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1

Batra, Inder P. "Origin of conductance quantization." Surface Science 395, no. 1 (January 1998): 43–45. http://dx.doi.org/10.1016/s0039-6028(97)00601-8.

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2

Sorée, Bart, Wim Magnus, and Wim Schoenmaker. "Conductance quantization and dissipation." Physics Letters A 310, no. 4 (April 2003): 322–28. http://dx.doi.org/10.1016/s0375-9601(03)00351-7.

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3

Nöckel, J. U. "Conductance quantization and backscattering." Physical Review B 45, no. 24 (June 15, 1992): 14225–30. http://dx.doi.org/10.1103/physrevb.45.14225.

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4

Cosby, Ronald M., Dustin R. Humm, and Yong S. Joe. "Nanoelectronics using conductance quantization." Journal of Applied Physics 83, no. 7 (April 1998): 3914–16. http://dx.doi.org/10.1063/1.366626.

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5

SARMA, S. DAS, and SONG HE. "THEORY OF ELECTRON TRANSPORT THROUGH QUANTUM CONSTRICTIONS IN SEMICONDUCTOR NANOSTRUCTURES." International Journal of Modern Physics B 07, no. 19 (August 30, 1993): 3375–404. http://dx.doi.org/10.1142/s0217979293003279.

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Detailed numerical results are presented for the calculated conductance of quantum point contacts, or, narrow constrictions between high mobility two-dimensional electron systems fabricated on semiconductor nanostructures. The conductance is calculated from the two-terminal multichannel transmission matrix formalism using the recursive single-particle Green’s function technique. The Green’s functions are obtained recursively for a tight-binding two-dimensional disordered Anderson lattice model representing the constriction. The conductance is calculated as a function of the shape and the size of the constriction (i.e., its geometry), the temperature, and, the elastic disorder in the system. Our main results, which are consistent with experimental findings, are: (1) increase of elastic scattering destroys the quantization; (2) for a fixed amount of disorder (i.e., for a given value of the elastic mean free path), the conductance quantization is poorer for longer constrictions; (3) in general, the quantization is poorer for higher quantum numbers or subbands; (4) constrictions with sharper geometry have sharper quantization, but may have quantum resonances associated with their sharp corners; (5) the quantum resonances (in sharp constrictions) are suppressed for shorter constriction lengths and at higher temperatures; (6) in general, higher temperatures lower the quantization quality by smoothening out the conductance except for sharp constrictions where at the lowest temperatures the quantum resonances show up, adversely affecting the quantization; (7) in smooth or adiabatic constrictions, the conductance quantization is smooth (but not extremely accurate) but, adiabaticity is not a necessary requirement for conductance quantization; (8) in general, geometry, finite temperature, and finite disorder effects do not allow better than 1% type accuracy in the quantization (compared with integral multiples of 2e2/h) even in the best of circumstances; (9) increase of elastic disorder smoothly takes the system from a conductance quantized regime to the regime of universal conductance fluctuations; and, (10) inelastic scattering, which we treat only in a very crude phenomenological model, behaves similar to thermal effects in broadening and smearing the sharpness of the conductance quantization. We also discuss the effect of an external magnetic field on the conductance quantization phenomenon. Some results are given for the conductance of two constrictions in series.
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6

Takayanagi, Kunio, Yukihito Kondo, and Hideo Ohnishi. "Conductance Quantization of Gold Nanowire." Materia Japan 40, no. 12 (2001): 1000. http://dx.doi.org/10.2320/materia.40.1000.

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7

Bascones, E., G. Gómez-Santos, and J. J. Sáenz. "Statistical significance of conductance quantization." Physical Review B 57, no. 4 (January 15, 1998): 2541–44. http://dx.doi.org/10.1103/physrevb.57.2541.

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8

Krompiewski, S. "Conductance quantization in ferromagnetic nanowires." Journal of Physics: Condensed Matter 12, no. 7 (February 3, 2000): 1323–28. http://dx.doi.org/10.1088/0953-8984/12/7/315.

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9

Kivelson, S., and S. A. Trugman. "Quantization of the Hall conductance from density quantization alone." Physical Review B 33, no. 6 (March 15, 1986): 3629–35. http://dx.doi.org/10.1103/physrevb.33.3629.

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10

Ooka, Yutaka, Teruo Ono, and Hideki Miyajima. "Conductance quantization in ferromagnetic Ni nanowire." Journal of Magnetism and Magnetic Materials 226-230 (May 2001): 1848–49. http://dx.doi.org/10.1016/s0304-8853(00)00881-7.

