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Magneto-Optical Properties of Topological Insulators and Kondo Effects in Quantum Dots

Thesis Info

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Author

Rahim, Kulsoom

Program

PhD

Institute

Quaid-I-Azam University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Physics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/10266/1/Kulsoom%20Rahim_Phy_2019_QAU_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726598826

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This thesis has two parts, based on work carried out during my PhD. The first part comprises discussion of magneto-optical properties of ultra thin films of topological insulators (TI) with broken inversion symmetry. We explore the magneto-optical properties of thin film topological insulators (TFTI). Topological insulators are materials with insulating bulk and symmetry protected gapless surface states. In the TIs we consider, spin-Orbit Interaction (SOI) inverts valence and conduction bands and gapless surface states appear as the bulk gap closes at the interface of a topological insulator with conventional insulator. We study the magneto-optical response of ultrathin films of topological insulators in the presence of an external magnetic field with hybridization and broken inversion symmetry. We find that inversion symmetry breaking results in Landau level crossings and opening of additional optical transition channels. Inversion symmetry can be broken due to interaction with a substrate or electrical gating. A phase transition from normal to topological insulating phase occurs by tuning system parameters with measureable signatures in static (dc) and dynamic (optical) conductivity. Moreover, we find that the optical Hall conductivity plateaus remain robust against a significant range of disorder strength. In the second part we discuss Kondo effect in a complex Quantum Dot (QD) in the presence SOI and analyze its influence on fixed points and Kondo temperature. We model a quantum dot (QD) in the Coulomb blockade regime with two localized orbitals connected to two external leads with SOI in the leads. The lead electrons couple to the dot state in different angular momentum modes in the presence of SOI. We develop an effective Hamiltonian for the system and study the multiparameter RG flows by renormalization group analysis in the weak coupling regime. Previous studies have shown that in the absence of SOI for odd electrons in the dot SU(4) and SU(2) Kondo fixed points are stable and for even electrons a universal stable fixed point exists. We determine the fixed points in the presence of SOI. We determine the Kondo temperature by numerically solving the RG equations and show that the Kondo temperature is enhanced by the SOI.
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مولانا مفتی عتیق الرحمن عثمانی

مفتی عتیق الرحمن صاحب عثمانی رحمۃ اﷲ علیہ
دوبرس ہاں دوبرس پہلے کی بات
آرہی ہے خودبخود ہونٹوں پہ آج
تھااِسی ماہ مئی میں بارہ کا دن
جب ہوا تھاشیخ کایومِ وفات
اُن کا مسلک تھاہر اک کی عافیت
خویش ہو یا غیر ہو سب کا بھلا!!
بعدازختمِ قرآنِ کریم اور درود،فاتحہ خوانی نیز دعائے مغفرت اورتعزیت کے ایصالِ ثواب برائے روحِ پاک جناب مفتی عتیق الرحمن صاحب عثمانی ؒ ساکن کڑانظام جامع مسجددہلی، منجانب مدرسہ دارالاصلاح شاہی مسجد بارگ والی سُوہنہ ضلع گوڑگانوہ ہریانہ برموقعہ اُن کی دوسری برسی بتاریخ ۱۲؍مئی ۱۹۸۶ء بمطابق ۲؍رمضان المبارک (۱۴۰۶ھ)
مرحوم جناب مفتی عتیق الرحمن صاحب عثمانی رحمۃ اﷲ علیہ علم وانسانیت کے آفتاب کسرِ نفسی کے جوہرِ انسانیت کے چراغ اﷲ کے عاشق، رسول کے شیدا، فدا کارِ ملّت غرباء پرور، بیکس نواز قوم گیر ملّت ساز، خدا ترس، رحم دل، مشفق، شفیق، انکسارِ سادہ منکسر المزاج، علاوہ ازیں وہ بہت سی خوبیوں کے مالک تھے۔ بالخصوص قوم کے ایک ایسے ممتاز ہردلعزیز سچّے قائد جن کی شہرت دہلی سے گزرکر باہر بیرون میں پورے ملک اور ملک سے باہر دورتک پہنچ رہی تھی جس کی بناء پر ان کی زندگی دن بدن روشن ہوتی جارہی تھی اور جس کی وجہ سے اُن کانام اورکام ہمہ گیر اہمیت کامرکز بناہوا تھالہٰذا اسی لیے آج بھی پوری ملّت اُن کے لیے سر پیٹ رہی ہے اور پیٹتی رہے گی۔
دراصل حقیقت یہ ہے کہ مخلص مجاہد، دانشور ،مدبّر، مفکّر، مبلّغ اورسچّا قائد کہ یہ ایسی شخصیتیں ہیں جن کے حسین کردار اور اعلیٰ کارناموں میں ملّت کے وجود کی ضمانت پوشیدہ ہے لہٰذا اسی لیے یہ شخصیتیں ملّت کے لیے حاصلِ عمرکی حیثیت رکھتی ہیں۔افسوس کہ آج ہم ایسی ہی عظیم شخصیت سے جناب مفتی عتیق الرحمن صاحب عثمانی ؒ سے محروم ہوکر اُن کے سوگ میں بیٹھے...

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