Uniaxial pressure can dramatically change the properties of low-dimensional systems and induce electronic phase transitions. The first-discovered molecular massless Dirac electron system α-(BEDT-TTF)2I3 has intensively been studied because of its unique features, such as the Fermi energy being very close to the Dirac point, strong electron correlation, and the quantum phase transition from the charge-ordered insulating state. However, the Dirac state is realized only under high pressure of 15 kbar, which limits the measurement of physical properties (e.g., experimental determination of band dispersion and density of states). Here, we demonstrate that the Dirac state of α-(BEDT-TTF)2I3 can be realized by applying uniaxial bending strain without confining it in a pressure cell. Uniaxial strain below 1% completely suppresses the metal–insulator transition observed at ambient pressure. Under strain, a characteristic temperature dependence of magnetoresistance associated with the formation of the n = 0 Landau level is observed, indicating the realization of the massless Dirac state.

Dirac electrons in solids have been one of the central issues in condensed matter physics. The quasi-two-dimensional molecular conductor α-(BEDT-TTF)2I3 [BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene], consisting of alternating BEDT-TTF (conducting) and I3− (insulating) layers, is the first discovered molecular Dirac fermion system.11. K. Kajita, Y. Nishio, N. Tajima, Y. Suzumura, and A. Kobayashi, J. Phys. Soc. Jpn. 83, 072002 (2014). https://doi.org/10.7566/JPSJ.83.072002 At ambient pressure, this compound exhibits a metal–insulator transition to the charge-ordered state at 135 K.22. K. Bender, I. Hennig, D. Schweitzer, K. Dietz, H. Endres, and H. J. Keller, Mol. Cryst. Liq. Cryst. 108, 359 (1984). https://doi.org/10.1080/00268948408078687 Hydrostatic pressure lowers the transition temperature and suppresses above 15 kbar.33. N. Tajima, S. Sugawara, M. Tamura, Y. Nishio, and K. Kajita, J. Phys. Soc. Jpn. 75, 051010 (2006). https://doi.org/10.1143/JPSJ.75.051010 The band calculation indicated that the material is a massless Dirac electron system under high pressure.44. S. Katayama, A. Kobayashi, and Y. Suzumura, J. Phys. Soc. Jpn. 75, 054705 (2006). https://doi.org/10.1143/JPSJ.75.054705 Indeed, the interlayer negative magnetoresistance and the quantum oscillations under hole doping indicated the presence of the Dirac electrons (Fig. 1).5,65. N. Tajima, S. Sugawara, R. Kato, Y. Nishio, and K. Kajita, Phys. Rev. Lett. 102, 176403 (2009). https://doi.org/10.1103/PhysRevLett.102.1764036. N. Tajima, T. Yamauchi, T. Yamaguchi, M. Suda, Y. Kawasugi, H. M. Yamamoto, R. Kato, Y. Nishio, and K. Kajita, Phys. Rev. B 88, 075315 (2013). https://doi.org/10.1103/PhysRevB.88.075315Unlike graphene, α-(BEDT-TTF)2I3 is a bulk material in which the Fermi level is pinned very close to the Dirac point (the doping concentration due to the defect of I3− is the order of ppm), being a platform to investigate the physics of the Dirac point. Also, the Dirac fermion phase is adjacent to the charge-ordered insulating state.7,87. M. Hirata, K. Ishikawa, K. Miyagawa, M. Tamura, C. Berthier, D. Basko, A. Kobayashi, G. Matsuno, and K. Kanoda, Nat. Commun. 