• Zhang, Y. J. et al. Enhanced intrinsic photovoltaic effect in tungsten disulfide nanotubes. Nature 570, 349–353 (2019).

    Article 
    ADS 

    Google Scholar
     

  • Tokura, Y. & Nagaosa, N. Nonreciprocal responses from non-centrosymmetric quantum materials. Nat. Commun. 9, 3740 (2018).

    Article 
    ADS 

    Google Scholar
     

  • Yuan, H. et al. Generation and electric control of spin-valley-coupled circular photogalvanic current in WSe2. Nat. Nanotechnol. 9, 851–857 (2014).

    Article 
    ADS 

    Google Scholar
     

  • Yang, S. H., Naaman, R., Paltiel, Y. & Parkin, S. S. P. Chiral spintronics. Nat. Rev. Phys. 3, 328–343 (2021).

    Article 

    Google Scholar
     

  • Naaman, R., Paltiel, Y. & Waldeck, D. H. Chiral molecules and the electron spin. Nat. Rev. Chem. 3, 250–260 (2019).

    Article 

    Google Scholar
     

  • Nakajima, R. et al. Giant spin polarization and a pair of antiparallel spins in a chiral superconductor. Nature 613, 479–484 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Sun, R. et al. Inverse chirality-induced spin selectivity effect in chiral assemblies of π-conjugated polymers. Nat. Mater. 23, 782–789 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Eckvahl, H. J. et al. Direct observation of chirality-induced spin selectivity in electron donor–acceptor molecules. Science 382, 197–201 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Kishine, J., Ovchinnikov, A. S. & Tereshchenko, A. A. Chirality-induced phonon dispersion in a noncentrosymmetric micropolar crystal. Phys. Rev. Lett. 125, 245302 (2020).

    Article 
    ADS 

    Google Scholar
     

  • Ishito, K. et al. Truly chiral phonons in α-HgS. Nat. Phys. 19, 35–39 (2023).

    Article 

    Google Scholar
     

  • Ueda, H. et al. Chiral phonons in quartz probed by X-rays. Nature 618, 946–950 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Yen, Y. et al. Controllable orbital angular momentum monopoles in chiral topological semimetals. Nat. Phys. 20, 1912–1918 (2024).

    Article 

    Google Scholar
     

  • Yang, Q. et al. Monopole-like orbital-momentum locking and the induced orbital transport in topological chiral semimetals. Proc. Natl Acad. Sci. USA 120, e2305541120 (2023).

    Article 

    Google Scholar
     

  • Joseph, N. B., Bandyopadhyay, A. & Narayan, A. Chirality-tunable nonlinear Hall effect. Chem. Mater. 36, 8602–8612 (2024).


    Google Scholar
     

  • Cheng, B. et al. Giant nonlinear Hall and wireless rectification effects at room temperature in the elemental semiconductor tellurium. Nat. Commun. 15, 5513 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Nakai, R. & Nagaosa, N. Nonreciprocal thermal and thermoelectric transport of electrons in noncentrosymmetric crystals. Phys. Rev. B 99, 115201 (2019).

    Article 
    ADS 

    Google Scholar
     

  • Osada, T. & Kiswandhi, A. Possible nonlinear anomalous thermoelectric effect in organic massive Dirac fermion system. J. Phys. Soc. Jpn 90, 053704 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Zeng, C., Nandy, S. & Tewari, S. Fundamental relations for anomalous thermoelectric transport coefficients in the nonlinear regime. Phys. Rev. Res. 2, 032066(R) (2020).

    Article 

    Google Scholar
     

  • Zeng, C., Nandy, S., Taraphder, A. & Tewari, S. Nonlinear Nernst effect in bilayer WTe2. Phys. Rev. B 100, 245102 (2019).

    Article 
    ADS 

    Google Scholar
     

  • Yu, X. Q., Zhu, Z. G., You, J. S., Low, T. & Su, G. Topological nonlinear anomalous Nernst effect in strained transition metal dichalcogenides. Phys. Rev. B 99, 201410(R) (2019).

    Article 
    ADS 

    Google Scholar
     

  • Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015).

    Article 
    ADS 

    Google Scholar
     

  • Yamaguchi, T., Nakazawa, K. & Yamakage, A. Microscopic theory of nonlinear Hall effect induced by electric field and temperature gradient. Phys. Rev. B 109, 205117 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Arisawa, H., Fujimoto, Y., Kikkawa, T. & Saitoh, E. Observation of nonlinear thermoelectric effect in MoGe/Y3Fe5O12. Nat. Commun. 15, 6912 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Chang, C. W., Okawa, D., Majumdar, A. & Zettl, A. Solid-state thermal rectifier. Science 314, 1121–1124 (2006).

