Introduction

The first n-type (electron-doped) copper oxide superconductor, Nd2−xCexCuO4 (NCCO), was discovered in 19891,2. Soon after, comparisons between electric and thermoelectric transport measurements revealed that the optimally doped NCCO (x = 0.15) actually contained both electron and hole charge carriers3, later confirmed by the angular-dependent photoemission spectroscopy (ARPES)4,5 and the magnetoresistance quantum oscillation experiments6,7. The coexistence of electron and hole charge carriers has been observed in other n-type copper oxide superconductors as well, such as the optimally doped La2−xCexCuO48,9 and Pr2−xCexCuO410,11. Therefore, the competition between electron- and hole-bands becomes a common feature in n-type copper oxide superconductors12.

A typical picture for this coexistence of electron- and hole-bands comes from a Fermi surface reconstruction. Here, a commensurate (π,π) spin-density-wave (SDW) or antiferromagnetism (AFM) order results in band folding of a large full hole Fermi surface, leading to a new Fermi surface with both electron- and hole-pockets at (π,0) and (π/2,π/2), respectively13,14. This picture can be used to explain some intriguing properties, e.g. the kink in Hall coefficient10, the strange metal behavior15, the anomalous temperature dependent superfluid density16, and the in-plane anisotropic magnetoresistance17,18, as a function of Ce doping. Meanwhile, AFM order and spin fluctuations have indeed been observed by neutron scattering, spanning over the underdoped regime19 and extending to the overdoped side20 in the (T, x) phase diagram. Thus, the evolution of electronic states by Ce dopants (x) is naturally associated with the Fermi surface reconstruction induced by AFM, invoking the relation between AFM and superconductivity21. Besides Ce substitution, other methods such as deoxygenation22, irradiation23, and pressure24 have also been used to explore the two-band feature. However, in these cases the intrinsic electronic properties are always obscured by the concomitant lattice change and disorder.

Recently, the electric double-layer transistor (EDLT), technique has been developed to generate very large electric field and accumulating high-density charge carriers to 1014 ~ 1015 cm−2 at the interface between a sample and an ionic liquid25. The EDLTs can tune electronic band structures of various materials. Namely, a gate voltage of several volts can realize the same effect as application of hundreds of volts in traditional solid gated MOSFETs, which is prohibitive in reality due to the gate leakage current in solid-state dielectrics. A series of remarkable experiments have been carried out on materials such as La2−xSrxCuO426, YBa2Cu3O7−δ27,28, ZrNCl29, SrTiO330, and KTaO331, where electrostatic modulation of carriers was used to demonstrate turning superconductivity on/off. Moreover, electrostatic gating using EDLT has been effective in probing emergent electronic phases and mapping comprehensive electronic phase diagrams26,27.

In this paper, we exploit EDLT to uncover the interrelationship between electron- and hole-bands in an n-type copper oxide superconductor. We study Pr2−xCexCuO4 (x = 0.15) ultrathin films under electrostatically doping via ionic liquid. In the mixed state, an abnormal temperature- and field-dependent Hall resistivity is observed, which is remarkably suppressed in a positive electrostatic field. Meanwhile, the pristine positive Hall signal is reversed in the normal state. The rich Hall information in the mixed state invokes a consideration of energy dispersion near the Fermi surface, as well as the two-band feature. However, in the normal state, though the two-band model can account for both longitudinal resistivity (ρxx) and Hall resistivity (ρxy), the charge carrier concentrations of electrons and holes are always simultaneously increased/decreased in positive/negative electrostatic field, in contrast to the commonly expected anti-correlation between them, where the Fermi surface reconstruction results in reduced holes but enhanced electrons. Our results suggest that a dramatic change of electronic states arises within the regime of AFM or SDW. We therefore propose that effective Coulomb repulsion must play an important role in the evolution of electronic states in this system.

