛♥ês✳ ✷✷

✸✳✸ ❮♦♥ ♠♦❧❡❝✉❧❛r ✈✐rt✉❛❧ H₂+ ❝r✐❛❞♦ ♣♦r ✉♠ ❝❛♠♣♦ ❞❡ ❧❛s❡r ✐♥t❡♥s♦✳ ✳ ✳ ✳ ✷✹

✸✳✹ ❈❛♠♣♦ ❞❡ ❧❛s❡r ✐♥t❡♥s♦ ❡ ♦ ❝♦♥tr♦❧❡ ❞❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛ p₋d ✳ ✳ ✳ ✸✷

✸✳✺ ❘❡s✉❧t❛❞♦s ❡ ❉✐s❝✉ssõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✻ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻

✹ ■♥st❛❜✐❧✐❞❛❞❡ ❞❡ t✉♥❡❧❛♠❡♥t♦ ❡ ✐♦♥✐③❛çã♦ ❞♦ ♣ó❧❛r♦♥ ♠❛❣♥ét✐❝♦ ♣♦r ✉♠❛ r❛❞✐❛çã♦ ❞❡ ❧❛s❡r ❧✐♥❡❛r♠❡♥t❡ ♣♦❧❛r✐③❛❞❛ ✹✼ ✹✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✷ ▼♦❞❡❧♦ t❡ór✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✸ ❘❡s✉❧t❛❞♦s ❡ ❉✐s❝✉ssõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

✹✳✹ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵

✺ ❋♦r♠❛s ❛❧t❡r♥❛t✐✈❛s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛ ❝♦rr❡❧❛çã♦ ❡❧❡trô♥✐❝❛ ✻✶ ✺✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✺✳✷ ❈♦rr❡❧❛çã♦ ❡❧❡trô♥✐❝❛ ✈✐❛ ❢✉♥çã♦ ❞❡ ●r❡❡♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✺✳✷✳✶ ❈á❧❝✉❧♦ ❞❛ ✐♥t❡❣r❛❧ ❞❡ ❞♦✐s ❜✉r❛❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✺✳✷✳✷ ❈á❧❝✉❧♦ ❞❛ ✐♥t❡❣r❛❧ ❞❡ ❞♦✐s ❜✉r❛❝♦s ♥♦s ❡st❛❞♦s s ❡ ♣ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✷✳✸ ❘❡s✉❧t❛❞♦s ❡ ❞✐s❝✉ssõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✺✳✸ ❈♦rr❡❧❛çã♦ ❡❧❡trô♥✐❝❛ ✈✐❛ ❣❛✉ss✐❛♥❛s ♣r✐♠✐t✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵

✺✳✸✳✶ ❈á❧❝✉❧♦ ❞❛ ❝♦rr❡❧❛çã♦ ❡❧❡trô♥✐❝❛ ❝♦♥s✐❞❡r❛♥❞♦ ❢✉♥çõ❡s ❣❛✉ss✐✲ ❛♥❛s ♣r✐♠✐t✐✈❛s ❞♦ t✐♣♦ ✶s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✺✳✸✳✷ ❈á❧❝✉❧♦ ❞❛ ❝♦rr❡❧❛çã♦ ❡❧❡trô♥✐❝❛ ❝♦♥s✐❞❡r❛♥❞♦ ❢✉♥çõ❡s ♣r✐♠✐✲

t✐✈❛s ♣❛r❛ ❡st❛❞♦s ❡①❝✐t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✺✳✸✳✸ ❘❡s✉❧t❛❞♦s ❡ ❞✐s❝✉ssõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✺✳✹ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽

✻ ❈♦♥❝❧✉sõ❡s ❡ ♣❡rs♣❡❝t✐✈❛s ✼✾

❆♣ê♥❞✐❝❡ ❆ ✽✷

✻✳✶ ❆rt✐❣♦s ♣✉❜❧✐❝❛❞♦s ❡ s✉❜♠❡t✐❞♦s ♥♦ ♣❡rí♦❞♦ ❞❡ ❡❧❛❜♦r❛çã♦ ❞❛ t❡s❡✳ ✳ ✳ ✽✷

❘❡❢❡rê♥❝✐❛s ✶✶✸

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✺✳✶ ❱❛❧♦r❡s ❞❛s ❡♥❡r❣✐❛s ❈♦✉❧♦♠❜✐❛♥❛s ❞♦ é①❝✐t♦♥(le = 3)♣❛r❛ ❞✐❢❡r❡♥t❡s r❛③õ❡s ❡♥tr❡ lh ❡ le✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✶✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ✉♠ ♣♦ç♦ ❡ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦✳ ✳ ✳ ✳ ✳ ✸ ✶✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞❡ ✉♠ ♣♦t❡♥❝✐❛❧ ♣❛r❛❜ó❧✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✷✳✶ ❊sq✉❡♠❛ ❞❛ ❝♦♥✜❣✉r❛çã♦ ❡s♣❛❝✐❛❧ ❞❡ ❞♦✐s ♣♦♥t♦s q✉â♥t✐❝♦s ✭❛✮ ❡ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❝♦♥✜♥❛♠❡♥t♦ ♥❛ ❞✐r❡çã♦ ❞❡ z ✭❜✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

✷✳✷ ❋✉♥çã♦ ❞❡ ♦♥❞❛ ❞♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧ ❡①❛t❛ ✭❧✐♥❤❛ ❝♦♥tí♥✉❛ ❛③✉❧✮ ❡ ❛♣r♦①✐♠❛❞❛ ✭❧✐♥❤❛ tr❛❝❡❥❛❞❛ ✈❡r♠❡❧❤❛✮ ♣❛r❛ ✉♠ ú♥✐❝♦ ♣♦♥t♦ q✉â♥t✐❝♦ ❞❡ ●❛❆s✴Al0.3Ga0.7As ❝♦♠ V0 = 240 meV ❛♥❞ lw = 250➴✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✸ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❞❡t❡r♠✐♥❛❞♦s ♣❡❧❛s ❢✉♥çõ❡s ❞❡ ❜❛s❡ ❋❇❊

❡①❛t❛ ✭❧✐♥❤❛ só❧✐❞❛ ❛③✉❧✮ ❡ ❛♣r♦①✐♠❛❞❛✱ ❋❇❆ ✭❧✐♥❤❛ tr❛❝❡❥❛❞❛s ✈❡r♠❡✲ ❧❤❛ ✮ ♣❛r❛ ❉◗❉ ❝♦♠ lw = 150➴❡ lb = 20➴✳ ✭❛✮ ▼♦str❛ ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❢✉♥❞❛♠❡♥t❛❧ ♥❛ ❞✐r❡çã♦ z ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✷✳✹ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❞❡t❡r♠✐♥❛❞♦s ♣❡❧❛s ❢✉♥çõ❡s ❞❡ ❜❛s❡ ❋❇❊ ❡①❛t❛ ✭❧✐♥❤❛ só❧✐❞❛ ❛③✉❧✮ ❡ ❛♣r♦①✐♠❛❞❛✱ ❋❇❆ ✭❧✐♥❤❛ tr❛❝❡❥❛❞❛s ✈❡r✲ ♠❡❧❤❛ ✮ ♣❛r❛ ❉◗❉ ❝♦♠ lw = 150➴❡ lb = 20➴✳ ✭❜✮ ♦ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✺ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❝❛❧❝✉❧❛❞♦s ✉s❛♥❞♦ ❢✉♥çõ❡s ❞❡ ❜❛s❡ ❡①❛t❛

❞♦ ❙◗❉ ✭❧✐♥❤❛s só❧✐❞❛s ❛③✉✐s✮ ❡ ❛♣r♦①✐♠❛❞❛s✱ ✭❧✐♥❤❛s tr❛❝❡❥❛❞❛s ✈❡r✲ ♠❡❧❤❛s✮ ♣❛r❛ ♦ ♣♦♥t♦ q✉â♥t✐❝♦ ❞✉♣❧♦ ❝♦♠ lw = 250 ❡ lb = 20✳ ✭❛✮ ♠♦str❛ ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❞♦ ❡st❛❞♦ ❧✐❣❛❞♦ ♥❛ ❞✐r❡çã♦ z✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✷✳✻ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❝❛❧❝✉❧❛❞♦s ✉s❛♥❞♦ ❢✉♥çõ❡s ❞❡ ❜❛s❡ ❡①❛t❛ ❞♦ ❙◗❉ ✭❧✐♥❤❛s só❧✐❞❛s ❛③✉✐s✮ ❡ ❛♣r♦①✐♠❛❞❛s✱ ✭❧✐♥❤❛s tr❛❝❡❥❛❞❛s ✈❡r✲ ♠❡❧❤❛s✮ ♣❛r❛ ♦ ♣♦♥t♦ q✉â♥t✐❝♦ ❞✉♣❧♦ ❝♦♠ lw = 250 ❡ lb = 20✳ ✭❜✮ ♦ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾

✸✳✶ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ♣❛r❛ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❝❛r❣❛ ❞♦ ●❛❆s ❞♦♣❛❞♦ ❝♦♠ ✉♠ ú♥✐❝♦ ▼♥ ❛♥t❡s ✭♣❛✐♥❡❧ s✉♣❡r✐♦r✮ ❡ ❞❡♣♦✐s ✭♣❛✐♥❡❧ ✐♥❢❡r✐♦r✮ ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ❞❡ ❧❛s❡r ✐♥t❡♥s♦✳ ❆ s❡t❛ ✈❡r♠❡❧❤❛ ♣❛r❛ ❝✐♠❛ r❡♣r❡s❡♥t❛ ♦ s♣✐♥ ❞♦ ▼♥✱ ❡♥q✉❛♥t♦ ❛ s❡t❛ ❛♠❛r❡❧❛ ♣❛r❛ ❜❛✐①♦ ✐♥❞✐❝❛ ❛ ❛♣❧✐❝❛çã♦ ❞♦ ❧❛s❡r✳ ❖ ✰ ❡ ✲ ❞❡♥♦t❛♠ ❛s ❝❛r❣❛s ❞♦ ❜✉r❛❝♦ ❡ ❞♦ r❡❝❡♣t♦r ▼♥✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✷ ❊✈♦❧✉çã♦ ❞❛s ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ❞♦ ❜✉r❛❝♦ ❞♦s ♦r❜✐t❛✐s ❞❡ ❡♥❡r❣✐❛ ♠❛✐s