7, 12666 (2016). https://doi.org/10.1038/ncomms126668. M. Hirata, K. Ishikawa, G. Matsuno, A. Kobayashi, K. Miyagawa, M. Tamura, C. Berthier, and K. Kanoda, Science 358, 1403 (2017). https://doi.org/10.1126/science.aan5351 The effect of electron correlations in the Dirac state and the quantum phase transition between these phases are of great interest.99. Y. Unozawa, Y. Kawasugi, M. Suda, H. M. Yamamoto, R. Kato, Y. Nishio, K. Kajita, T. Morinari, and N. Tajima, J. Phys. Soc. Jpn. 89, 123702 (2020). https://doi.org/10.7566/JPSJ.89.123702 However, since the Dirac fermion phase is realized only in a pressure cell, essential experiments, such as the direct observation of the band dispersion and density of states, are limited. In this paper, we attempt to realize the Dirac state of α-(BEDT-TTF)2I3 without a pressure cell by applying uniaxial strain via a bending substrate.In recent years, the uniaxial strain has rapidly gained attention as a method for controlling electronic properties.10,1110. C. W. Hicks, M. E. Barber, S. D. Edkins, D. O. Brodsky, and A. P. Mackenzie, Rev. Sci. Instrum. 85, 065003 (2014). https://doi.org/10.1063/1.488161111. C. W. Hicks, D. O. Brodsky, E. A. Yelland, A. S. Gibbs, J. A. N. Bruin, M. E. Barber, S. D. Edkins, K. Nishimura, S. Yonezawa, Y. Maeno, and A. P. Mackenzie, Science 344, 283 (2014). https://doi.org/10.1126/science.1248292 It has conventionally been applied to molecular conductors because the technique is particularly suitable due to its soft lattice and anisotropic electronic properties.12–1512. M. Maesato, Y. Kaga, R. Kondo, and S. Kagoshima, Rev. Sci. Instrum. 71, 176 (2000). https://doi.org/10.1063/1.115018013. N. Tajima, A. Tajima, M. Tamura, Y. Nishio, and K. Kajita, J. Phys. Soc. Jpn. 71, 1832 (2002). https://doi.org/10.1143/JPSJ.71.183214. S. Kagoshima and R. Kondo, Chem. Rev. 104, 5593 (2004). https://doi.org/10.1021/cr030653915. T. Yamamoto, R. Kato, H. M. Yamamoto, A. Fukaya, K. Yamasawa, and I. Takahashi, Rev. Sci. Instrum. 78, 083906 (2007). https://doi.org/10.1063/1.2777191 Indeed, α-(BEDT-TTF)2I3 can be the narrow-gap semiconducting state (possibly the Dirac state by analogy from later hydrostatic pressure measurements) by uniaxial pressures of approximately 5 kbar, one-third of the hydrostatic pressure case. In the conventional method, the sample is encapsulated in an epoxy resin and pressurized in a pressure cell. Here, we report the effect of uniaxial strains produced by bending the substrate16,1716. M. Suda, Y. Kawasugi, T. Minari, K. Tsukagoshi, R. Kato, and H. M. Yamamoto, Adv. Mater. 26, 3490 (2014). https://doi.org/10.1002/adma.20130579717. Y. Kawasugi and H. M. Yamamoto, Crystals 12, 42 (2022). https://doi.org/10.3390/cryst12010042 on a thin single crystal laminated on a flexible substrate, which leads to the Dirac state of the crystal. Because this method requires no pressure medium covering the sample surface, it will be useful in measurements with surfaces exposed to the air or the vacuum, such as photoelectron and tunneling spectroscopy measurements.The 15-nm-thick Au electrodes were patterned on a polyethylene terephthalate substrate (Teflex FT7, Teijin DuPont Films Japan Limited) using photolithography. Thin single crystals of α-(BEDT-TTF)2I3, with thicknesses of several hundred nanometers, were electrochemically synthesized from a chlorobenzene solution of BEDT-TTF and tetrabutylammonium triiodide by applying 5 μA for approximately 20 h. A thin crystal was transferred into 2-propanol with a pipette and laminated onto the substrate.1717. Y. Kawasugi and H. M. Yamamoto, Crystals 12, 42 (2022). https://doi.org/10.3390/cryst12010042 When lamination, we manually aligned the crystallographic axes (a or b) parallel to the direction of uniaxial strain (along the long side of the rectangle substrate) and confirmed with optical images through a polarizer. The sample-laminated substrate was fixed on the measurement probe with a