The Pr2−xCexCuO4 (PCCO, x = 0.15) ultrathin films were fabricated on (00l)-oriented SrTiO3 (STO) substrates by a pulsed laser deposition technique10. The optimized PCCO sample (~7 unit cells, see Supplementary Note for discussion on effective thickness) starts to show superconductivity at 20 K, comparable to the bulk Tc. The transition width is broader than thicker films as is usually the case26,27. After patterning into a standard Hall bar for ρxx and ρxy measurements as illustrated in Fig. 1a, we chose DEME-TFSI as the ionic-liquid dielectric (IL) to guarantee the best tunability. The gate voltage Vg is applied above the melting point of the IL (180 K for DEME-TFSI). The threshold voltage for electrochemical reaction (beyond which the resistance changed irreversibly) was found to be ~2.5 V for PCCO/DEME-TFSI; for the data reported below |Vg| ≤ 2 V and the resistivity was reproducible on cooling and re-warming to >180 K. The electric transport data were then taken by sweeping the magnetic field at a fixed temperature T, so that the Hall signal could be precisely determined32. The measurements of ρxx and ρxy were carried out at designated temperatures, 20, 15, and 10 K, corresponding to onset, zero resistance, and below Tc, respectively. We claim that all the experimental results can be repeated.

Figure 1: Electric double-layer transistor (EDLT) and resistivity.
figure 1

(a) Schematic of gate configuration for charge transfer doping with DEME-TFSI ionic liquid electrolyte. Pt wire is used as gate electrode. (b) Temperature dependent resistivity of optimal doping Pr2−xCexCuO4 (x = 0.15) ultrathin film. The resistivity of the normal state is enhanced in −2 V and reduced in +2 V. The ρ-T curves are enlarged near the transition temperature Tc in the lower inset. Tc is almost unaffected by electrostatic field, and the onset Tc = 20 K, which is comparable to the value of bulk. The transition width is broader than thicker film as usual in ultrathin film. At 210 K, the ionic liquid used is in liquid state and the gate voltage applied can be continuously changed. The upper inset shows the gate voltage dependent resistivity before (blue) and after (pink) the gating experiment. Both curves are reversible and overlap with each other, which excludes an electrochemical reaction as the source of the change of electronic states in this work.

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Figure 1b shows temperature dependent resistivity ρxx (T) at zero magnetic field with Vg equal to −2, 0, +2 V. The resistivity is apparently tuned with the Tc almost unaffected as shown in the lower inset. Compared to the value at 0 V, the resistivity is enhanced for Vg = −2 V and reduced for Vg = + 2 V. Once the measurement in electrostatic fields was done, the resistivity was rechecked by sweeping the electric field above the melting point of DEME-TFSI. As demonstrated in the upper inset of Fig. 1b, the ρxx curve at 210 K after the gating experiments is reversible against the applied bias voltage, and overlap with the pristine data, which excludes an electrochemical reaction as the source of the change of electronic states in the present work.

Although the Tc remains the same, there is a dramatic change in ρxy at low temperatures, as tuned by the electrostatic field. In Fig. 2, ρxx and ρxy are displayed as T (10, 15, and 20 K), B (−9 to 9 T), and Vg (−2, 0, +2 V). For clarity, we summarize the distinct feature of ρxx and ρxy as follows: i) after the superconductivity is suppressed by the magnetic fields of 3, 1.5 and 0.5 T for 10, 15, 20 K, respectively. ρxx(B) is reduced from −2 to +2 V, not surprising as extrapolated from the high temperature resistivity; ii) above the upper critical field (Bc2), the normal state ρxy is positive without gating, which is slightly enhanced in −2 V. It is tuned to negative in +2 V at 10 K and 15 K; iii) below Bc2, a huge peak in ρxy is observed at 0 V once the sample enters into the mixed state. Moreover, the sign of the peak is reversed, i.e. positive at 15 K but negative at 10 K; iv) remarkably, the peak is retained in −2 V, but smeared out in +2 V.

Figure 2: Temperature, magnetic field, and electrostatic field dependent ρxx and ρxy with B⊥ab-plane.
figure 2

(a,c,e) Magnetic field dependent resistivity in −2, 0, +2 V and at 10, 15, 20 K, respectively. The resistivity of the normal state is reduced from −2 to +2 V. (b,d,f) Magnetic field dependent Hall resistivity in −2, 0, +2 V and at 10, 15, 20 K, respectively. In the normal state, ρxy is positive without gating, slightly enhanced in −2 V but tuned to negative in +2 V at 10 K and 15 K. Once in the mixed state, a huge peak in ρxy emerges at 0 V and the sign of the peak is reversed, i.e. positive at 15 K but negative at 10 K. Moreover, the peak is retained in −2 V, but smeared out in +2 V. The red dashed lines represent fittings to ρxx and ρxy simultaneously using the two-band model.(see text).