❜❛✐①❛s ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ ♣❛râ♠❡tr♦ α0 ❞♦ ❧❛s❡r✱ ♣❛r❛ α0❂✵ ✭❛✮ ❡ ✭❜✮✱ α0❂✺ ✭❝✮ ❡ ✭❞✮✱ ❡ α0❂✶✵ ✭❡✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✸✳✸ ❉♦✐s ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛ ♠❛✐s ❜❛✐①♦s ❞♦ ❝♦♠♣❧❡①♦ ❜✉r❛❝♦✲▼♥ ✭❧✐♥❤❛s só❧✐❞❛s✮ ❡ ✉♠ í♦♥ ♠♦❧é❝✉❧❛ r❡❛❧ ❞❡ ❤✐❞r♦❣ê♥✐♦H₂+ ✭❧✐♥❤❛s tr❛❝❡❥❛❞❛s✮

❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ ♣❛râ♠❡tr♦ α0 ❞♦ ❧❛s❡r✱ s❡♠ ❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛

p₋d✳ ❇❉ ❡ ❆❇ ❞❡♥♦t❛♠ ❡st❛❞♦ ❧✐❣❛❞♦ ❡ ❛♥t✐✲❧✐❣❛❞♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✹✵

✸✳✹ ❖s q✉❛tr♦ ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛ ♠❛✐s ❜❛✐①♦s ❞♦ ❝♦♠♣❧❡①♦ ❜✉r❛❝♦✲▼♥ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ ♣❛râ♠❡tr♦ ❞♦ ❧❛s❡r α0 ✭❇❉ ❞❡♥♦t❛ ✉♠ ♦r❜✐t❛❧ ❧✐❣❛❞♦✮✳ ❆ ✐♥s❡rçã♦ ♠♦str❛ ❛ ❡♥❡r❣✐❛ ❞♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧ ❞♦ í♦♥ ♠♦❧❡❝✉❧❛r r❡❛❧H₂+ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞❛ ♠❡t❛❞❡ ❞❛ ❞✐stâ♥❝✐❛ ✐♥t❡r♥✉❝❧❡❛r ✭α0 =

R/2✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷

✸✳✺ ❊♥❡r❣✐❛ ❞❡ tr♦❝❛ p₋d Eex ❞♦ ♦r❜✐t❛❧ ♠♦❧❡❝✉❧❛r ❧✐❣❛❞♦ ❞♦ ❝♦♠♣❧❡①♦ ❜✉r❛❝♦✲▼♥ ❞❡✜♥✐❞❛ ♣♦rEex =E1−Enex✱ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ ♣❛râ✲ ♠❡tr♦ ❞♦ ❧❛s❡r α0✳ Enex ❞❡♥♦t❛ ❛ ❡♥❡r❣✐❛ ❞♦ ♦r❜✐t❛❧ ♠♦❧❡❝✉❧❛r ❧✐❣❛❞♦ ♥❛ ❛✉sê♥❝✐❛ ❞❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛ p₋d✳ ❆s ✐♥s❡rçõ❡s ♠♦str❛♠ ❡s✲

q✉❡♠❛t✐❝❛♠❡♥t❡ ❛ ❢✉♥çã♦ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞♦ ❜✉r❛❝♦ ✭❧✐♥❤❛s s♦❧✐❞❛s✮ ❡ ❛s ❧♦❝❛❧✐③❛çõ❡s ❞♦ ❛❝❡✐t❛❞♦r ▼♥ ❝❛rr❡❣❛❞♦ ♥❡❣❛t✐✈❛♠❡♥t❡ ♣❛r❛ α0❂✵

✭à ❡sq✉❡r❞❛✮ ❡ α0 → ∞ ✭á ❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✻ ❊♥❡r❣✐❛ ❞❡ ❧✐❣❛çã♦Eb ❞♦ ♣ó❧❛r♦♥ ♠❛❣♥ét✐❝♦ ❞♦ ❝♦♠♣❧❡①♦ ❜✉r❛❝♦✲▼♥

❞❡✜♥✐❞♦ ♣♦r Eb =E1−Enb✱ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ ♣❛râ♠❡tr♦ ❞♦ ❧❛s❡r

α0✳ Enb❞❡♥♦t❛ ❛ ❡♥❡r❣✐❛ ❞♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧ ❞♦ ❝♦♠♣❧❡①♦ ❜✉r❛❝♦✲ ▼♥ ♥❛ ❛✉sê♥❝✐❛ ❞❛s ✐♥t❡r❛çõ❡s ❞❡ tr♦❝❛p₋d❡ ❈♦✉❧♦♠❜✳ ❆s ✐♥s❡rçõ❡s

♠♦str❛♠ ❡sq✉❡♠❛t✐❝❛♠❡♥t❡ ❛ ❢✉♥çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ✭❧✐♥❤❛s só❧✐❞❛s✮ ❡ ❛s ❧♦❝❛❧✐③❛çõ❡s ❞♦ ❛❝❡✐t❛❞♦r ▼♥ ❝❛rr❡❣❛❞♦ ♥❡❣❛t✐✈❛♠❡♥t❡ ♣❛r❛α0❂✵

✭à ❡sq✉❡r❞❛✮ ❡ α0 → ∞ ✭à ❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✶ ❱❛❧♦r❡s ✐❞❡❛✐s ❞♦ ♣❛râ♠❡tr♦ ✈❛r✐❛❝✐♦♥❛❧λ♣❛r❛ ♦ í♦♥ ♠♦❧❡❝✉❧❛r ❞❡ ❤✐✲

❞r♦❣ê♥✐♦ ✭❧✐♥❤❛ tr❛❝❡❥❛❞❛ ❛③✉❧✮ ❡ ♦ ♣ó❧❛r♦♥ ♠❛❣♥ét✐❝♦ ✭❧✐♥❤❛ ✈❡r♠❡❧❤❛ só❧✐❞❛✮ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞❡ α0✳ P❛r❛ ❝♦♠♣❛r❛çã♦ ❝♦♠ ♦ ♣❛râ♠❡tr♦ λ ❞♦ í♦♥ ♠♦❧❡❝✉❧❛r ❞❡ ❤✐❞r♦❣ê♥✐♦✱ ♦ ❛❝❡✐t❛❞♦r ♥ã♦ ♠❛❣♥ét✐❝♦ é ❝♦♥s✐✲

❞❡r❛❞♦ ♥♦ ❝á❧❝✉❧♦✳ P▼ ❡ H₂+ ❞❡♥♦t❛♠ ♣ó❧❛r♦♥ ♠❛❣♥ét✐❝♦ ❡ ♦ í♦♥ ❞❡

❤✐❞r♦❣ê♥✐♦ ♠♦❧❡❝✉❧❛r✱ r❡s♣❡❝t✐✈❛♠❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✷ ❊♥❡r❣✐❛ ❞❡ ❧✐❣❛çã♦ ❞♦ ♦r❜✐t❛❧ ♠♦❧❡❝✉❧❛r ❞♦ ♣ó❧❛r♦♥ ♠❛❣♥ét✐❝♦ ✭❛✮ ❡ ♦

í♦♥ ♠♦❧❡❝✉❧❛r ❞❡ ❤✐❞r♦❣ê♥✐♦ ✭❜✮✱ ❝❛❧❝✉❧❛❞♦ ♣❡❧♦ ❱▲❈❆❖ ✭❧✐♥❤❛s tr❛❝❡✲ ❥❛❞❛s✮ ❡ ♦ ▲❈❆❖ ♣❛❞rã♦ ✭❧✐♥❤❛s só❧✐❞❛s✮✱ ❡♠ ❢✉♥çã♦ ❞♦ ♣❛râ♠❡tr♦ ❞♦ ❧❛s❡r α0✳ P▼ ❡ H₂+ ❞❡♥♦t❛♠ ♣ó❧❛r♦♥ ♠❛❣♥ét✐❝♦ ❡ í♦♥ ❞❡ ❤✐❞r♦❣ê♥✐♦

♠♦❧❡❝✉❧❛r✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❈♦♠♦ ♠♦str❛❞♦✱ ♦ ❛❝❡✐t❛❞♦r ♥ã♦ ♠❛❣✲ ♥ét✐❝♦ é t❛♠❜é♠ ❝♦♥s✐❞❡r❛❞♦ ♥♦ ❝á❧❝✉❧♦✳ ▲❈❆❖ ❡ ❱▲❈❆❖ ❞❡♥♦t❛♠ ❛ ❝♦♠❜✐♥❛çã♦ ♣❛❞rã♦ ❡ ✉♠❛ ❝♦♠❜✐♥❛çã♦ ✈❛r✐❛❝✐♦♥❛❧ ❧✐♥❡❛r ❞❡ ♦r❜✐t❛✐s ❛tô♠✐❝♦s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✹✳✸ ❈✉r✈❛s ❞❡ ❝♦♥t♦r♥♦ ❞❛s ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ❞♦ ❜✉r❛❝♦ ♥♦ ❡st❛❞♦ ❢✉♥❞❛✲ ♠❡♥t❛❧ ❞♦ ●❛❆s ❞♦♣❛❞♦ ❝♦♠ ♠❛♥❣❛♥ês ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ ♣❛râ✲ ♠❡tr♦ α0❂✵ ✭❛✮✱ α0❂✺ ✭❜✮ ❡ α0❂✶✵ ✭❝✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✹✳✹ ❊♥❡r❣✐❛ t♦t❛❧ET✱ ✭❛✮ ❡♥❡r❣✐❛ ❞❡ tr♦❝❛Eex✱ ✭❜✮ ❡♥❡r❣✐❛ ❞❡ ❧✐❣❛çã♦Ecb ❞❡✈✐❞♦ ❛♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❈♦✉❧♦♠❜ s♦③✐♥❤♦ ✭❝✮ ❡ ❡♥❡r❣✐❛ ❞❡ ❧✐❣❛çã♦ Eb ❞❡✈✐❞♦ ❛ ❛♠❜♦s ♦s ♣♦t❡♥❝✐❛s ❞❡ ❈♦✉❧♦♠❜ ❡ ❞❡ tr♦❝❛ ✭❞✮ ♦ ♣ó❧❛r♦♥ ♠❛❣♥ét✐❝♦ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ ♣❛râ♠❡tr♦ ❞♦ ❧❛s❡r α0 ♦♥❞❡ Eex =