    Article 
    ADS 

    Google Scholar
     

  • Li, B., Wang, L. & Casati, G. Thermal diode: rectification of heat flux. Phys. Rev. Lett. 93, 184301 (2004).

    Article 
    ADS 

    Google Scholar
     

  • Hidaka, Y., Pu, S. & Yang, D. L. Nonlinear responses of chiral fluids from kinetic theory. Phys. Rev. D 97, 016004 (2018).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Toshio, R., Takasan, K. & Kawakami, N. Anomalous hydrodynamic transport in interacting noncentrosymmetric metals. Phys. Rev. Res. 2, 032021(R) (2020).

    Article 

    Google Scholar
     

  • Bottom, V. E. The Hall effect and electrical resistivity of tellurium. Science 115, 570–571 (1952).

    Article 
    ADS 

    Google Scholar
     

  • Lin, S. et al. Tellurium as a high-performance elemental thermoelectric. Nat. Commun. 7, 10287 (2016).

    Article 
    ADS 

    Google Scholar
     

  • Peng, H., Kioussis, N. & Snyder, G. J. Elemental tellurium as a chiral p-type thermoelectric material. Phys. Rev. B 89, 195206 (2014).

    Article 
    ADS 

    Google Scholar
     

  • Adams, A. R., Baumann, F. & Stuke, J. Thermal conductivity of selenium and tellurium single crystals and phonon drag of tellurium. Phys. Status Solidi B 23, K99–K104 (1967).

    Article 
    ADS 

    Google Scholar
     

  • Mun, E., Bud’Ko, S. L., Torikachvili, M. S. & Canfield, P. C. Experimental setup for the measurement of the thermoelectric power in zero and applied magnetic field. Meas. Sci. Technol. 21, 055104 (2010).

    Article 
    ADS 

    Google Scholar
     

  • Resel, R. et al. Thermopower measurements in magnetic fields up to 17 tesla using the toggled heating method. Rev. Sci. Instrum. 67, 1970–1975 (1996).

    Article 
    ADS 

    Google Scholar
     

  • Nakazawa, K., Yamaguchi, T. & Yamakage, A. Nonlinear charge transport properties in chiral tellurium. Phys. Rev. Mater. 8, L091601 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Koma, A. & Tanaka, S. Etch pits and crystal structure of tellurium. Phys. Status Solidi B 40, 239–248 (1970).

    Article 
    ADS 

    Google Scholar
     

  • Nakazawa, K., Yamaguchi, T. & Yamakage, A. Nonlinear charge and thermal transport properties induced by orbital magnetic moment in chiral crystalline cobalt monosilicide. Phys. Rev. B 111, 045161 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Yoda, T., Yokoyama, T. & Murakami, S. Orbital Edelstein effect as a condensed-matter analog of solenoids. Nano Lett. 18, 916–920 (2018).

    Article 
    ADS 

    Google Scholar
     

  • Maruggi, G. P., Ferreira, J., Baggio-Saitovitch, E., Enderlein, C. & Silva Neto, M. B. Hedgehog orbital texture in p-type tellurium and the antisymmetric nonreciprocal Hall response. Phys. Rev. Mater. 7, 014204 (2023).

    Article 

    Google Scholar
     

  • Zhao, X. et al. Controllable synthesis of high-quality two-dimensional tellurium by a facile chemical vapor transport strategy. iScience 25, 103594 (2022).

    Article 
    ADS 

    Google Scholar
     

  • Hou, D. et al. Observation of temperature-gradient-induced magnetization. Nat. Commun. 7, 12265 (2016).

    Article 
    ADS 

    Google Scholar
     

  • Chun, S. H., Salamon, M. B., Tomioka, Y. & Tokura, Y. Breakdown of the lattice polaron picture in La0.7Ca0.3MnO3 single crystals. Phys. Rev. B 61, R9225(R) (2000).

    Article 
    ADS 

    Google Scholar
     

  • Rani, D., Kangsabanik, J., Suresh, K. G. & Alam, A. Disorder-mediated quenching of magnetization in NbVTiAl: theory and experiment. J. Magn. Magn. Mater. 551, 169124 (2022).

    Article 

    Google Scholar
     

  • Caldwell, R. S. & Fan, H. Y. Optical properties of tellurium and selenium. Phys. Rev. 114, 664–675 (1959).

    Article 
    ADS 

    Google Scholar