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The Hall resistivity manifests its complexity as 1) in the normal state, the sign reversal with decreasing temperature and in positive electric field, and 2) in the mixed state, the appearance of a huge peak and its sign reversal versus temperature in zero and negative electric fields, but suppressing in positive electric field. Since it has been argued that Hall conductivity is a better quantity to exhibit vortex dynamics in the mixed state33, we also plot the corresponding Hall conductivity as seen in Fig. 3a–c. Consequently, some subtle features becomes more discernible. For instance, the tiny peak at ~0.06 T in 0, −2V (Fig. 2f) becomes prominent in the σxy(B) plot (Fig. 3c), where the σxy drops quickly and changes sign as the mixed state is entered.

Figure 3: Temperature, magnetic field, and electrostatic field dependent Hall conductivity.
figure 3

(a–c) Magnetic field dependent Hall conductivity in −2, 0, +2 V and at 10, 15, 20 K, respectively. The Hall conductivity can be fit by (blue dashed lines), and C1 is proportional to . Red dashed lines are the fittings to the normal states. In order to zoom in the feature at low magnetic field, the x axis in (a,b) is plotted in logarithmic scale. (d) Temperature and electrostatic field dependent C1. Dashed lines are drawn to guide the eye. The abrupt change in both amplitude and sign in such a narrow temperature range indicates a dramatic change of electronic states.

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In the mixed state, the Hall conductivity consists of two parts, from the vortex motion and from the quasiparticles inside the core of the vortices. According to the time-dependent Ginzburg-Landau (TDGL) equation derived from the BCS theory, there is a simple expression for near Bc2 (ref. 34):

Here, , with N(μ) the chemical potential dependent density of states and EF the Fermi energy35. Without loss of generality, the Hall conductivity can thus be written as:

This expression does work for our experimental σxy(B) as demonstrated in Fig. 3a–c, where the blue dashed lines are the fits (see Supplementary Information). The temperature dependent C1 is plotted in Fig. 3d, which has opposite sign at 10 K and 15 K in all electrostatic fields. And, the amplitude is notably suppressed at +2 V. Since the C1 is associated with the energy derivative of the density states at the Fermi level, the abrupt change in both amplitude and sign in such a narrow temperature range implies a novel electronic state. As found by Sr dopants in hole-doped La2−xSrxCuO4, the sign reversal of C1 is ascribed to experiencing a van Hove singularity with increasing Sr doping, resulting in a remarkable change in the density of states and affecting Tc prominently36. In our case, such a dramatic change of C1(T) more likely originates from the competition between two bands since the Tc of the electrostatic doped PCCO remains the same as discussed below.

A two-band model is thereby expected to capture the main characteristics of the normal-state ρxx and ρxy. For a simple two-carrier Drude model, the ρxx and ρxy are expressed as:

where and . The n, τ, and m* represent charge carrier concentration, relaxation time, and effective mass, respectively. The subscript i = h or e correspond to the hole or electron band. Using Eqs (3 and 4), the experimental data of ρxx and ρxy were fitted at the same time (red dashed lines in Fig. 2) to arrive at the best self-consistent fitting parameters. As fitted by the two-band model, the carrier concentration falls in the range of 1019 ~ 1020 cm−3, in agreement with the values estimated from the ARPES data11. Note that using a single band model to fit the data would give an unreasonable charge carrier concentration of (~1023 cm−3).

We find that, ne and nh at fixed temperatures are always simultaneously enhanced in the positive electric field and reduced in the negative electric field, which is unusual in that typically an anti-correlation between ne and nh is expected from any aspect of electrostatic doping or the reconstruction of Fermi surface. Intuitively, the electric field will attract one type of charge carriers but repel the other. The evolution of a large hole Fermi surface into small hole and electron pockets, caused by the reconstruction, will lead to a competition between ne and nh as well. Thus, the simultaneous enhancement or reduction of ne and nh is unexpected. Another puzzling observation is that the electrostatic doping results in a dramatic change in Hall signal whereas the Tc remains the same.