ET −Enex✱Ecb =E1−Ec✱ Eb =E1−Enb✱E1 é ❛ ❡♥❡r❣✐❛ ❞♦ ♣ó❧❛r♦♥ ♠❛❣♥ét✐❝♦ ♦❜t✐❞❛ r❡s♦❧✈❡♥❞♦ ❛ ❡q✉❛çã♦ 3.22✱Enex✱Ec ❡Enb ❞❡♥♦t❛♠ ❛s ❡♥❡r❣✐❛s ❞♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧ ❞♦ ♣ó❧❛r♦♥ ♠❛❣♥ét✐❝♦ ♥❛ ❛✉sê♥❝✐❛ ❞❡ tr♦❝❛✱ ❞❡ ❈♦✉❧♦♠❜ ❡ ❞❡ ❛♠❜♦s ♦s t❡r♠♦s ❞❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛ ❡ ❞❡ ❈♦✉❧♦♠❜ ♥❛ ❍❛♠✐❧t♦♥✐❛♥❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾

✺✳✶ ❊♥❡r❣✐❛ ❢✉♥❞❛♠❡♥t❛❧ ❡♠ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ t❡r♠♦s ❝♦♥s✐❞❡r❛❞♦s ♣❛r❛ ❛ ❢✉♥çã♦ Qm−1/2(χ′)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✺✳✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✺✳✸ ❊♥❡r❣✐❛s ❞♦ é①❝✐t♦♥ ✭❡①❛t❛ ❡ ♥✉♠ér✐❝❛✮ r❡❢❡r❡♥t❡s ❛s ❝♦♥✜❣✉r❛çõ❡s

s₋s ❡p₋p ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞❡le✱ ♣❛r❛ ❞✐❢❡r❡♥t❡s r❛③õ❡s ❞❡le ❡ lh✳ ✻✾ ✺✳✹ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛ ♠♦❧❡❝✉❧❛r ✜①♦ ♦♥❞❡ ❛s

❢✉♥çõ❡s ❞❡ ❜❛s❡ sã♦ ❝❡♥tr❛❞❛s ♥♦s ✈❡t♦r❡s ♣♦s✐çõ❡sRA✳ ❖ ✈❛❧♦r ❡♠ ✉♠

✈❡t♦r ♣♦s✐çã♦ r✱ ❞❡ ✉♠❛ ❢✉♥çã♦ ❞❡ ❜❛s❡ ❝❡♥tr❛❞❛ ❡♠ RA✱ ❞❡♣❡♥❞❡rá

❞❡ r₋RA✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✺✳✺ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s s❡✐s ❝❡♥tr♦s ✭RA✱RB✱RC✱ RD✱R_P ❡ RQ✮ ❡♥✈♦❧✲

✈✐❞♦s ♥❛ ✐♥t❡❣r❛❧ ❞❡ ❞♦✐s ❡❧étr♦♥s ❞❡ ✉♠ s✐st❡♠❛ ♠♦❧❡❝✉❧❛r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✺✳✻ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s ❞♦✐s ❝❡♥tr♦s R_P ❡ R_Q ❡♥✈♦❧✈✐❞♦s ♥❛ ✐♥t❡❣r❛❧ ❞❡

❞♦✐s ❡❧étr♦♥s ❞❡ ✉♠ s✐st❡♠❛ ♠♦❧❡❝✉❧❛r ❞✐❛tô♠✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺

❈❛♣ít✉❧♦ ✶

■♥tr♦❞✉çã♦

❯♠ ♣♦♥t♦ q✉â♥t✐❝♦ ♣♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ✉♠ ❝♦♥✜♥❛♠❡♥t♦ ❞❡ ❡❧étr♦♥s ♥♦ ✐♥t❡r✐♦r ❞❡ ✉♠ ♣❡q✉❡♥♦ ✈♦❧✉♠❡✳ ❊♠ ♠✉✐t♦s ❝❛s♦s✱ ♦s ♣♦♥t♦s q✉â♥t✐❝♦s sã♦ ❝♦♥s✐❞❡✲ r❛❞♦s t❛♠❜é♠ ❝♦♠♦ ♣❡q✉❡♥❛s ✐❧❤❛s ❜✐❞✐♠❡♥s✐♦♥❛✐s ❞❡ ❡❧étr♦♥s q✉❡ sã♦ ❧❛t❡r❛❧♠❡♥t❡ ❝♦♥✜♥❛❞♦s ♣♦r ✉♠ ♣♦t❡♥❝✐❛❧ ❛rt✐✜❝✐❛❧✳ ❖s ♣♦♥t♦s q✉â♥t✐❝♦s tê♠ ❞❡s♣❡rt❛❞♦ ♠✉✐t♦ ✐♥t❡r❡ss❡ ♥❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛ ❞❡✈✐❞♦ ❛s s✉❛s ♣♦ssí✈❡✐s ❛♣❧✐❝❛çõ❡s t❡❝♥♦❧ó❣✐❝❛s✳ ❉❡ ❢❛t♦✱ ✈✐❞r♦s ❞♦♣❛❞♦s ❝♦♠ ♣♦♥t♦s q✉â♥t✐❝♦s s❡♠✐❝♦♥❞✉t♦r❡s tê♠ s✐❞♦ ❡st✉❞❛❞♦s ❞❡✈✐❞♦ ❛ s✉❛s ✐♥t❡r❡ss❛♥t❡s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❡ ❡❧❡trô♥✐❝❛s✱ ❝♦♠ ❛♣❧✐❝❛çõ❡s ❡♠ ❞✐s♣♦s✐t✐✈♦s ó♣t✐❝♦s✱ ♠♦❞✉❧❛❞♦r❡s ❞❡ ❧✉③✱ ❧❛s❡rs ❬✶✱ ✷❪ ❡ ♥❛ ❝♦♠♣✉t❛çã♦ q✉â♥t✐❝❛ ❬✸❪✳ P♦♥t♦s q✉â♥t✐❝♦s✱ t❛♠❜é♠ ❝♦♥❤❡❝✐❞♦s ♣❡❧❛ s✐❣❧❛ ◗❉s ✭❞♦ ✐♥❣❧ês ✏◗✉❛♥t✉♠ ❞♦ts✑✮ sã♦ ♠✉✐t❛s ✈❡③❡s ❝❤❛♠❛❞♦s ❞❡ át♦♠♦s ❛rt✐✜❝✐❛✐s ❬✹❪✱ ♣♦r ❛♣r❡s❡♥t❛r❡♠ ✉♠ ♣♦t❡♥❝✐❛❧ ❞❡ ✐♥t❡r❛çã♦ q✉❡ ❝❛✐ ✐♥✈❡rs❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ à ❞✐stâ♥❝✐❛ 1/r ❡ ❡♥❡r❣✐❛

q✉❛♥t✐③❛❞❛ ❡♠ ✈❛❧♦r❡s ❞✐s❝r❡t♦s✱ ❝♦♠♦ ❡♠ ✉♠ át♦♠♦ r❡❛❧✳ ❆ ❞✐st✐♥çã♦ ❜ás✐❝❛ ❞♦s át♦♠♦s ♥❛t✉r❛✐s ❡ ❛rt✐✜❝✐❛✐s ❡stá ♥♦ ❢❛t♦ q✉❡ ♦s ♣♦♥t♦s q✉â♥t✐❝♦s ♣♦❞❡♠ ❝♦♥✜♥❛r t❛♥t♦ ❡❧étr♦♥s ❝♦♠♦ ❜✉r❛❝♦s✱ ❡♥q✉❛♥t♦ át♦♠♦s r❡❛✐s só ♣♦❞❡♠ ❝♦♥✜♥❛r ❡❧étr♦♥s✱ ❞❡✈✐❞♦ ❛♦ ♣♦t❡♥❝✐❛❧ ♣♦s✐t✐✈♦ ❞♦ ♥ú❝❧❡♦✳ ❆❧é♠ ❞✐ss♦ ♦ ❝♦♥✜♥❛♠❡♥t♦ ❧❛t❡r❛❧ ❡♠ ♣♦♥t♦s q✉â♥t✐❝♦s é ❣❡r❛❧♠❡♥t❡ ❜❡♠ ❝♦♠♣♦rt❛❞♦ ❡ ♣♦❞❡ s❡r ❝♦♥tr♦❧❛❞♦✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❈♦✉❧♦♠❜ ♣♦ss✉✐ ✉♠❛ s✐♥❣✉❧❛r✐❞❛❞❡ ♥♦ ♥ú❝❧❡♦ ❡ é ✜①❛❞♦ ♣❡❧♦ ♥ú♠❡r♦ ❞❡ ♣rót♦♥s ❞♦ át♦♠♦✳ P♦r ✜♠✱ ♦s ♣♦♥t♦s q✉â♥t✐❝♦s ♣♦ss✉❡♠ ✉♠❛ s❡♣❛r❛çã♦ ❡♥tr❡ ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛ ♠❡♥♦r ❞♦ q✉❡ ❛ s❡♣❛r❛çã♦ ♠é❞✐❛ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦s ❝♦♠ át♦♠♦s