piezo nanopositioner so that we could bend the substrate in the cryostat. Assuming that the bent substrate is an arc of a circle, the strain S is estimated as S=4tx/(l2+4x2), where t (= 177 μm) and l (= 12 mm) are the thickness and the length of the substrate, and x is the displacement of the piezo nanopositioner.1717. Y. Kawasugi and H. M. Yamamoto, Crystals 12, 42 (2022). https://doi.org/10.3390/cryst12010042 The maximum compressive strain is approximately 1% with our measurement setup. This method is considered to cause more inhomogeneous strain compared to conventional hydrostatic and uniaxial pressure measurements because of the inhomogeneous mounting condition or shape of the sample crystal, as shown later. However, the strain effect is not only a surface effect. The strain difference between the top and bottom should be much less than the applied strain because the α-(BEDT-TTF)2I3 crystal is more than two orders of magnitude thinner than the substrate. Although the correspondence between the bending strain and hydrostatic pressure should depend on the material, about 0.8% corresponded to 1 kbar in the case of κ-(BEDT-TTF)2Cu2(CN)3.Figure 2 shows the temperature (T) dependence of the resistivity (ρ) under compressive strains along the crystallographic a-axis. The metal–insulator transition temperature TC monotonically decreases with applying uniaxial strains, and the transition is suppressed at 0.81%. By determining TC from the peak of d(ln ρ)/d(1/T), we can describe the strain-temperature phase diagram [Fig. 2(b)], which is reminiscent of that of hydrostatic pressure. By inverting the sample against the nanopositioner, we confirmed that tensile strain along the a-axis inversely raised the transition temperature [Fig. 2(c)]. On the other hand, we found that compressive strain along the b-axis also raised the transition temperature, as shown in Fig. 2(d).These results differ from the conventional uniaxial strain effects on α-(BEDT-TTF)2I3. According to the literature,1313. N. Tajima, A. Tajima, M. Tamura, Y. Nishio, and K. Kajita, J. Phys. Soc. Jpn. 71, 1832 (2002). https://doi.org/10.1143/JPSJ.71.1832 the compressive strain of more than 5 kbar in the a-axis direction results in a narrow-gap semiconducting state, while the compressive strain of more than 3 kbar in the b-axis direction results in a metal with a large Fermi pocket. Conventionally, the uniaxial strain on organic conductors has been applied by encapsulating the crystals with epoxy resin, sealing them in a pressure cell, and applying pressure. This method suppresses the Poisson effect and allows more accurate measurements of the effect of compression in a specific direction. In our method, compression in the a-axis (b-axis) causes elongation in the b-axis (a-axis), resulting in a more significant change in in-plane anisotropy. The large anisotropy may have caused the differences from the conventional uniaxial strain effects. Specifically, the a-axis compression resulted in the realization of the Dirac state with little strain. In contrast, the b-axis compression enhanced the insulating behavior, probably because the a-axis elongation effect was dominant.We measured the magnetic field effect on the strained samples to confirm whether the massless Dirac state is realized indeed. Figure 3 shows the temperature dependence of the in-plane resistivity under magnetic fields perpendicular to the conducting plane. The maximum magnetoresistance reached approximately 102, showing that the electronic state is different from the metallic state of α-(BEDT-TTF)2I3. The resistivity vs temperature