Universal Features of the Mott-Metal Crossover in the Hole Doped J = 1/2 Insulator Sr 2 IrO 4 Umesh Kumar Yadav Centre for Condensed Matter Theory Department of Physics Indian Institute of Science August 28, 2014 Quantum Condensed Matter Journal Club Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped28, J 2014 = 1/2 Insulator 1 / 27 Sr
Outline of the talk What are the Mott-Hubbard, Charge Transfer and Slater Insulators? What are the J = 1/2 Insulators? How do Iridates differ from Cuprates? What are the common features of doped Iridates and Cuprates? What are the causes of universal features of Mott-metal crossover in the Iridates? Is Sr 2 IrO 4 Mott insulator or Slater insulator? Conclusions and future directions Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped28, J 2014 = 1/2 Insulator 2 / 27 Sr
Let us start the talk with followings The physics of the doped Mott-insulators is controversial since a long time. Problem to understand their physics are followings: 1. Strong electron correlations, 2. Competing electronic orders e.g. in case of cuprates charge density wave and stripe order, 3. Long range magnetic order, 4. Fluctuations and Fermi surface instabilities, 5. etc... Common understanding: Charge insulation in most known Mott insulators arises due to Coulomb repulsion only. Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped28, J 2014 = 1/2 Insulator 3 / 27 Sr
As an example consider the case of hole doped Cuprates Understanding the origin of exotic phases like Pseudogap and Strange metal (Marginal Fermi liquid) is not clear. There are many proposals that they arise because of: 1. Metal-insulator transition, 2. Some density wave instabilities, 3. Fluctuations of the superconductivity, 4. Existence of a Quantum critical point, 5. etc... Are really they responsible? Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped28, J 2014 = 1/2 Insulator 4 / 27 Sr
Can we do something simple? One can ignore it. But as we know after finding the conventional SC (Liquid He, 1911) it took around 46 years to have a microscopic theory known as BCS theory (1957). Cuprates are only 28 years old (first Cuprate, La 2 x Ba x CuO 4, was discovered in 1986), we still have some hope. We could try a system with clean phase diagram (Hence Lesser competing orders) and different mechanism which forbids electron double occupancy. One example of such systems is R h doped Sr 2 IrO 4. Goal: To find the universal features (Low energy properties that do not depend on the details of the interactions) and their origin for doped Mott-insulators across the Mott-metal crossover. Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped28, J 2014 = 1/2 Insulator 5 / 27 Sr
1.1. Strongly correlated system 9 Mott-Hubbard and charge transfer insulators d-band d-band Δ= ε d -ε p interaction U U charge gap Fermi level, ε F Δ= ε d -ε p interaction U ε F Charge gap U p-band p-band (a) Mott-Hubbard Insulator (b) Charge-Transfer Insulator Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped28, J 2014 = 1/2 Insulator 6 / 27 Sr
Slater insulators Slater insulators: Magnetically driven insulators Weak coupling insulator due to LRO a soft gap in SSB at T < T c spin density wave (SDW) S z (x) cos(2k q F x) E(k) = E F ± ɛ 2 k + 2, (T) T c T E(k) E(k) 2a E F 1/a 1/a k 1/2a 1/2a k thermodynamic MITs Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped28, J 2014 = 1/2 Insulator 7 / 27 Sr
Electronic structure of the elements of our interest La 2 x Sr x CuO 4 : 57La [Xe] 5d 1 6s 2 38Sr [Kr] 5s 2 29Cu [Ar] 3d 10 4s 1 Cu 2+ 3d 9 8O 1s 2 2s 2 2p 6 Sr 2 Ir 1 x Rh x O 4 : 77Ir [Xe] 4f 14 5d 7 6s 2 Ir 4+ 5d 5 45Rh [Kr] 4d 8 5s 1 Rh 4+ 4d 5 Ir and Rh are isovalent. Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped28, J 2014 = 1/2 Insulator 8 / 27 Sr
Cuprates: Charge-transfer insulator Lee, Nagaosa, and Wen: Dopin Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped28, J 2014 = 1/2 Insulator 9 / 27 Sr
rule, since the J eff ¼ 1=2 is branched off from the J 5=2 (5d Sr 2 IrO 5=2 ) manifold due to the large crystal field as depicted in 4 : Spin-Orbit coupled J = 1/2 Mott-insulator Fig. 1(e). As a result, with the filled J eff ¼ 3=2 band and FIG. 1. Schematic energy diagrams for the 5d 5 (t 5 2g ) configuration Yadav (a) (Centre without for Condensed SOMatter Universal and Theory Features U, Department (b) of thewith Mott-Metal of Physics an Crossover unrealistically Indian Institute in theof Hole Science) August Doped 28, large J 2014 = 1/2U Insulator 10 / 27 Umesh Kumar Sr
drawn in Fig. 4.4. Phase diagram of La 2 x Sr x CuO 4 (LSCO) cuprate Figure 4.4: Phase diagram of La 2 x Sr x CO 4 (LSCO). Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 11 / 27 Sr
An early stage Phase diagram of Sr 2 Ir 1 x Rh x O 4 Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 12 / 27 Sr
Details about samples used All the ARPES, transport and magnetization data are taken from bulk Sr 2 Ir 1 x Rh x O 4 samples. Self flux technique is used to grow single crystals from quantities SrCl 2, SrCO 3, IrO 2 and RhO 2. Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 13 / 27 Sr