✷

r❡❛✐s✳ ❊♥q✉❛♥t♦ ♦s ♣♦♥t♦s q✉â♥t✐❝♦s tê♠ ❡♥❡r❣✐❛ ❞❛ ♦r❞❡♠ ❞❡ ❞❡③❡♥❛s ❞❡ ♠❡❱ ♦s át♦♠♦s ♥❛t✉r❛✐s ❛♣r❡s❡♥t❛♠ ❡ss❛ ❡♥❡r❣✐❛ ❞❛ ♦r❞❡♠ ❞❡ ❡❱✳ ❖ ❝♦♥✜♥❛♠❡♥t♦ ❧❛t❡r❛❧ é ♦❜t✐❞♦ ❛tr❛✈és ❞❛ ❞❡✜♥✐çã♦ ❢ís✐❝❛ ❞❛s ❜♦r❞❛s ❞❛ ❡str✉t✉r❛ ❞♦ ♣♦♥t♦ q✉â♥t✐❝♦ ❬✺❪✳

❆ ♠❛♥❡✐r❛ ♠❛✐s ❝♦♠✉♠ ❞❡ s❡ ♦❜t❡r ♣♦♥t♦s q✉â♥t✐❝♦s✱ ❡♠ ♣r✐♠❡✐r♦ ❧✉❣❛r✱é ❛ ♣r♦❞✉çã♦ ❞❡ ✉♠❛ ❡str✉t✉r❛ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ✉♠ ♣♦ç♦ q✉â♥✲ t✐❝♦✳ ❊ss❛ ❡str✉t✉r❛ é ❣❡r❛❧♠❡♥t❡ ♣r♦❞✉③✐❞❛ ♣♦r ❡♣✐t❛①✐❛ ✭❈r❡s❝✐♠❡♥t♦ ♦✉ s♦❜r❡✲ ❝r❡s❝✐♠❡♥t♦ ♦r✐❡♥t❛❞♦ ❞❡ ✉♠ ❝r✐st❛❧ s♦❜r❡ ♦✉tr♦ ♣ré✲❡①✐st❡♥t❡ q✉❡ ❛♣r❡s❡♥t❛ r❡tí❝✉❧♦ ❝r✐st❛❧✐♥♦ ❡ ❝❛r❣❛s ✐ô♥✐❝❛s s❡♠❡❧❤❛♥t❡s✮ ♣❛r❛ s❡ t❡r ✉♠ ❝♦♥tr♦❧❡ ♣r❡❝✐s♦ ❞❛ ❡s♣❡ss✉r❛ ❞♦ ✜❧♠❡ ❬✻❪✳ P❛r❛ ✐ss♦✱ ✉♠ ♣❛❞rã♦ ❣❡♦♠étr✐❝♦ ❞❡s❡♥❤❛❞♦ ♥❛s ❧❛t❡r❛✐s ❞❛ ❡str✉t✉r❛ é tr❛♥s❢❡r✐❞♦ ♣❛r❛ ❛ ❛♠♦str❛✱ ❛♣ós ♦ ❝r❡s❝✐♠❡♥t♦✱ ♣♦r ❧✐t♦❣r❛✜❛ ❞❡ ❛❧t❛ r❡s♦❧✉çã♦✳ ❯♠ ❛t❛q✉❡ q✉í♠✐❝♦ s✉❜s❡q✉❡♥t❡ ❝♦rró✐ ❛ ❛♠♦str❛ ❛té ❛ ❝❛♠❛❞❛ ❜✐❞✐♠❡♥s✐♦♥❛❧✱ ♣r♦❞✉✲ ③✐♥❞♦ ❛s ♥❛♥♦❡str✉t✉r❛s ❞❡s❡❥❛❞❛s✳ ❆ ❋✐❣✉r❛ ✶✳✶ ✐❧✉str❛ ❡st❡ t✐♣♦ ❞❡ ❝♦♥✜♥❛♠❡♥t♦✳ ◆❡st❡ ❝❛s♦✱ ♦s ♣♦♥t♦s ♣♦ss✉✐rã♦ ♦ ❢♦r♠❛t♦ ❞❡ ✉♠❛ ❧❡♥t❡✱ ❝♦♠ ❛s ❞✐♠❡♥sõ❡s tr❛♥s✈❡r✲ s❛✐s ❜❡♠ ♠❛✐♦r❡s ❞♦ q✉❡ ❛ s✉❛ ❡s♣❡ss✉r❛✳ ❉❡st❛ ♠❛♥❡✐r❛✱ ♦ ♠♦✈✐♠❡♥t♦ ❞♦s ❡❧étr♦♥s ♣♦❞❡ s❡r ❝♦♥s✐❞❡r❛❞♦ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❡ ❡st❛s ❡str✉t✉r❛s sã♦ ❝♦♠✉♠❡♥t❡ ❝❤❛♠❛❞❛s ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ✈❡rt✐❝❛✐s✳

❆s ❞✐♠❡♥sõ❡s tí♣✐❝❛s ❞♦s ♣♦♥t♦s q✉â♥t✐❝♦s sã♦ ❞❛ ♦r❞❡♠ ❞❡ ✶ ❛ ✶✵✵♥♠✱ q✉❡ r❡s✉❧t❛♠ ❡♠ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ q✉❛♥t✐③❛çã♦ ❞♦s ❡❧étr♦♥s ♣r❡s♦s ♥♦s ❜✉r❛❝♦s✳ ❖s ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛ ✈❛r✐❛♠ ❞❛ ♦r❞❡♠µeV❛té ❞❡③❡♥❛s ❞❡ ♠❡❱✳

✸

❋✐❣✉r❛ ✶✳✶✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ✉♠ ♣♦ç♦ ❡ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦✳

tr♦❧á✈❡✐s✳ ❈♦♠ ♦ ❛✈❛♥ç♦ ❞♦s ❡st✉❞♦s ❞❡st❛ ár❡❛✱ ❡s♣❡r❛✲s❡ q✉❡ ♥♦✈❛s ♣r♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s r❡❧❛❝✐♦♥❛❞❛s ❝♦♠ ♦s s♣✐♥s s❡❥❛♠ ❞❡s❝♦❜❡rt❛s✳ ❊st❡ ❢❛t♦ ♣♦❞❡rá ❛❜r✐r ♥♦✈❛s ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❛ ✉t✐❧✐③❛çã♦ ❞♦s ♥í✈❡✐s ♥❛t✉r❛✐s ❞♦ s♣✐♥ ❞♦ ❡❧étr♦♥ ✭✏s♣✐♥ ✉♣✑ ❡ ✏s♣✐♥ ❞♦✇♥✑✮ ♣❛r❛ ❝r✐❛r ♣r♦♣♦st❛s ❞❡ q✉❜✐ts✳ ❖s q✉❜✐ts sã♦ ♦s ♣♦rt❛❞♦r❡s ❞❡ ✐♥❢♦r♠❛çã♦ ❡♠ s✐st❡♠❛s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ q✉â♥t✐❝♦ ❞❡ ✐♥❢♦r♠❛çã♦ ✭❝♦♠♣✉t❛çã♦ q✉â♥t✐❝❛✮❬✽❪✳ ❆❧é♠ ❞✐ss♦✱ ❛ s♣✐♥trô♥✐❝❛ ❬✾❪ é ✉♠❛ ❞❛s ❛♣❧✐❝❛çõ❡s ♠❛✐s ♣r♦♠✐ss♦r❛s ❞❡st❡s ❞✐s♣♦s✐✲ t✐✈♦s✱ ♣♦✐s ♥❡st❛ ❡s❝❛❧❛ ❞❡ t❛♠❛♥❤♦✱ é ♣♦ssí✈❡❧ ♠❛♥✐♣✉❧❛r ♦s s♣✐♥s ✐♥❞✐✈✐❞✉❛❧♠❡♥t❡ ♦❜t❡♥❞♦ ❞✐s♣♦s✐t✐✈♦s q✉❡ ♣♦❞❡rã♦ r❡✈♦❧✉❝✐♦♥❛r ❛ ♠✐❝r♦❡❧❡trô♥✐❝❛ ❬✶✵✱ ✶✶❪✳

✹

❝♦rr❡❧❛çã♦ ❡❧❡trô♥✐❝❛✱ ♦✉ s❡❥❛✱ ♥ã♦ ❧❡✈❛♠ ❡♠ ❝♦♥t❛ ❛ ✐♥t❡r❛çã♦ ❡❧étr♦♥✲❡❧étr♦♥ ❡♥tr❡ ◗❉s✳ ❯❧t✐♠❛♠❡♥t❡ ❡♥❝♦♥tr❛✲s❡ ♠✉✐t♦s ❡st✉❞♦s r❡❛❧✐③❛❞♦s ❝♦♠ ♣♦♥t♦s q✉â♥t✐❝♦s✱ ♣♦ré♠ ✉t✐❧✐③❛♥❞♦ ❛♣❡♥❛s ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦ ❝♦♠ ❞♦✐s ♦✉ ♠❛✐s ❡❧étr♦♥s ❬✻✱ ✶✷✱ ✶✸❪✳

