Evolution of electronic states in n-type copper oxide superconductor via electric double layer gating

The occurrence of electrons and holes in n-type copper oxides has been achieved by chemical doping, pressure, and/or deoxygenation. However, the observed electronic properties are blurred by the concomitant effects such as change of lattice structure, disorder, etc. Here, we report on successful tuning the electronic band structure of n-type Pr2−xCexCuO4 (x = 0.15) ultrathin films, via the electric double layer transistor technique. Abnormal transport properties, such as multiple sign reversals of Hall resistivity in normal and mixed states, have been revealed within an electrostatic field in range of −2 V to + 2 V, as well as varying the temperature and magnetic field. In the mixed state, the intrinsic anomalous Hall conductivity invokes the contribution of both electron and hole-bands as well as the energy dependent density of states near the Fermi level. The two-band model can also describe the normal state transport properties well, whereas the carrier concentrations of electrons and holes are always enhanced or depressed simultaneously in electric fields. This is in contrast to the scenario of Fermi surface reconstruction by antiferromagnetism, where an anti-correlation is commonly expected.


Supplementary
The data in the table are from the fits using two-band model.

Supplementary Note 1| Measurements
For the EDLT measurements, a four point probe Hall bar geometry (see Fig. 1a in the main text) was patterned by placing pre-patterned PDMS on the surface of PCCO thin film and performing dry etching with Ar plasma. The ohmic contact was formed by wire bonding Au wire with ductile Indium pallet. After mounting the sample on a cryostat PCB board, the samples were covered with the ionic liquid N, N-diethyl-N-methyl-N-(2-methoxyethyl) ammonium bis (triuoromethylsulphonyl) imide (DEME-TFSI, Kanto Corporation) and an adjacent Pt wire was used as a gate electrode. Ionic liquid application was performed inside a N2 filled glove box and transferred to the measurement cryostat within 5 minutes to minimize electrochemical reaction of DEME-TFSI with molecules in the ambient atmosphere. Gate voltage was applied in situ at the temperature about 230 K inside the cryostat. Below 170 K the DEME-TFSI freezes and the longitudinal and transverse four probe resistance was measured as a function of temperature and perpendicular magnetic field. After each temperature sweep, gate voltage modulation was done by warming the sample up to 230 K and changing gate voltage.

Supplementary Note 2| Calculated quantities
The Fermi surfaces (FS) of both electrons and holes of PCCO thin film are cylindrical. The radius and the height of the FS are kF and 2π/d respectively, where kF is the Fermi wave length and d is the distance between two copper dioxide planes. Since the charge carriers are those particles enclosed by the FS, we can calculate kF by the equation: = (2 ) 1/2 (S1) where n is the charge carrier density obtained in our fitting and the value of d has been given in supplementary ref. 1. Then, using the equations: = ℎ 2 (S2) . 2), we subsequently deduce the ratios of mean free paths le/lh and effective masses ℎ * / * as shown in the main text. Here, σ is the conductivity of each band obtained from the two-band fitting.

Supplementary Note 3| Effective thickness
In general, we calculate the resistivity by taking into account the total thickness of the sample, i.e, t ~ 10 nm (7 unit cells). In our work, there is only one superconducting transition temperature. Meanwhile, the positive and negative electric fields result in remarkable differences in the transport. Therefore, it is unlikely that there are multiple channels contributing to the electric transport, i.e, several unit cells at the top are tuned by the electric field but the other unit cells at the bottom still hold the Tc. It is naturally expected that the bottom several unit cells are insulating (namely, dead layer), whereas the top several unit cells can be tuned and contribute to electric transport. Thus, the effective thickness (teff) may be smaller than t when calculating the quantities of the electric transport. For instance, if = ,, then one can get = , = , = × , = × , = × 1 2 , * = * × . Since the teff cannot be precisely estimated in this system, we still use t for all the calculations, which may cause an underestimation of the carrier concentrations, but not change the ratio of quantities of hole-band to electron-band (Fig. 4a, b, c). Our analyses and conclusions do not stand on the effective thickness.

Supplementary Note 4| Electrochemical reaction vs. electrostatic doping
We have shown in the main text that Tc is almost unaffected by the electrostatic voltage less than 2.5 V. Actually, we do observe a change of Tc if Vg > 2.5 V (see Fig. S1), where the change is caused by electrochemical reaction, rather than electrostatic tuning. We are interested in the intrinsic behavior of electronic states in electric fields, therefore, to avoid the influence from electrochemical reaction we only focus on the regime of lower gating voltage. Figure S1 Temperature dependent resistance of sample 2 in electric fields of 0, 1.5 and 2.5 V. Both Tc onset and Tc zero are obviously tuned in 3.5 V, but the R-T curve exhibits two superconducting transitions which indicates an electrochemical reaction rather than electrostatic tuning.
Carton S1 Band structure evolution with chemical doping and electrostatic doping. The effective change transfer gap drops with chemical doping or electrostatic doping due to the Cu-O Coulomb repulsion and weakening on-site Coulomb interaction, which is in accordance with the two-band fitting results, where the carrier concentrations of electrons and holes are always enhanced (depressed) simultaneously in +2 V (-2 V).