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Topology in Condensed Matter: Tying Quantum Knots Tutorial: by Jaydeep Sau

575 views · Published 6 July 2016 · 1:49:43 · Indexed 20 September 2026

Channel: International Centre for Theoretical Sciences · 2016 · Science & Technology

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School on Current Frontiers in Condensed Matter Research

URL: http://www.icts.res.in/program/cficmr16

DATES: Monday 20 Jun, 2016 - Wednesday 29 Jun, 2016 

VENUE : Ramanujan Lecture Hall, ICTS Bangalore

DESCRIPTION:
Understanding strongly interacting quantum many body systems is one of the major frontiers in present day physics. Condensed matter physics provides a wide panoply of systems where strong interaction between constituent particles play a dominant role; some examples of such systems are high temperature superconductors, spin-liquids, fractional quantum Hall systems, and ultracold atoms in the strong-coupling regime. Recent additions to this list include topological insulators/superconductors, transition metal oxides and their heterostructures. These materials have the added feature that they have strong spin-orbit coupling. The interplay of strong interactions and strong spin-orbit coupling is presently a frontier area of research in condensed matter physics.

This program aims to introduce graduate students and post-docs to different aspects of strongly interacting systems focusing on ideas which are recently animating the condensed matter community world-wide. The program will consist of a week-long pedagogical lectures from 20.06.2016 to 26.06.2016 on frontier areas, followed by three days of a discussion meeting from 27.06.2016 to 29.06.2016 on related topics, presenting and discussing the latest situation in these areas.

The school lecturers are :

Subir Sachdev (Harvard University)
Mohit Randeria ( The Ohio State University)
Jainendra Jain ( Penn State University)
Jay D. Sau ( University of Maryland, College Park ) 
Kedar Damle (Tata Institute of Fundamental Research, Mumbai)
Vijay Shenoy (Indian Institute of Science, Bangalore)
Diptiman Sen (Indian Institute of Science, Bangalore)
Students and post-docs interested in attending this program should click on the link "APPLY" on top of this page and follow the instructions.

ORGANIZERS: Subhro Bhattacharjee, Jainendra Jain, H R Krishnamurthy, Krishnendu Sengupta and Rajdeep Sensarma

Table of Contents (powered by https://videoken.com)
0:00:11 Chem insulators
0:01:55 change in reflection matrix dr: dr dq = 2xi
0:14:22 t/T
0:14:31 Majorana signatures: 4n-periodic Josephson effect, Andree conductance quantization
0:14:52 as an annulus, which is referred to as the Corbin disk:
0:17:13 Corbin Disk
0:32:05 Where do the pumped electrons come from and go to?
0:33:01 right-moving skipping orbit
0:34:37 The chirality of the edges is determined by the orientation of the magnetic field
0:34:42 A closer look at the chiral
0:34:53 that the ribbon has a finite width in the direction.
0:36:07 on the details of the confining potential
0:36:57 In general, however, we expect the energy E
0:37:03 TU DC quacu to me TIamoman.
0:44:15 theory of a single chiral edge state, neglecting the bulk
0:44:43 right-moving skipping orbit
0:46:08 The harmless anomaly of the chiral edges
0:46:25 The harmless anomaly of the chiral edges 11
0:46:50 Let's consider the equation _ = nV(K - KF ) which describes these chiral states.
0:47:06 pallel to the momentum k. (In the Hall cylinder,
0:48:06 The momentum changes according to the equation hk = -e&. After a time t,
0:50:34 This property of the edge is referred to as the chiral anomaly.
0:51:45 consideration is only the edge of something else!
0:52:26 To conclude our case about chiral edge states,
1:08:17 electrons in Landau levels
1:10:06 of amplitudes on the two sites A and B.
1:10:40 strength , one obtains the Bloch Hamiltonian:
1:11:14 Here a; are the three vectors in the figure,
1:11:55 Discrete symmetries of graphene 1
1:14:15 The symmetries of graphene were discussed intensively in the video, so let's review them.
1:15:04 they couple sites of same type: A with A and with B.
1:15:38 they are purely imaginary and, furthermore, they all have the same chirality,
1:16:19 Since the magnetic field is weak,
1:16:37 entire Brillouin Zone. For instance, we can consider the following closed path C,
1:20:10 exp(-i fo E[k(1)] dt ), which an eigenstate of the Hamiltonian accumulates with time.
1:20:18 Here, A(k) = i ( w(k) I Vk y
1:21:30 direction,
1:21:52 ly(n, 1 = 1)) = dkx ." exp liy(kx) - 10(k,)] ly ( kx ,
1:22:42 something strange. While 0(kx) is a truly periodic function of k, because E(kx) = E
1:23:12 combination y(kx) - 0(kx) as large as possible (just like before,
1:23:55 which are obtained by taking the derivatives of ly(k)) with respect to kx and k,
1:24:44 an integer number.
1:25:00 r(kx) - O(kx ) = Wkx.
1:25:11 The main advantage of introducing the analogy with the magnetic field is that it motivates us to use Stokes theorem.
1:32:22 monopole was never observed. For our Chem number in the Brillouin zone
1:33:07 Summary: extending the model to sinful electrons and photons
1:34:06 The following sketch describes the situation in the case / = 1:
1:34:36 BHZ model. In essence,
1:37:40 Chrome
1:39:54 equivalently ),

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