curves exhibit characteristic peak structures under magnetic fields, as in the case of hydrostatic pressure [Fig. 3(a)]. The peaks correspond to characteristic temperatures below which only the n = 0 Landau level contributes to the electronic conduction (quantum limit) and cannot be simulated using a parabolic energy band.18,1918. T. Morinari and T. Tohyama, Phys. Rev. B 82, 165117 (2010). https://doi.org/10.1103/PhysRevB.82.16511719. I. Proskurin, M. Ogata, and Y. Suzumura, Phys. Rev. B 91, 195413 (2015). https://doi.org/10.1103/PhysRevB.91.195413 The peak temperature Tp is roughly scaled by B, reflecting the energy spacing of the Landau levels of 2eℏvF2B, as shown in Fig. 3(b). However, the intercept with zero magnetic field is quite large, possibly because inhomogeneous strain broadens the Landau levels compared to the case of hydrostatic pressures.2020. A. Mori, Y. Kawasugi, R. Doi, T. Naito, R. Kato, Y. Nishio, and N. Tajima, J. Phys. Soc. Jpn. 91, 045001 (2022). https://doi.org/10.7566/JPSJ.91.045001 Also, the slope of the Tp vs B curve, which is proportional to effective vF, is roughly five times less than that of the bulk crystal under hydrostatic pressure.33. N. Tajima, S. Sugawara, M. Tamura, Y. Nishio, and K. Kajita, J. Phys. Soc. Jpn. 75, 051010 (2006). https://doi.org/10.1143/JPSJ.75.051010 The carrier density estimated from the Hall effect (∼5×1010 cm−2 per conducting layer at 2 K) is also larger than that of the bulk crystal strained with the conventional epoxy resin method (∼2×109 cm−2 per conducting layer at 1.5 K1313. N. Tajima, A. Tajima, M. Tamura, Y. Nishio, and K. Kajita, J. Phys. Soc. Jpn. 71, 1832 (2002). https://doi.org/10.1143/JPSJ.71.1832) implying the effect of the inhomogeneous strain.Finally, we demonstrate that the bending strain can suppress the metal–insulator transition more simply without a nanopositioner. Figure 4 shows an optical image and ρ vs T plots of a manually bent (compressive strain along the a-axis) sample. The applied strain is approximately 2% and suppresses the metal–insulator transition as the measurements using a nanopositioner [red dot in Fig. 4(b)]. After the measurement, we stretched back the sample, then the metal–insulator transition recovered. Thus, a rough manual operation can suppress charge ordering of α-(BEDT-TTF)2I3.

In conclusion, by applying bending uniaxial strains, we have realized the Dirac state of α-(BEDT-TTF)2I3 without encapsulating it in a pressure cell. Compared to conventional uniaxial strain application methods, the metal–insulator transition is suppressed with only a small amount of a-axis strain. Our method likely modifies the in-plane anisotropy of the material more significantly, resulting in a drastic change, which is also possible in other materials. The metal–insulator transition has been suppressed even in manually bent samples without a piezo nanopositioner. It is expected to be applied to photoelectron and tunneling spectroscopy measurements.

We would like to acknowledge the Toyobo Film Solutions Limited for providing the PET films. This work was supported by JSPS KAKENHI (Grant Nos. JP19K03730, JP19H00891, and JP22K03534).

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Yoshitaka Kawasugi: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Haruto Suzuki: Data curation (equal); Formal analysis (equal); Visualization (equal). Hiroshi M. Yamamoto: Conceptualization (equal); Funding acquisition (lead); Methodology (equal); Supervision (equal); Writing – review & editing (equal). Reizo Kato: Funding acquisition (equal); Project administration (equal); Supervision (equal). Naoya Tajima: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

