Research Overview. Vijay B. Shenoy. February 13, Centre for Condensed Matter Theory, IISc Bangalore

Transcription

1 Research Overview Vijay B. Shenoy Centre for Condensed Matter Theory, IISc Bangalore February 13, / 18

2 Research Group Jayantha Vyasanakere Yogeshwar Prasad Saraswat Sudeep Kumar Ghosh Amal Medhi Vijay Shenoy 2 / 18

3 Research Interests Theoretical quantum condensed matter physics Cold Atom Physics Graphene/Topological Insulators Strongly Correlated Electrons 3 / 18

4 Cold Atoms 4 / 18

5 c S Tc kf Fermions in Synthetic Non-Abelian Gauge Fields 2-body Many body Rashbons BW ABM BEC TF BCS RBEC λa sc -1-2 Spherical 1 kf as? Λ -3 Prolate Oblate -4 EP S EO Bound state for any attraction arxiv: Rashba SOC induces BCS-BEC Rashbon BEC arxiv: Phase diagram, High T c Pseudogap regime arxiv: Excitations.6.16 k F a s -1/4 Traps/Potentials Overall RG Picture c S / k F λ / k F λ/k F -1/2-1 infinity 1 1/2 1/4 z ω 1/2 ρ(r, z) / ω 3/2 R λ λ/k F Emergent Galilean Invariance Rashbon-rashbon interactions arxiv: /2 2 3 r ω Shrinking of Clouds Novel Hamiltonians arxiv: vr vf v = 1 v = arxiv: v 5 / 18

6 Feshbach Resonances, Upper Branch Physics Broad and narrow Feshbach resonances R Feshbach resonances RG flow diagram u Upper branch phase diagram E / E 1.2 (a) B R F υ κ/κ, χ/χ (b) κ χ T = 3E F /k F a s (116.96) (Unpublished) Upper branch: Explanation of violation of Tan s theorem, no magnetic instability 6 / 18

7 Superfluid from Band Insulators ( ) Realization of a fermionic superfluid state in the 1-band TB limit Trick to overcome entropy removal problem create a superfluid from a band insulator Tune negative U in a bi-layer band insulator.8 (b) g(ǫ) ǫ g(ǫ) ǫ T/t Pseudogap Superfluid Experimental realization: Orthogonally shaken bilayer U/t T T BKT 7 / 18

8 Topological Insulators 8 / 18

9 Correlation Physics in Topological Insulators Mott transition at edge states of topological insulators (Medhi et al., ) Two routes: Synchronous and Asynchronous Determined by topological resilience compressibility of the edge states Key message All Mott physics is local! 9 / 18

10 Field Theories of Topological Insulators A continuum field theory to describe edge states of topological insulators in 2 and 3 dimensions A new natural boundary condition that correctly captures the nature of wave functions at the edges n i ( S n ij Γ n ab jψ b + ia m i Λ m ab Ψ b) = 1 ǫ =1 t sp =.5 natural BC fixed BC TB.1 ǫ =.45 t sp =.5 analytic TB Ψ y 1e L (Medhi et al., ) Non-monotonic dependence of the gap on the thickness of ribbon! Possible applications? 1 / 18

11 Graphene 11 / 18

12 Graphene: Sensory-organ like response Zigzag edge terminated nanoribbons subjected to edge potentials V A A W VB B (Bhowmick, )...show Weber-Fechner (sensory-organ like) response! ( ) V W /a N sgn(v ) ln, V th te V th 12 / 18

13 Graphene: Magnetism Zigzag edge terminated nanoribbons have sensory-organ like response! V A A VB W B ( ) Magnetic structure of zigzag edge ribbons (Hubbard model) Undoped Doped First order transition from Anti-Ferro to Ferro as a function of doping...occurs at a critical doping (128.34) δ c = C(U) a 1, C(U) = W ( ) 1 ln ln(u/6) ( ) π 1+ 2 ln(u/6) 13 / 18

14 Graphene: Superconductivity Electron correlations drive superconductivity Pairing with d + id symmetry SC Order Parameter, Φ ( 1 4 ) Doping, x Breaks time reversal symmetry Optimum doping around x.15 SC Correlation function, F(r) (89.244) Distance, r 14 / 18

15 Strongly Correlated Systems, High T c 15 / 18

16 Strongly Correlated Electrons - High T c Variational approach: Developed a new O(N) method for optimization of variational wavefunction Material dependencies of the cuprate phase diagram ODLRO, Φ( 1 4 ) M Φ t < t /t =.3, J/t = M.4.2 t /t =.3 t > 1, t =. t =.3, t =.6 8, t =.12, t = ODLRO, Φ ( 1 4 ) Electron Doping, x Hole Doping, x (Pathak et al., 29) Phase diagram determined by a single parameter FSCP Suggestions for raising T c : Convex bare Fermi surface 16 / 18

17 Strongly Correlated 2D systems A general wavefunction for spin-singlet ground states Estimate of condensation energy Condensationenergy per site, E c (Pathak, Ph. D. Thesis (21)) Doping, x J/t =.3 82 site Tilted Square Lattice In the extremely correlated liquid (U = ), Luttinger theorem holds 17 / 18

18 Vijay Shenoy, Brief Vitae B. Tech (IIT Madras, 1992), M. S. (Georgia Tech., 1994), Ph. D. (Brown, 1994) Publications: 65, Hirsch Index: 27 Ph. D. supervised (3): Murali Palla (28, Post Doc Singapore), Somnath Bhowmick (21, Post Doc Upssala (Sweden), Offered faculty position at IIT Kanpur), Sandeep Pathak (21, Post Doc UC Santa Cruz) Recognition: Fellow IAS, Raja Ramanna Prize (211), DAE-SRC Outstanding Research Investigator (21), NASI-Scopus Young Scientist Award (29), Ramanujan Fellowship (27), INAE Young Engineer Award (25), INSA Medal for Young Scientist (22), Associate, Indian Academy of Sciences (2126), IITK Director s citation for outstanding tutor (2), Elected Member of Sigma-Xi (1998), Brown University Teaching Fellowship (1998), Caltech Special Fellowship (1997), Brown University Fellowship ( ) Visit home page shenoy to download latest papers 18 / 18