P❛r❛ ❡st✉❞❛r ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦ ❝♦♥s✐❞❡r❛♠♦s ♦ ♠♦❞❡❧♦ ❞❡ ✉♠ ♣♦♥t♦ s❡♠✐✲ ❝♦♥❞✉t♦r ❞❡ ✜❧♠❡s ✜♥♦s ❞❡ ❢♦r♠❛ ❝✐r❝✉❧❛r❡s✳ ❊ss❛s ❡str✉t✉r❛s sã♦ ♦❜t✐❞❛s ❛tr❛✈és ❞❡ ✜❧♠❡s ❞❡ ●❛❆s ✭❆rs❡♥❡t♦ ❞❡ ●á❧✐♦✮✱ ■♥❆s✭❆rs❡♥❡t♦ ❞❡ ❮♥❞✐♦✮ ❡ ❆❧●❛❆s ✭❆rs❡♥❡t♦ ❞❡ ●á❧✐♦ ❡ ❆❧✉♠í♥✐♦✮ ❬✹❪✳ ❆s ❞✐♠❡♥sõ❡s tí♣✐❝❛s ♣❛r❛ ❡ss❡ t✐♣♦ ❞❡ ♠❛t❡r✐❛❧ ❞❡ s❡♠✐✲ ❝♦♥❞✉t♦r é ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ❞❡ ✸✵♥♠ ❛ ✶✵✵♥♠✳ ❊ss❡s ♠❛t❡r✐❛✐s tê♠ ♣r♦♣r✐❡❞❛❞❡s ❡❧❡trô♥✐❝❛s s✉♣❡r✐♦r❡s ❛♦s ❞♦ s✐❧í❝✐♦✳ P♦ss✉✐ ✉♠❛ rá♣✐❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ s❛t✉r❛çã♦ ❡ ❛❧t❛ ♠♦❜✐❧✐❞❛❞❡ ❡❧❡trô♥✐❝❛✳ ❆❧é♠ ❞✐ss♦✱ ❞✐s♣♦s✐t✐✈♦s ❞❡ ●❛❆s ❣❡r❛♠ ♠❡♥♦s r✉í❞♦ ❞♦ q✉❡ s✐❧í❝✐♦ q✉❛♥❞♦ ♦♣❡r❛❞♦s ❛ ❛❧t❛s ❢r❡qüê♥❝✐❛s✳ ❆ ❥✉st❛♣♦s✐çã♦ ❞❡ ❝❛♠❛❞❛s ❞❡ss❡s ✜❧♠❡s✱ ♣♦r ❡①❡♠♣❧♦s ●❛❆s✱ ■♥❆s ❡ ❆❧●❛❆s ✐rá ❢♦r♠❛r ✉♠❛ ❡str✉t✉r❛ ❝✐❧í♥❞r✐❝❛ ❝♦♠ ✉♠ ❝♦♥✜♥❛♠❡♥t♦ ❞❡ ❡❧étr♦♥s ❜✐❞✐♠❡♥s✐♦♥❛❧ q✉❡ ♣♦❞❡ s❡r ♠♦❞❡❧❛❞♦ ♣♦r ✉♠ ♣♦t❡♥❝✐❛❧ ❧❛t❡r❛❧ ❞♦ t✐♣♦ ♣❛r❛❜ó❧✐❝♦✱ ❝♦♠♦ ♠♦str❛ ♥❛ ❋✐❣✉r❛ ✶✳✷✳

❈♦♥❢♦r♠❡ ♦ t❛♠❛♥❤♦ ❡ ❛ ❢♦r♠❛ ❞♦ ❝♦♥✜♥❛♠❡♥t♦ ❞❡ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦✱ ♦ ♣♦t❡♥❝✐❛❧ ❡ ❛s ❡s❝❛❧❛s ❞❛s ❡♥❡r❣✐❛s sã♦ ♠♦❞✐✜❝❛❞❛s t❛♠❜é♠ q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛s ❝♦♠ ♦s át♦♠♦s r❡❛✐s✳ ❆ ♠❛ss❛ ❞♦s ❡❧étr♦♥s ❡♠ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦ ❞✐❢❡r❡♠ ❞❛ ♠❛ss❛ ❞❡ ✉♠ ❡❧étr♦♥ ❧✐✈r❡✱ ❞❡✈✐❞♦ ❛♦ ❛❝♦❧❤✐♠❡♥t♦ ❞♦ ♠❛t❡r✐❛❧ s❡♠✐❝♦♥❞✉t♦r✳ ●❡r❛❧♠❡♥t❡✱ ♦s ❡❧étr♦♥s ❞❡ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦ ♣♦❞❡♠ s❡r ❞❡s❝r✐t♦s ❝♦♠ ✉♠❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ♠❛ss❛ ❡❢❡t✐✈❛✳ ❉❡✈✐❞♦ ❛ ❡st❛s ❞✐❢❡r❡♥ç❛s✱ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❈♦✉❧♦♠❜ ❡ ♦s ❡❢❡✐t♦s ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ sã♦ ♠✉✐t♦ ♠❛✐s ❛❝❡♥t✉❛❞♦s ♥♦s ♣♦♥t♦s q✉â♥t✐❝♦s✱ ❡♠ ❝♦♠♣❛r❛çã♦ ❝♦♠ át♦♠♦s r❡❛✐s✳ ■ss♦ é ✐♥t❡r❡ss❛♥t❡✱ ♣♦✐s ♣❛r❛ ♠✉✐t♦s ❡❧étr♦♥s ♦ ❡❢❡✐t♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♣♦❞❡ s❡r ❡st✉❞❛❞♦ ❞❡ ❢♦r♠❛ ❝♦♥tr♦❧❛❞❛ ❝♦♠ ❛ ❛❧t❡r❛çã♦ ❞❛ ✈♦❧t❛❣❡♠ ❡ ❛ ❛❧t❡r❛çã♦ ❞❛s t❡♥sõ❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✳

❉❡✈✐❞♦ ❛♦ ❝♦♥✜♥❛♠❡♥t♦ ❞❛ r❡❞❡ ❝r✐st❛❧✐♥❛ ❞♦s ❡❧étr♦♥s ❡ ♦s ❜✉r❛❝♦s✱ t❡♠♦s q✉❡ ❧❡✈❛r ❡♠ ❝♦♥t❛ ❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ♠❛ss❛ ❡❢❡t✐✈❛✱m∗_{✳ ❆ ✉t✐❧✐③❛çã♦ ❞♦ s✐st❡♠❛ ❞❡}

✺

-160 -120 -80 -40 0 40 80 120 160 -160

-120 -80

-40 0

40 80

120 160 0

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

E(meV)

x(Angstrom) y(Angstrom)

E(meV)

❋✐❣✉r❛ ✶✳✷✿ ❘❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞❡ ✉♠ ♣♦t❡♥❝✐❛❧ ♣❛r❛❜ó❧✐❝♦✳

t❛♠❡♥t❡ ♥❡st❡ s✐st❡♠❛✳ ❉❡st❛ ❢♦r♠❛✱ ♣❛❞r♦♥✐③❛✲s❡ q✉❡ ❛s ❡q✉❛çõ❡s sã♦ ❡s❝r✐t❛s ♥♦ s✐st❡♠❛ ■♥t❡r♥❛❝✐♦♥❛❧ ❞❡ ❯♥✐❞❛❞❡s ✭❙■✮ ❡ t♦❞♦s ♦s ❝á❧❝✉❧♦s s❡rã♦ r❡❛❧✐③❛❞♦s ❧❡✈❛♥❞♦ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ♦ s✐st❡♠❛ ❞❡ ✉♥✐❞❛❞❡s ❊❆❯✳ ◆❡st❡ s✐st❡♠❛✱ ❛ ❝❛r❣❛ ❞♦ ❡❧étr♦♥(e)✱

❛ ♠❛ss❛ ❡❢❡t✐✈❛ ❞♦ ❡❧étr♦♥(m∗_)❡(~₎sã♦ ✐❣✉❛✐s ❛ ✉♠✳ ❖ ❝♦♥❝❡✐t♦ ❞❡ ♠❛ss❛ ❡❢❡t✐✈❛ é ✐♠♣♦rt❛♥t❡ ♣❛r❛ ❧❡✈❛r ❡♠ ❝♦♥s✐❞❡r❛çã♦ ♦s ❡❢❡✐t♦s ❞❛ r❡❞❡ ❡ ❞❛ ✐♥t❡r❛çã♦ ❞♦s ❡❧étr♦♥s ❞❡ ✈❛❧ê♥❝✐❛ ❝♦♠ ♦s ❞❡ ❝❛r♦ç♦✳

✻

✶✮ ❊st✉❞❛r ❛s ❡str✉t✉r❛s ❡❧❡trô♥✐❝❛s ❞❡ ❉◗❉s ✭❞♦ ✐♥❣❧ês ✏❉♦✉❜❧❡ ◗✉❛♥t✉♠ ❉♦ts✑✮ ❛❝♦♣❧❛❞♦s ✈❡rt✐❝❛❧♠❡♥t❡✱ ✉s❛♥❞♦ ♦ ♠ét♦❞♦ ▲❈❆❖ ✭❞♦ ✐♥❣❧ês ✏▲✐♥❡❛r ❈♦♠❜✐✲ ♥❛t✐♦♥ ♦❢ ❆t♦♠✐❝ ❖r❜✐t❛❧s✑✮✳ ❆❝❤❛♠♦s q✉❡ ♣❛r❛ ❛t✐♥❣✐r ✉♠❛ ❜♦❛ ♣r❡❝✐sã♦ ❡ ♦❜t❡r ✉♠❛ rá♣✐❞❛ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦s ❝á❧❝✉❧♦s✱ ✉♠❛ ❡s♣❡❝✐❛❧ ❛t❡♥çã♦ ❞❡✈❡ s❡r ❞❛❞❛ ♥❛ ❡s❝♦❧❤❛ ❞❛s ❢✉♥çõ❡s ❞❡ ❜❛s❡✳ ❉❡♠♦♥str❛♠♦s q✉❡ ❛s ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ❞♦s ♣♦♥t♦s q✉â♥t✐❝♦s s❡r✈❡♠ ❝♦♠♦ ❢✉♥çõ❡s ❞❡ ❜❛s❡ ✐❞❡❛✐s ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞❡ ♦r❜✐t❛✐s ♠♦❧❡❝✉❧❛r❡s ❞❡ ❉◗❉s✳

