Galvanomagnetic effects in electron- doped superconducting compounds D. S. Petukhov 1, T. B. Charikova 1, G. I. Harus 1, N. G. Shelushinina 1, V. N. Neverov 1, O. E. Petukhova 1, A. A. Ivanov 2 1 Institute of Metal Physics UB RAS, Ekaterinburg 2 Moscow Engineering Physics Institute, Moscow

Topics  Introduction  The aim of the work  Experiment: samples, experimental equipment  Results  Conclusion 2

Introduction There is no universally accepted mechanism of the superconducting state formation in HTSC Studies of galvanomagnetic phenomena provide important information about the behavior of carriers in the normal state of HTSC Properties of the superconductor in the normal state determine its properties in the superconducting state There are questions concerning the physical picture of normal and mixed state of HTSC Clarify the features of the superconducting state in HTSC 3

Introduction Various researchers have found features of the behavior Hall resistivity dependencies on the temperature and magnetic field. YBa 2 Cu 3 O 7 Nd 1.85 Ce 0.15 CuO 4+δ Hagen S. J. PRB V.47 P.1064 (1993) 4

Introduction K. Jin PRB V.78 P (2008) Pr 2-x Ce x CuO 4 La 2-x Ce x CuO 4 Y. Dagan PRB V.76 P (2007) 5

Introduction A. Casaca PRB V.59 P (1999) YBa 2 Cu 3 O 7  There is a sign change in the mixed state.  A similar anomaly is observed in many materials.  Trend dependence of the Hall resistance does not depend on the sign of the majority charge carriers.  The presence or absence of anomaly depends on the purity of the sample. 6

Introduction The sign change of the Hall coefficient in the mixed state can be explained: Thermoelectric models Models of Nozieres-Vinen and Bardeen-Stephen Pinning models Two-band/two-gap models 7

Hall coefficient in the normal state Nie Luo arXiv:cond-mat/ v2, P. 1 (2000) 8

Shubnikov de Haas oscillations M.V. Kartsovnik New Journal of Physics V13, P (2011) 9 Nd 2-x Ce x CuO 4+δ

ARPES data Armitage N.P. Rev. Mod. Phys. V82, P (2010) Armitage N.P. PRL V88, P (2002) Matsui H. PRL V94, P (2005) Matsui H. PRL V75, P (2007) 10 Nd 2-x Ce x CuO 4+δ

The aim of the work The aim of the work was to investigate magnetic field dependence of the resistivity and Hall effect of electron-doped superconductor in the normal and mixed state, in order to study the dynamics of Abrikosov vortices in the resistive state in the electron-doped cuprate superconductor. 11

Experiment: the samples Ivanov A.A., Galkin S.G., Kuznetsov A.V. et al., Physica C, V. 180,P. 69 (1991) 12 In the experiments, we used single-crystal films Nd 2-x Ce x CuO 4+δ /SrTiO 3 (x = 0.15; 0.17; 0.18) with orientation (001). The thicknesses of the films were Å (x = 0.15), 1000 Å (x = 0.17) and 3100 Å (x = 0.18). The films were subjected to heat treatment (annealing) under various conditions. Optimal doped region ( х= 0.15): □the optimally annealing in the vacuum(60 min, Т = 780°С, р = mmHg); □the non-optimally annealing in the vacuum(40 min, Т = 780°С, р = mmHg); □As grown (without annealing); Overdoped region ( х= 0.17): □ the optimally annealing in a vacuum ( Т = 780°С, р = mmHg); Overdoped region ( х= 0.18): □ the optimally annealing in a vacuum (35 min, Т = 600°С, р = mmHg).

The measurement equipment Hall effect measurements were carried out with 4-contact method in the solenoid, "Oxford Instruments" (IMP UD RAS) and SQUID- magnetometer MPMS XL firm Quantum Design (IMP UD RAS) in magnetic fields up to 90 kOe at the temperature of Т = (1.7 – 4.2) К. 13

Results: Hall coefficient in the normal state (T=4.2K B=9T) 14 Charikova T. B., Physica C, V. 483,P. 113 (2012)

Dependences of the Hall coefficient on the magnetic field for optimally annealing Nd 2-x Ce x CuO 4+δ x=0.15, 0.17,

The theoretical model We used the Bardeen-Stephen model, which has been adapted to respond to two types of carriers (electrons and holes). Each of the carriers gives a contribution to the conductivity and Hall coefficient: where R e, σ e - is the contribution of electrons, and R h, σ h - the contribution of the holes. Bardeen-Stephen model gives an expression for the resistivity and Hall coefficient for one type of carrier in the form: i=e, h. where ρ ni = 1/en i μ i are resistivities in the normal state, R ni = ± 1/en i are Hall coefficients in the normal state, H c2 i are upper magnetic fields, H p is depinning field, n i, μ i are carrier concentrations and mobilities, respectively (for electrons i=e and for holes i=h). Thus, if H H c2 i, then the samples are in the normal state and R i =R ni, ρ xxi =ρ ni. 16 In the calculations, the fields H c2 e, H c2 h, H p are found graphically from the dependence of R(H) and ρ xx (H), the mobilities are close in magnitude: μ h /μ e ~1. As a result of the calculations parameters n e, n h, μ e, μ h were obtained.

Dependences of R H (H) and ρ xx (H) for optimally annealing Nd 1.85 Ce 0.15 CuO 4+δ T=4.2К 17

Dependences of R H (H) and ρ xx (H) for optimally annealing Nd 1.83 Ce 0.17 CuO 4+δ T=4.2К 18

Dependences of R H (H) and ρ xx (H) for optimally annealing Nd 1.82 Ce 0.18 CuO 4+δ T=4.2К 19

The main parameters of the samples Nd 2-x Ce x CuO 4+δ (optimally annealing) xn e,cm -3 n h,cm -3 b=μ h /μ e ∙ ∙ ∙ ∙ ∙ ∙

Dependences of R H (H) and ρ xx (H) for optimally annealing Nd 1.85 Ce 0.15 CuO 4+δ T=4.2К 21

Dependences of R H (H) and ρ xx (H) for non- optimally annealing Nd 1.85 Ce 0.15 CuO 4+δ T=4.2К 22

Dependences of R H (H) and ρ xx (H) for as grown Nd 1.85 Ce 0.15 CuO 4+δ T=4.2К 23

The main parameters of the samples Nd 1.85 Ce 0.15 CuO 4+δ Sample n e,cm -3 n h,cm -3 b=μ h /μ e Optimally annealing 6.3∙ ∙ Non-optimally annealing 1.1∙ ∙ As grown1.6∙ ∙

Conclusion  The model is based on a simple Drude model for the normal state and semi-phenomenological model for the Bardeen-Stephen mixed state (modified considering the coexistence of electrons and holes) can to qualitatively describe the behavior of the Hall coefficient.  The possibility of such descriptions allows us to consider the relationship of the hole and electron subsystems as one of the important properties inherent in cuprate HTSC. 25