Xiang et al.37 have proposed that Fermi surface reconstruction by AFM or SDW is not the sole picture to account for the coexistence of electron and hole bands. In their picture, electrons and holes come from the upper Hubbard band and the Zhang-Rice singlet band (via hybridization among Cu 3d and O 2p orbits), respectively. In this picture, the effective Coulomb repulsion U, from either the on-site Coulomb repulsion or between Cu 3d and O 2p bands can drop with chemical doping or electrostatic doping due to the Cu-O Coulomb repulsion and weakening on-site Coulomb interaction. For the parent compound (x = 0) the effective U separates the electron and hole bands. U decreases with increasing doping, so the first appearance of the electron band (i.e., crossing the Fermi surface) will gradually pull up the hole band, resulting in the coexistence of electron and hole pockets on the Fermi surface. In this case, the tuning of U by electrostatic doping accounts for the unexpected correlation between ne and nh (see the illustration of band evolution in Fig. 4d). In n-type cuprates, it is known that Tc is not solely determined by carrier concentration of either electron- or hole-band, but more sensitive to the balance between these two bands. For instance, the system goes to over-doped regime if nh ≫ ne, or to under-doped regime if nh ≪ ne. The optimally doped samples have been confirmed to be a compensated metal. In this work, the calculated conductivities, mean free paths, and effective masses of electrons and holes are almost equal in values as seen in Fig. 4a–c, a small tuning tips the balance between the electron and hole bands and results in the sign reversal. However, the absolute values of the quantities for each band are not apparently changed. Since the balance between electron and hole pockets is the key factor to achieve the extremely large magnetoresistance observed in potential type II Weyl semimetal WTe238,39, we can attribute the electrostatic field independent Tc to the nearly unchanged balance between electron and hole pockets.

Figure 4: Fitting quantities and schematic diagram.
figure 4

(a–c) Relative conductivities, mean free paths, and effective masses of holes to electrons, respectively. The values of these quantities only slightly deviate from unity with varying temperature and electrostatic field. (d) SDW boundary (dashed line) is taken from ref. 17, where the Fermi surface reconstruction happens at xFS ~ 0.16. The inset shows the temperature and electrostatic dependent carrier concentrations. The carrier concentrations of electrons and holes are always enhanced or depressed simultaneously in +2 V, or −2 V respectively. The tuning of electronic state stays within the range of the AFM or SDW phase, so here we put the inset inside the SDW phase.

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We now turn to the origin of the huge peak in ρxy(B), at Vg = −2 V and 0 V and T = 10 K and 15 K. Our reversible electrostatic tuning is not expected to introduce considerable additional pinning centers, thus, we rule out a pinning change as the primary cause40. The cutoff of the mean free path (l) by the vortex core can also possibly induce an abrupt change in ρxy, whereas this requires a clear difference between le and lh, which is also not the case (see Fig. 4a). Considering the vortex motion analog to that in superfluid 4He, Hagen et al.41 have obtained:

where vp is the flux-line velocity parallel to the applied transport current, ρs is the superfluid density, and η′ is the viscosity factor of flux line in the normal direction. The vp can generate a transverse electric field given by Faraday’s law:

In this framework, the appearance of the huge peak in −2 V, 0 V could be linked to the sudden increase of the superfluid density upon entering into the mixed state, but the suppression of the peak in +2 V remains a mystery, subject to further research.

In conclusion, we have succeeded in tuning optimally doped PCCO (x = 0.15) ultrathin films via EDLT and observed a complex Hall signal as a function temperature, magnetic field, as well as electric field. In the mixed state, the dramatic change of Hall conductivity invokes the presence of two-type carriers. In the normal state, although the two-band model can fit the resistivity and the Hall resistivity well at the same time, the simultaneous enhancement or reduction of electrons and holes indicates the tuning of electronic state stays within the range of the AFM or SDW phase. The Tc remains constant with electrostatic doping yet a dramatic change in electronic state has been observed. To reconcile these observations, we therefore suggest that the Coulomb repulsion, tunable in the electrostatic field, is playing an important role.

Additional Information

How to cite this article: Jin, K. et al. Evolution of electronic states in n-type copper oxide superconductor via electric double layer gating. Sci. Rep. 6, 26642; doi: 10.1038/srep26642 (2016).