❈❛♣ít✉❧♦ ✷

❊st✉❞♦ ❞❡ ❉♦✐s P♦♥t♦s ◗✉â♥t✐❝♦s

✷✳✶ ■♥tr♦❞✉çã♦

❈♦♠♦ ❥á ♠❡♥❝✐♦♥❛❞♦ ♥❛ ✐♥tr♦❞✉çã♦✱ ♦s ♣♦♥t♦s q✉â♥t✐❝♦s s✐♠♣❧❡s ❡ ❛❝♦♣❧❛❞♦s sã♦ ❝❤❛♠❛❞♦s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❞❡ át♦♠♦s ❡ ♠♦❧é❝✉❧❛s ❛rt✐✜❝✐❛✐s ❬✶✹❪✳ ◆ã♦ ♦❜st❛♥t❡ ♦s ♣♦♥t♦s q✉â♥t✐❝♦s tê♠ ❛s ✈❛♥t❛❣❡♥s ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ s❡✉ ♣♦t❡♥❝✐❛❧ ❞❡ ❝♦♥✜♥❛✲ ♠❡♥t♦ s❡r ❛❥✉stá✈❡❧ ❡ ❞♦ ♥ú♠❡r♦ ❞❡ s❡✉s ❝❛rr❡❛❞♦r❡s s❡r❡♠ ❝♦♥tr♦❧á✈❡✐s ❬✶✹❪✳ P♦r ❡①❡♠♣❧♦✱ ♦ ❜❧♦q✉❡✐♦ ❞❡ ❈♦✉❧♦♠❜ ♣❡r♠✐t❡ q✉❡ ❡❧étr♦♥s ♣♦ss❛♠ s❡r ❛❞✐❝✐♦♥❛❞♦s ♦✉ r❡♠♦✈✐❞♦s ✉♠ ❛ ✉♠✱ ❝♦♠ ✉♠ s✐♠♣❧❡s ❡❧❡tr♦❞♦✳ ❈♦♠♦ r❡s✉❧t❛❞♦✱ ❛s ♣r♦♣r✐❡❞❛❞❡s ♠❛❣♥ét✐❝❛s✱ ❡❧étr✐❝❛s ❡ ó♣t✐❝❛s ❞❡ ✉♠ ú♥✐❝♦ ♣♦♥t♦ q✉â♥t✐❝♦ ✭❙◗❉✮ ❡ ❞❡ ❞♦✐s ♣♦♥t♦s q✉â♥t✐❝♦s ❛❝♦♣❧❛❞♦s ✭❉◗❉✮ ♣♦❞❡♠ s❡r ♣❧❛♥❡❥❛❞❛s✳

❆ r❡❛❧✐③❛çã♦ ❞❡ ✉♠ ❝♦♥tr♦❧❡ ♣r❡❝✐s♦ ❡♥tr❡ ♦ ❛❝♦♣❧❛♠❡♥t♦ ❞❡ ❞♦✐s ♣♦♥t♦s q✉â♥t✐❝♦s é ❞❡ ♣❛rt✐❝✉❧❛r ✐♥t❡r❡ss❡ ♣❛r❛ ♦♣❡r❛çã♦ ❞❡ q✉❜✐ts ❬✶✺❪✳ ❊st✉❞♦s ❡①t❡♥s✐✈♦s ❞❡ t✉♥❡❧❛♠❡♥t♦ ❡♠ s❡♠✐❝♦♥❞✉t♦r❡s✱ ❬✶✻❪ ♥❛♥♦t✉❜♦s ❞❡ ❝❛r❜♦♥♦✱ ❬✶✼✱ ✶✽❪ ❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ❣r❛❢❡♥♦ ❬✶✾❪ ❢♦r❛♠ r❡❛❧✐③❛❞♦s t❛♥t♦ t❡♦r✐❝❛♠❡♥t❡ q✉❛♥t♦ ❡①♣❡r✐♠❡♥t❛❧✲ ♠❡♥t❡ ❡ ♠✉✐t❛s ♣r♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ♥❡ss❡s ❛✐♥❞❛ s❡rã♦ ❞❡s❝♦❜❡rt❛s✳ ❊♠❜♦r❛ s✐❣♥✐✜✲ ❝❛♥t❡s ♣r♦❣r❡ss♦s tê♠ s✐❞♦ r❡❛❧✐③❛❞♦s✱ ❛✐♥❞❛ ❢❛❧t❛ ✉♠❛ t❡♦r✐❛ ❛❜r❛♥❣❡♥t❡ ❞❛ ❡str✉t✉r❛ ❡❧❡trô♥✐❝❛ ❞❡ ♠♦❧é❝✉❧❛s ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s✳ ❊st❡ ❢❛t♦ ♠♦t✐✈♦✉ ❛ r❡❛❧✐③❛r ✉♠ ❡st✉❞♦

✽

♠❛✐s ❝♦♠♣❧❡t♦ ❡st❡♥❞❡♥❞♦ ♦ ❡st✉❞♦ ❞❡ ✉♠ ❙◗❉ ❞❡ ●❛❆s ♣❛r❛ ✉♠ ❉◗❉ ✈❡rt✐❝❛❧✳ ❆ ❡s❝♦❧❤❛ ❞❡ ❢✉♥çõ❡s ❞❡ ❜❛s❡ ❛❞❡q✉❛❞❛s ❞❡s❡♠♣❡♥❤❛ ✉♠ ♣❛♣❡❧ ♠✉✐t♦ ✐♠♣♦rt❛♥t❡ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ❡str✉t✉r❛ ❡❧❡trô♥✐❝❛ ❞❛s ♠♦❧é❝✉❧❛s ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s✳ ❖s ♦r❜✐✲ t❛✐s ❛tô♠✐❝♦s✱ ♦s q✉❛✐s tê♠ s✐❞♦ ✉t✐❧✐③❛❞♦ ❝♦♠ s✉❝❡ss♦ ❝♦♠♦ ❢✉♥çõ❡s ❞❡ ❜❛s❡ ♣❛r❛ ❡①♣❛♥❞✐r ❛s ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ❞♦s ❙◗❉✱ ♣♦❞❡♠ ♥ã♦ s❡r ❛❞❡q✉❛❞❛s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞♦s ❉◗❉✳ ◆❡st❡ ❝❛♣ít✉❧♦✱ ♥ós ✜③❡♠♦s ✉♠❛ ❝♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣♦r ❞✉❛s ❞✐❢❡r❡♥t❡s ❜❛s❡s ❡ ♦s r❡s✉❧t❛❞♦s ❛♣♦♥t❛r❛♠ ♣❛r❛ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ✉♠❛ ❜❛s❡ ❛❞❡q✉❛❞❛ ♣❛r❛ r❡s♦❧✈❡r ♦s ♣♦♥t♦s q✉â♥t✐❝♦s ❞✉♣❧♦s ✈❡rt✐❝❛✐s✳ ◆ós ❞❡♠♦♥str❛♠♦s q✉❡ ❛s ❢✉♥çõ❡s ❞❡ ❜❛s❡ ❝♦♠♣♦st❛s ♣♦r ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ❡①❛t❛s ♣❛r❛ ✉♠ ú♥✐❝♦ ♣♦♥t♦ q✉â♥t✐❝♦ ♣♦❞❡♠ ❢♦r♥❡❝❡r r❡s✉❧t❛❞♦s ❝♦♠ ❛❧t❛ ♣r❡❝✐sã♦✳ ▼♦str❛♠♦s t❛♠❜é♠ q✉❡✱ q✉❛♥❞♦ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ♦s ♣♦♥t♦s q✉â♥t✐❝♦ ❞✐♠✐♥✉✐✱ ♦s ❡st❛❞♦s ❡❧❡trô♥✐❝♦s ❡✈♦❧✉❡♠ ❣r❛❞✉❛❧♠❡♥t❡ ❞❡ ✉♠❛ ♥❛t✉r❡③❛ ❛tô♠✐❝❛ ♣❛r❛ ✉♠❛ ♠♦❧❡❝✉❧❛r✳

✷✳✷ ▼♦❞❡❧♦

❖ ♣♦t❡♥❝✐❛❧ ❞❡ ❝♦♥✜♥❛♠❡♥t♦ V(x, y, z) ❞♦ ♥♦ss♦ s✐st❡♠❛ é ❝♦♠♣♦st♦ ❞❡

❞♦✐s ♣♦♥t♦s q✉â♥t✐❝♦s ✈❡rt✐❝❛✐s ✐❞ê♥t✐❝♦s GaAs/AlxGa1−xAs✱ q✉❡ é ❞❡s❝r✐t♦ ♣♦r ✉♠ ♣♦t❡♥❝✐❛❧ ♣❛r❛❜ó❧✐❝♦ ❡♠(x, y)✭V_k(x, y)✮ ❡ ♦ ♣♦t❡♥❝✐❛❧ q✉❛❞r❛❞♦ ✭V_⊥(z)✮ ❛♦ ❧♦♥❣♦ ❞❛

❞✐r❡çã♦z✳ ❊♥tã♦✱ ♦ ❍❛♠✐❧t♦♥✐❛♥♦ ❞♦ s✐st❡♠❛ ♣♦❞❡ s❡r ❡s❝r✐t♦

H = p

2

2m +V(x, y, z), ✭✷✳✶✮

♦♥❞❡

V_k(x, y) = mω

2 0

2 (x

2_+y2_{), ✭✷✳✷✮}

V_⊥(z) = 

   