REFERENCES

1. K. Kajita, Y. Nishio, N. Tajima, Y. Suzumura, and A. Kobayashi, J. Phys. Soc. Jpn. 83, 072002 (2014). https://doi.org/10.7566/JPSJ.83.072002, Google ScholarCrossref2. K. Bender, I. Hennig, D. Schweitzer, K. Dietz, H. Endres, and H. J. Keller, Mol. Cryst. Liq. Cryst. 108, 359 (1984). https://doi.org/10.1080/00268948408078687, Google ScholarCrossref, ISI3. N. Tajima, S. Sugawara, M. Tamura, Y. Nishio, and K. Kajita, J. Phys. Soc. Jpn. 75, 051010 (2006). https://doi.org/10.1143/JPSJ.75.051010, Google ScholarCrossref4. S. Katayama, A. Kobayashi, and Y. Suzumura, J. Phys. Soc. Jpn. 75, 054705 (2006). https://doi.org/10.1143/JPSJ.75.054705, Google ScholarCrossref5. N. Tajima, S. Sugawara, R. Kato, Y. Nishio, and K. Kajita, Phys. Rev. Lett. 102, 176403 (2009). https://doi.org/10.1103/PhysRevLett.102.176403, Google ScholarCrossref6. N. Tajima, T. Yamauchi, T. Yamaguchi, M. Suda, Y. Kawasugi, H. M. Yamamoto, R. Kato, Y. Nishio, and K. Kajita, Phys. Rev. B 88, 075315 (2013). https://doi.org/10.1103/PhysRevB.88.075315, Google ScholarCrossref7. M. Hirata, K. Ishikawa, K. Miyagawa, M. Tamura, C. Berthier, D. Basko, A. Kobayashi, G. Matsuno, and K. Kanoda, Nat. Commun. 7, 12666 (2016). https://doi.org/10.1038/ncomms12666, Google ScholarCrossref8. M. Hirata, K. Ishikawa, G. Matsuno, A. Kobayashi, K. Miyagawa, M. Tamura, C. Berthier, and K. Kanoda, Science 358, 1403 (2017). https://doi.org/10.1126/science.aan5351, Google ScholarCrossref9. Y. Unozawa, Y. Kawasugi, M. Suda, H. M. Yamamoto, R. Kato, Y. Nishio, K. Kajita, T. Morinari, and N. Tajima, J. Phys. Soc. Jpn. 89, 123702 (2020). https://doi.org/10.7566/JPSJ.89.123702, Google ScholarCrossref10. C. W. Hicks, M. E. Barber, S. D. Edkins, D. O. Brodsky, and A. P. Mackenzie, Rev. Sci. Instrum. 85, 065003 (2014). https://doi.org/10.1063/1.4881611, Google ScholarScitation, ISI11. C. W. Hicks, D. O. Brodsky, E. A. Yelland, A. S. Gibbs, J. A. N. Bruin, M. E. Barber, S. D. Edkins, K. Nishimura, S. Yonezawa, Y. Maeno, and A. P. Mackenzie, Science 344, 283 (2014). https://doi.org/10.1126/science.1248292, Google ScholarCrossref12. M. Maesato, Y. Kaga, R. Kondo, and S. Kagoshima, Rev. Sci. Instrum. 71, 176 (2000). https://doi.org/10.1063/1.1150180, Google ScholarScitation, ISI13. N. Tajima, A. Tajima, M. Tamura, Y. Nishio, and K. Kajita, J. Phys. Soc. Jpn. 71, 1832 (2002). https://doi.org/10.1143/JPSJ.71.1832, Google ScholarCrossref14. S. Kagoshima and R. Kondo, Chem. Rev. 104, 5593 (2004). https://doi.org/10.1021/cr0306539, Google ScholarCrossref15. T. Yamamoto, R. Kato, H. M. Yamamoto, A. Fukaya, K. Yamasawa, and I. Takahashi, Rev. Sci. Instrum. 78, 083906 (2007). https://doi.org/10.1063/1.2777191, Google ScholarScitation, ISI16. M. Suda, Y. Kawasugi, T. Minari, K. Tsukagoshi, R. Kato, and H. M. Yamamoto, Adv. Mater. 26, 3490 (2014). https://doi.org/10.1002/adma.201305797, Google ScholarCrossref17. Y. Kawasugi and H. M. Yamamoto, Crystals 12, 42 (2022). https://doi.org/10.3390/cryst12010042, Google ScholarCrossref18. T. Morinari and T. Tohyama, Phys. Rev. B 82, 165117 (2010). https://doi.org/10.1103/PhysRevB.82.165117, Google ScholarCrossref19. I. Proskurin, M. Ogata, and Y. Suzumura, Phys. Rev. B 91, 195413 (2015). https://doi.org/10.1103/PhysRevB.91.195413, Google ScholarCrossref20. A. Mori, Y. Kawasugi, R. Doi, T. Naito, R. Kato, Y. Nishio, and N. Tajima, J. Phys. Soc. Jpn. 91, 045001 (2022). https://doi.org/10.7566/JPSJ.91.045001, Google ScholarCrossref© 2023 Author(s). Published under an exclusive license by AIP Publishing.