Crystal Structure, MDC and schematic of energy bands Figure 1 a Sr 2 IrO 4 La 2 CuO 4 c1 Mott b c2 J 3/2 J 1/2 LHB J 1/2 UHB E µ! Mott X! " M!" (#, 0)!!" X/Y! (#, 0)! J 3/2 J 1/2 LHB J 1/2 UHB E c3 (inconsistent with ARPES) µ! Mott E B =0.2eV E F J 3/2 J 1/2 LHB J 1/2 UHB E Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 14 / 27 Sr
Resistivity and magnetism as a function of doping 10 6 250!(2K) /! (300K) 10 5 10 4 10 3 10 2 10 1 200 150 100 50 T N (K) 10 0 0 0.00 0.05 0.10 0.15 0.20 Rh Doping Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 15 / 27 Sr
Band structure along high symmetry directions 0.0 b1 c1 d1 a d X! M!" X E F Sr 2 Ir 0.85 Rh 0.15 O 4 c b Sr 2 IrO 4 E-E F (ev) Sr 2 Ir 0.85 Rh 0.15 O 4 E-E F (ev) -0.4-0.8-1.2 0.0-0.4-0.8-1.2 b2 c2 d2 X!" X! X! " X M X Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 16 / 27 Sr
MDC and ARPES EMIP at zero and finite dopings a " # T = 50K c x=0% x=15% x=0% "# (!, 0) 0.0-0.2 b x=15% 200meV " # "# (!, 0) 400meV E-E F (ev) -0.4-0.6-0.8-1.0 E F 200meV -1.2 " # (!, 0) " # " # (!, 0) " # Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 17 / 27 Sr
Understanding the process of hole doping a 0.30 b Initial 2! SO /3 J=1/2 "µ (ev) 0.20! SO /3 J=3/2 Ir 4+ Rh 4+ 0.10 0.00 0.00 0.05 0.10 Rh Doping 0.15 0.20 Final 2! SO /3! SO /3 J=1/2 J=3/2 Ir 5+ Rh 3+ Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 18 / 27 Sr
Doping and temperature dependence of the gap a Rh = 15%, T = 50K b NFL d Gap Size (mev) 40 30 20 10 " # FS1 "# FS2!1!2 c e Intensity (a.u.) Intensity (a.u.) Rh=15% T N =17K -0.20-0.10 0.00 0.10 E-E F (ev) Rh=4% T N =170K! 2 Ultra UDC! 1-0.20-0.10 0.00 0.10 E-E F (ev) PG LRAFM 0 0.00 0.05 0.10 0.15 Rh Doping Intensity (a.u.) Rh=11% T N =57K FS1 FS2 25K 25K 50K 50K 75K 75K -0.20-0.10 0.00 0.10 E-E F (ev) Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 19 / 27 Sr
Fitting of the EDC curves The energy distribution curves (EDCs) are fitted with following equation BG + A+Bω 1+e (ω+ )/k B T which is a Fermi function with variable edge width k B T and with leading edge midpoint shifted from the chemical potential by the gap value. ω is the energy relative to Fermi energy and BG is the background counts. A and B are the fitting coefficients. Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 20 / 27 Sr
Resistivity as a function of temperature c 0.025 x=11%! a ($ cm) 0.020 0.015 0.010 O0 0 100 200 300 T (K) Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 21 / 27 Sr
Is Iridates or Slater insulator (SI) or Mott insulator (MI)? The SI is a mean field concept that ignores short range AF correlations. At best one considers them as fluctuations of long range AF order. One should expect that gap in SI would go zero as long range AFM order tends to zero (around PT point). As there is no clear change in band structure seen for parent and doped compounds across the onset of long range AFM order. It suggests that the long range magnetic order is not necessary to have a gap in Iridates. Sr 2 IrO 4 is a Mott insulator. Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 22 / 27 Sr
Distortion in crystal structure and schematic of energy bands Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 23 / 27 Sr
/K) ( cm) c ( cm) log ( cm) a ( cm) Temperature dependence of resistivity 0 50 100 150 200 250 300 350 400 10 5 Sr 2 IrO 4-10 3 c 10 1 10-1 1.6 10-1 1.2 10-1 8 10-2 (a) (b) 10-9 = 0 I = 0.05 ma T MI 3.5 10-2 c a T a c a ~ T 6 10-4 4 10-4 2 10-4 2.5 10-2 0 10 0 0 5 10 15 20 T (K) T a 4 10-2 I = 0.05 ma a 0 10 0 0 50 100 150 200 250 300 350 400 T (K) 300 (c) Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory = Features 0Department of the Mott-Metal of Physics Crossover IndianSr Institute in the IrO of Hole Science) August Doped 28, J 2014 = 1/2 Insulator 24 / 27 Sr
Conclusions and future directions A smooth crossover is seen from a MI Sr 2 IrO 4 to a bad metal hole doped Sr 2 IrO 4. Doped Iridates exhibit all exotic features (means Pseudogaps, Fermi arcs and MFL ) that are present in Cuprates, despite the different mechanism that forbids electron double occupancy. Universal features of Mott-metal crossover are not related to preformed electron pairing, quantum criticality or density wave instabilities. The short range Anti-Ferromagnetic correlations are playing indispensable role to govern the exotic properties of Iridates. Sr 2 IrO 4 is a Mott insulator. The short range AFM correlations may be responsible for the Pseudogaps and SM phases in the Cuprates too. Due to large Spin-orbit coupling in Sr 2 IrO 4, it may be an interesting Topological insulator system. Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 25 / 27 Sr
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Thanks for your kind attention Umesh Kumar Yadav (Centre for Condensed Matter Universal Theory Features Department of the Mott-Metal of Physics Crossover Indian Institute in theof Hole Science) August Doped 28, J 2014 = 1/2 Insulator 27 / 27 Sr