   

V0, |z| ≤lb/2 or |z| ≥lb/2 +lw

0, ❝❛s♦ ❝♦♥trár✐♦

✭✷✳✸✮

♦♥❞❡m∗ _{é ❛ ♠❛ss❛ ❡❢❡t✐✈❛ ❞♦ ❡❧étr♦♥ ❡ω}

✾

❤❛r♠ô♥✐❝♦ ♥♦ ♣❧❛♥♦ (x, y)✳ ❖ ♣♦t❡♥❝✐❛❧ V_⊥(z) é ♠♦str❛❞♦ ❡sq✉❡♠❛t✐❝❛♠❡♥t❡ ♥❛

❋✐❣✉r❛ ✷✳✶

❋✐❣✉r❛ ✷✳✶✿ ❊sq✉❡♠❛ ❞❛ ❝♦♥✜❣✉r❛çã♦ ❡s♣❛❝✐❛❧ ❞❡ ❞♦✐s ♣♦♥t♦s q✉â♥t✐❝♦s ✭❛✮ ❡ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❝♦♥✜♥❛♠❡♥t♦ ♥❛ ❞✐r❡çã♦ ❞❡ z ✭❜✮✳

P❛r❛ r❡s♦❧✈❡r ❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ❡❧❡trô♥✐❝❛HΨ(x, y, z) = EΨ(x, y, z)✱

❝♦♠ ♦ ❍❛♠✐❧t♦♥✐❛♥♦ H ❞❛❞♦ ♣❡❧❛ ❡q✉❛çã♦ ✷✳✶✱ ❡①♣❛♥❞✐♠♦s ❛ Ψ(x, y, z) ❝♦♠♦ ✉♠

♣r♦❞✉t♦ ❞❡ ❞✉❛s ♦✉tr❛s ❢✉♥çõ❡s t❛❧ ❝♦♠♦

Ψ(x, y, z) = ψ(x, y)φ(z), ✭✷✳✹✮

❝♦♠ ❡st❛ ❡①♣❛♥sã♦✱ ❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ♦r✐❣✐♥❛❧ s❡ ❞✐✈✐❞❡ ❡♠ ❞✉❛s ♦✉tr❛s ❡q✉❛çõ❡s✳ ❆ ♣r✐♠❡✐r❛ é ❞❛❞❛ ♣♦r

−~ 2

2m

∂2 ∂x2 +

∂2 ∂y2

+V_k(x, y)

ψ(x, y) =E_kψ(x, y), ✭✷✳✺✮

♦♥❞❡ ψ(x, y)❡ E_k sã♦ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❡ ❛ ❡♥❡r❣✐❛ ❞♦ ❡❧étr♦♥ ❡♠

✉♠ ♣♦t❡♥❝✐❛❧ ♣❛r❛❜ó❧✐❝♦✳ ❆ s❡❣✉♥❞❛ ❡q✉❛çã♦ é ❞❡s❝r✐t❛ ♣❡❧❛ s❡❣✉✐♥t❡ ❡q✉❛çã♦

− ~

2

2m d2

dz2 +V⊥(z)

✶✵

♦♥❞❡ φ(z) ❡ E_⊥ sã♦ ❛s ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ❡ ❛ ❡♥❡r❣✐❛ ❞♦ ❝♦♥✜♥❛♠❡♥t♦ ❞♦ ❡❧étr♦♥ ♥❛

❞✐r❡çã♦ z✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❆ ❡♥❡r❣✐❛ t♦t❛❧ E é ❞❛❞❛ ♣❡❧❛ s♦♠❛ ❞❛s ❡♥❡r❣✐❛s E_k ❡ E_⊥✳

■♥✐❝✐❛❧♠❡♥t❡ ✈❛♠♦s ❞❡t❡r♠✐♥❛r ♦s ❛✉t♦❡st❛❞♦s ❡ ❛✉t♦✈❛❧♦r❡s ❞❡ ✉♠ ❡❧étr♦♥ ❡♠ ✉♠ ❙◗❉ ♣❛r❛❜ó❧✐❝♦ s✉❜♠❡t✐❞♦s ❛ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡①t❡r♥♦B ✳ ❈♦♠♦ s❛❜❡✲

♠♦s✱ ❡st❡s sã♦ ♦s ❛✉t♦❡st❛❞♦s ❞♦s ❡st❛❞♦s ❞❡ ❋♦❝❦✲❉❛r✇✐♥ ❬✷✵❪✱ ♦✉ s❡❥❛✱ψ(x, y)_⊗χσz✱ q✉❡ sã♦ ❞❡s❝r✐t♦s ♣♦r três ♥ú♠❡r♦s q✉â♥t✐❝♦s ✭n+, n−, σz✮✱ ♦♥❞❡ n+(n−) = 0,1,2, ...✱

σz é ♦ ♥ú♠❡r♦ q✉â♥t✐❝♦ ❞❡ s♣✐♥ ❡ χσz é ♦ ❝♦rr❡s♣♦♥❞❡♥t❡ s♣✐♥♦r✳ ❊st❡s ❡st❛❞♦s

ψ(x, y) ♣♦❞❡♠ s❡r ❡①♣r❡ss♦✱ ❡①♣❧✐❝✐t❛♠❡♥t❡✱ ❝♦♠♦ ❬✷✵❪

ψ(x, y) = Hn+(x/l0)Hn−(y/l0)

p

2n+n−n₊!n

−!πl20

e−

(x2+y2)

2l2_{0 ,} ✭✷✳✼✮

♦♥❞❡ Hn(ξ) ❞❡♥♦t❛ ♦s ♣♦❧✐♥ô♠✐♦ ❞❡ ❍❡r♠✐t❡ ❞❡ ♦r❞❡♠ n ❡ l0 =

p

(~_/mΩ) é ♦ ❝♦♠♣r✐♠❡♥t♦ ❝❛r❛❝t❡ríst✐❝♦ ❞♦ ♣♦♥t♦ q✉â♥t✐❝♦ ♥♦ ♣❧❛♥♦ (x, y) ❝♦♠ Ω2 _{= w}2

0 + w2

c 4 ✱ ♦♥❞❡ω0 é ❛ ❢r❡q✉ê♥❝✐❛ ❞♦ ♦s❝✐❧❛❞♦r ❤❛r♠ô♥✐❝♦ ❡s♣❛❝✐❛❧ ❡wc =eB/mé ❛ ❢r❡q✉ê♥❝✐❛ ❝í❝❧♦tr♦♥✳ ❖s ❛✉t♦✈❛❧♦r❡s ❝♦rr❡s♣♦♥❞❡♥t❡s sã♦ ❞❛❞♦s ♣♦r ❬✷✵❪

En+,n−

k = (n++n−+ 1)~Ω + (n+−n−)

~_wc

2 . ✭✷✳✽✮

❆ r❛③ã♦ ❡♥tr❡ ❛ ❢r❡q✉ê♥❝✐❛ t♦t❛❧ ❡ ❛ ❞❡ ❝í❝❧♦tr♦♥✱ Ω✴wc✱ ♠❡❞❡ ❛ ❝♦♠♣❡t✐çã♦ ❡♥tr❡ ❝♦♥✜♥❛♠❡♥t♦ ❡s♣❛❝✐❛❧ ❡ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✐♥❞✉③✐❞♦✳ ❊st❛ ú❧t✐♠❛ é ❝❛r❛❝t❡r✐✲ ③❛❞❛ ♣❡❧♦ ❝♦♠♣r✐♠❡♥t♦ ♠❛❣♥ét✐❝♦ ✭lc =

p

~_/mwc✮✳ ◗✉❛♥❞♦ ♦ ❝♦♥✜♥❛♠❡♥t♦ ❡s♣❛❝✐❛❧ é ♣❡q✉❡♥♦ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ ❛♦ ❝♦♥✜♥❛♠❡♥t♦ ❞✐♥â♠✐❝♦✱ ❝❛s♦ ❡♠ q✉❡ l0 > lc ♦✉

wc > 2

√

3

3 w0✱ ♦ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣✐❛ ❝♦♥s✐st❡ ❞❡ ♠ú❧t✐♣❧♦s ♥ú♠❡r♦s q✉â♥t✐❝♦s ✐♥❞❡①❛✲ ❞♦s ♣♦r n+✱ q✉❡ sã♦ s❡♣❛r❛❞♦s ✉♥s ❞♦s ♦✉tr♦s ♣♦r ~_w+✱ ♦♥❞❡ _{ω± = Ω±ω}c✱ ❡ ♣♦r

n₋ q✉❡ sã♦ s❡♣❛r❛❞♦s ✉♥s ❞♦s ♦✉tr♦s ♣♦r ~_w−✳ ❆ ♠❡❞✐❞❛ q✉❡ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛✉♠❡♥t❛✱En− ∼= (n−+ 1/2)~w−→0✱ ♦✉ s❡❥❛✱ ♦ ❡s♣❛ç❛♠❡♥t♦ ❡♥tr❡ ♦s ♥í✈❡✐s ❝♦♥s❡❝✉✲ t✐✈♦s ❞✐♠✐♥✉✐ ❡ ♦ ❝♦❧❛♣s♦ ♥♦s ♥í✈❡✐s ❞❡ ▲❛♥❞❛✉ ❝♦♠ ❛✉t♦✈❛❧♦r❡s ✈❛r✐❛♠ ❧✐♥❡❛r♠❡♥t❡ ❞❡♣❡♥❞❡♥t❡ ♥♦ ❝❛♠♣♦B✳ ◗✉❛♥❞♦ B _{= 0}✱ _{wc = 0} ❡ _{Ω =w0}✱ ❛ ❡①♣r❡ssã♦ ❞❛ ❡♥❡r❣✐❛

