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Controlling many-body states by the electric-field effect in a two-dimensional material

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To understand the complex physics of a system with strong electron–electron interactions, the ideal is to control and monitor its properties while tuning an external electric field applied to the system (the electric-field effect). Indeed, complete electric-field control of many-body states in strongly correlated electron systems is fundamental to the next generation of condensed matter research and devices1,2,3. However, the material must be thin enough to avoid shielding of the electric field in the bulk material. Two-dimensional materials do not experience electrical screening, and their charge-carrier density can be controlled by gating. Octahedral titanium diselenide (1T-TiSe2) is a prototypical two-dimensional material that reveals a charge-density wave (CDW) and superconductivity in its phase diagram4, presenting several similarities with other layered systems such as copper oxides5, iron pnictides6, and crystals of rare-earth elements and actinide atoms7. By studying 1T-TiSe2 single crystals with thicknesses of 10 nanometres or less, encapsulated in two-dimensional layers of hexagonal boron nitride, we achieve unprecedented control over the CDW transition temperature (tuned from 170 kelvin to 40 kelvin), and over the superconductivity transition temperature (tuned from a quantum critical point at 0 kelvin up to 3 kelvin). Electrically driving TiSe2 over different ordered electronic phases allows us to study the details of the phase transitions between many-body states. Observations of periodic oscillations of magnetoresistance induced by the Little–Parks effect show that the appearance of superconductivity is directly correlated with the spatial texturing of the amplitude and phase of the superconductivity order parameter, corresponding to a two-dimensional matrix of superconductivity. We infer that this superconductivity matrix is supported by a matrix of incommensurate CDW states embedded in the commensurate CDW states. Our results show that spatially modulated electronic states are fundamental to the appearance of two-dimensional superconductivity.

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Figure 1: Phase diagram of TiSe2 under electron doping.
Figure 2: Characterization of the field effect device and the resistance at different doping levels by gating.
Figure 3: Temperature dependence of the sheet resistance RS close to the K–T transition.
Figure 4: The magnetoresistance for a charge-carrier density of 5.9 × 1014 cm−2 shows periodic oscillation.

Change history

  • 13 January 2016

    Two Extended Data citations in the Methods were corrected.


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We thank L. Q. Chu, T. H. Ren, J. Y. Tan, J. Wu and H. Schmidt for experimental assistance, and S. Natarajan for assistance in preparing the manuscript. A.H.C.N. acknowledges many discussions with A. K. Geim and a private communication with P. Abbamonte. K.P.L. acknowledges a MOE Tier 1 grant, “2-D crystals as a platform for optoelectronics (R-143-000-556-112)”. G.E. acknowledges a National Research Foundation (NRF) Research Fellowship (NRF-NRFF2011-02). B.Ö. acknowledges support by the NRF, Prime Minister’s Office, Singapore, under its Competitive Research Programme (CRP award number NRF-CRP9-2011-3), and the SMF-NUS Research Horizons Award 2009-Phase II. A.H.C.N acknowledges the CRP award, “Novel 2D materials with tailored properties: beyond graphene” (NRF-CRP6-2010-05). All authors acknowledge the NRF, Prime Minister’s Office, Singapore, under its Medium-Sized Centre Programme.

Author information




L.J.L. performed the growth and characterization of the single crystal, L.J.L. and E.C.T.O’F. performed device fabrication and carried out the measurement, L.J.L., E.C.T.O’F., K.P.L., B.Ö. and A.H.C.N. analysed the data and wrote the manuscript. All authors commented on the manuscript.

Corresponding author

Correspondence to A. H. Castro Neto.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Characterization of the high quality of single-crystal TiSe2.

a, X-ray diffraction of both single-crystal and powder TiSe2 sample. The inset shows the as-grown TiSe2 single crystal. b, Raman spectroscopy pattern at both high temperature and low temperature. The two main phonon modes, Eg and A1g, are distinct, whereas only below TCDW are the peaks corresponding to CDW phonon mode detectable. The inset displays the unit cell of the TiSe2 lattice and the main phonon mode vectors.

Extended Data Figure 2 The Hall bar device and its characterization by Hall effect measurement.

a, Optical microscope picture. b, Atomic force microscope picture of the Hall bar device. c, Temperature dependence of the charge-carrier density measured by the Hall effect at different top gate voltages, VTG. Scale bar, 5 μm.

Extended Data Figure 3 Characterization of the K–T transition.

a, The current–voltage power-law fit for n = 5.9 × 1014 cm−2 at different temperatures is consistent with the behaviour of the 2D K–T transition. b, Temperature-dependent magnetoresistance of the superconducting transition at different fixed perpendicular magnetic fields for n = 2.67 × 1014 cm−2. c, The magnetoresistance data in b collapses into two sets of lines by so-called finite size scaling.

Extended Data Figure 4 The R versus T power-law fit indicates the existence of strong quantum fluctuation.

a, Temperature dependence of the sheet resistance for different doping levels. b, The data shown in a is plotted on a log–log scale.

Extended Data Figure 5 The magnetoresistance oscillation for charge-carrier densities of 1.3 × 1014 and 2.7 × 1014 cm−2.

a, c, Perpendicular magnetic-field-dependent magnetoresistance measured at different temperatures. b, d, Plots of dRS/dB against B and T for n =1.3 × 1014 cm−2 and n = 2.7 × 1014 cm−2, respectively.

Extended Data Figure 6 The conductance measured for a charge-carrier density of 2.1 × 1014 cm−2.

a, Magnetic field dependence at 0.1 K. b, Temperature dependence at zero magnetic field. a.u., arbitrary units.

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Li, L., O’Farrell, E., Loh, K. et al. Controlling many-body states by the electric-field effect in a two-dimensional material. Nature 529, 185–189 (2016).

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