✶✶

❆❣♦r❛✱ ✈❛♠♦s ♥♦s ❝♦♥❝❡♥tr❛r ♥❛ s♦❧✉çã♦ ❞❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ❛♦ ❧♦♥❣♦ ❞❛ ❞✐r❡çã♦z✱ ❡♠ q✉❡ ♦ ❛❝♦♣❧❛♠❡♥t♦ ❡♥tr❡ ♦s ❞♦✐s ♣♦♥t♦s ♦❝♦rr❡✳ P❛r❛ ❜❡♠ ❝♦♠♣r❡✲

❡♥❞❡r ♦ ❛❝♦♣❧❛♠❡♥t♦ ❞❡ t✉♥❡❧❛♠❡♥t♦✱ ✈❛♠♦s ❝♦♠❡ç❛r ❝♦♠ ✉♠❛ ❜r❡✈❡ r❡✈✐sã♦ ❞❛s ♣r✐♥❝✐♣❛✐s ♣r♦♣r✐❡❞❛❞❡s ❞❡ ✉♠ ú♥✐❝♦ ♣♦♥t♦ q✉â♥t✐❝♦✳ ❖ ❍❛♠✐❧t♦♥✐❛♥♦ ❞❡ ✉♠ ❙◗❉ ♣♦❞❡ s❡r ❞❡s❝r✐t♦ ♣♦r

HSQD =

p2 z

2m +VSQD(z) ✭✷✳✾✮

♦♥❞❡VSQD(z) é ❞❡✜♥✐❞♦ ♣♦r

VSQD(z) =

        

0, _|z_{| ≤}lw/2

V0, |z|> lw/2.

✭✷✳✶✵✮

❊st❡ ♣r♦❜❧❡♠❛ ❞❡ ❛✉t♦✈❛❧♦r ❞♦ ♣♦t❡♥❝✐❛❧ q✉❛❞r❛❞♦ é ❜❡♠ ❝♦♥❤❡❝✐❞♦ ❡ ❞✐s✲ ❝✉t✐❞♦ ♥❛ ❧✐t❡r❛t✉r❛ ❬✷✷❪✳ ❆s ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ♥♦r♠❛❧✐③❛❞❛s ♣❛r❛ ♦s ❡st❛❞♦s ❧✐❣❛❞♦s ❞❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r HSQDφSQD=ESQDφSQD sã♦ ❡s❝r✐t♦s ❝♦♠♦

φimpar_SQD (z) =                     

A0 ekIz, z <−lw/2

A1cos(kIIz), |z| < lw/2

A0 e−kIz, z > lw/2

✭✷✳✶✶✮

φpar_SQD(z) =                     

−B0 ekIz, z <−lw/2

B1sin(kIIz), |z| < lw/2

B0 e−kIz, z > lw/2,

✶✷

♦♥❞❡kI =

p

2m(V0−E)/~✱ kII =

√

2mE/~❡

A0 = A1cos

kIIlw

2

kIlw/2 ,

A1 =

1 kI

cos2

kIIlw

2

+ lw 2 +

1 2kII

sin2(kIIlw)

−1/2 ,

B0 = B1sin

kIIlw

2

kIlw/2 ,

B1 =

1 kI

sin2

kIIlw

2

+lw 2 −

1 2kII

sin2(kIIlw)

−1/2 ,

❡ ❛ ❛✉t♦❡♥❡r❣✐❛s ESQD sã♦ ❞❡t❡r♠✐♥❛❞♦s ♣❡❧❛s s❡❣✉✐♥t❡s ❡q✉❛çõ❡s tr❛♥s❝❡♥❞❡♥t❛✐s

kI = kII tan

kIIlw

2

✭✷✳✶✸✮ ❡

−kI = kII cotan

kIIlw

2

. ✭✷✳✶✹✮

❯♠ tr❛t❛♠❡♥t♦ ❛❧t❡r♥❛t✐✈♦ ❞❡ r❡s♦❧✉çã♦ ♣❛r❛ ❡st❡ ♣r♦❜❧❡♠❛ ❢♦✐ ❞❛❞♦ ♣♦r P❡❞❡rs❡♥ ❡ ❈❤❛♥❣ ❬✷✶❪✳ ❊❧❡s r❡s♦❧✈❡r❛♠ ❡st❡ ♠❡s♠♦ ♣r♦❜❧❡♠❛ ✐♥tr♦❞✉③✐♥❞♦✱ ✉♠ ♣❛râ♠❡tr♦ ✈❛r✐❛❝✐♦♥❛❧Lw ♥❛s ❢✉♥çõ❡s tr✐❣♦♥♦♠étr✐❝❛s✱ q✉❡ r❡♣r❡s❡♥t❛♠ ♦s ❡st❛❞♦s ❞❡ s✉❜✲❜❛♥❞❛s ❞❡ ♣♦ç♦s q✉â♥t✐❝♦s✳ ❚❛✐s ❢✉♥çõ❡s sã♦ ❡s❝r✐t❛s ❝♦♠♦

φaprox_SQD(z) = r

2 Lw

sin

sπ(z+Lw/2)

Lw

✭✷✳✶✺✮

✶✸

lw

Lw

= Vof f

2π2 [1 +cos(πlw/Lw)], ✭✷✳✶✻✮

♦♥❞❡ Vof f = 2mlw2V0/~2✳ ➱ ✐♠♣♦rt❛♥t❡ ♥♦t❛r q✉❡ ❡ss❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ t❡st❡ só é ❝♦♠♣❧❡t❛ ♥♦ ✐♥t❡r✈❛❧♦ [₋Lw, Lw] ❞❛ ❝♦♦r❞❡♥❛❞❛ z✳ ❆❧é♠ ❞✐ss♦✱ é ✐♥t❡r❡ss❛♥t❡ r❡ss❛❧t❛r q✉❡ ❛ ♠❡s♠❛ t❡♠ s✐❞♦ ❛♣❧✐❝❛❞♦ ❝♦♠ s✉❝❡ss♦ ♣❛r❛ r❡s♦❧✈❡r ♦s ♣r♦❜❧❡♠❛s ❞❡ ❙◗❉s ❞❡ ●❛❆s ❡ ■♥❆s ❬✷✶❪✳

❆❣♦r❛✱ ✈♦❧t❡♠♦s ❛♦s ♣r♦❜❧❡♠❛s ❞♦s ❉◗❉s✱ ❞❡✜♥✐❞❛ ♣❡❧♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❝♦♥✲ ✜♥❛♠❡♥t♦ ❞❡s❝r✐t♦ ♥❛ ❡q✉❛çã♦ ✷✳✷✳ ❆ ❡str✉t✉r❛ ❡❧❡trô♥✐❝❛ ❞❛ ♠♦❧é❝✉❧❛ ❞❡ ♣♦♥t♦ q✉â♥t✐❝♦ ❡ ❛s ❝♦rr❡s♣♦♥❞❡♥t❡s ❢✉♥çõ❡s ❞❡ ♦♥❞❛ sã♦ ♦❜t✐❞❛s ❝♦♠❜✐♥❛♥❞♦ ❧✐♥❡❛r♠❡♥t❡ ♦r❜✐t❛✐s ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s✳ ❉❡st❛ ❢♦r♠❛✱ ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ t♦t❛❧ ♥❛ ❞✐r❡çã♦ ❞♦ ❡✐①♦z ♣♦❞❡ s❡r ❡s❝r✐t❛ ❝♦♠♦

φnz(z) = n

X

j=1

cjχ(R)j (z) + 2n

X

j=n+1

cjχ(L)j (z). ✭✷✳✶✼✮

♦♥❞❡χ(R)_{(z) = φ}

SQD(z−α)✱ χ(L)(z) = φSQD(z+α)✱ ❡ α= (lb+lw)/2 φSQD é ❞❛❞♦ ♣❡❧❛s ❡q✉❛çõ❡s ✷✳✶✶ ❡ ✷✳✶✷✱ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❝♦♠ ❢✉♥çõ❡s ❞❡ ❜❛s❡ ❙◗❉ ❡①❛t❛ ❡ ♣♦r ✷✳✶✺ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❝♦♠ ❢✉♥çõ❡s ❞❡ ❜❛s❡ ❙◗❉ ❛♣r♦①✐♠❛❞❛✳ ❆ ❢✉♥çã♦ χ(R)_{(z) ❡ χ}(L)_(z) r❡♣r❡s❡♥t❛ ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❞♦ ❧❛❞♦ ❞✐r❡✐t♦ ❡ ❞♦ ❧❛❞♦ ❡sq✉❡r❞♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳

P♦r ❝❛✉s❛ ❞❛ ♥ã♦ ♦rt♦❣♦♥❛❧✐❞❛❞❡ ❞❛s ❢✉♥çõ❡s ❞❡ ❜❛s❡ χ(R) _{❡ χ}(L)_{✱ ✉♠ ♣r♦✲} ❜❧❡♠❛ ❞❡ ❛✉t♦✈❛❧♦r ❣❡♥❡r❛❧✐③❛❞♦HC_=ESCt❡♠ ❞❡ s❡r tr❛t❛❞♦✳ H❡Sr❡♣r❡s❡♥t❛♠

❛ ♠❛tr✐③ ❤❛♠✐❧t♦♥✐❛♥❛ ❡ ❛ ♠❛tr✐③ ❞❡ s♦❜r❡♣♦s✐çã♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❝✉❥♦s ❡❧❡♠❡♥t♦s sã♦ ❞❛❞♦s ♣♦r

Hi,j =

              

hχ(R)_{i |}H_|χ_j(R)_i, i_≤n and j _≤n

hχ(R)_{i |}H_|χ(L)_{j i}, i_≤n and j > n

hχ(L)_{i |}H_|χ(R)_{j i}, i > n and j _≤n

hχ(L)_{i |}H_|χ(L)_{j i}, i > n and j > n