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11

Yacoby, A., H. L. Stormer, Ned S. Wingreen, L. N. Pfeiffer, K. W. Baldwin, and K. W. West. "Nonuniversal Conductance Quantization in Quantum Wires." Physical Review Letters 77, no. 22 (November 25, 1996): 4612–15. http://dx.doi.org/10.1103/physrevlett.77.4612.

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12

Lehmann, H., T. Benter, I. von Ahnen, J. Jacob, T. Matsuyama, U. Merkt, U. Kunze, et al. "Spin-resolved conductance quantization in InAs." Semiconductor Science and Technology 29, no. 7 (May 12, 2014): 075010. http://dx.doi.org/10.1088/0268-1242/29/7/075010.

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13

Poncharal, Ph, St Frank, Z. L. Wang, and W. A. de Heer. "Conductance quantization in multiwalled carbon nanotubes." European Physical Journal D 9, no. 1 (December 1999): 77–79. http://dx.doi.org/10.1007/s100530050402.

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14

Nawrocki, Waldemar. "Electrical and thermal conductance quantization in nanostructures." Journal of Physics: Conference Series 129 (October 1, 2008): 012023. http://dx.doi.org/10.1088/1742-6596/129/1/012023.

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15

Sorée, Bart, Wim Magnus, and Wim Schoenmaker. "Nonequilibrium mesoscopic quantum transport and conductance quantization." Semiconductor Science and Technology 19, no. 4 (March 8, 2004): S235—S237. http://dx.doi.org/10.1088/0268-1242/19/4/079.

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16

Hickmott, T. W. "Fractional Quantization in ac Conductance ofAlxGa1−xAsCapacitors." Physical Review Letters 57, no. 6 (August 11, 1986): 751–54. http://dx.doi.org/10.1103/physrevlett.57.751.

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17

Kaufman, D., Y. Berk, B. Dwir, A. Rudra, A. Palevski, and E. Kapon. "Conductance quantization in V-groove quantum wires." Physical Review B 59, no. 16 (April 15, 1999): R10433—R10436. http://dx.doi.org/10.1103/physrevb.59.r10433.

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18

Shimizu, Masayoshi, Eiji Saitoh, Hideki Miyajima, and Yoshichika Otani. "Conductance quantization in ferromagnetic Ni nano-constriction." Journal of Magnetism and Magnetic Materials 239, no. 1-3 (February 2002): 243–45. http://dx.doi.org/10.1016/s0304-8853(01)00544-3.

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19

Yosefin, M., and M. Kaveh. "Conductance quantization in a general confining potential." Physical Review B 44, no. 7 (August 15, 1991): 3355–58. http://dx.doi.org/10.1103/physrevb.44.3355.

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20

Zwolak, Michael, James Wilson, and Massimiliano Di Ventra. "Dehydration and ionic conductance quantization in nanopores." Journal of Physics: Condensed Matter 22, no. 45 (October 29, 2010): 454126. http://dx.doi.org/10.1088/0953-8984/22/45/454126.

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21

Leng, Manhua, and Craig S. Lent. "Conductance quantization in a periodically modulated channel." Physical Review B 50, no. 15 (October 15, 1994): 10823–33. http://dx.doi.org/10.1103/physrevb.50.10823.

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22

Magnus, Wim, and Wim Schoenmaker. "Quantized conductance, circuit topology, and flux quantization." Physical Review B 61, no. 16 (April 15, 2000): 10883–89. http://dx.doi.org/10.1103/physrevb.61.10883.

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23

Katsnelson, M. I. "Conductance quantization in graphene nanoribbons: adiabatic approximation." European Physical Journal B 57, no. 3 (June 2007): 225–28. http://dx.doi.org/10.1140/epjb/e2007-00168-5.

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24

Zwolak, Michael, James Wilson, Johan Lagerqvist, and Massimiliano Di Ventra. "Dehydration and Ionic Conductance Quantization in Nanopores." Biophysical Journal 100, no. 3 (February 2011): 471a. http://dx.doi.org/10.1016/j.bpj.2010.12.2761.

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25

Bachmann, Sven, Alex Bols, Wojciech De Roeck, and Martin Fraas. "Quantization of Conductance in Gapped Interacting Systems." Annales Henri Poincaré 19, no. 3 (February 20, 2018): 695–708. http://dx.doi.org/10.1007/s00023-018-0651-0.

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26

Bezák, Viktor. "Conductance quantization of an ideal Sharvin contact." Annals of Physics 322, no. 11 (November 2007): 2603–17. http://dx.doi.org/10.1016/j.aop.2007.06.002.

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27

Faist, J., P. Guéret, and H. Rothuizen. "Observation of impurity effects on conductance quantization." Superlattices and Microstructures 7, no. 4 (January 1990): 349–51. http://dx.doi.org/10.1016/0749-6036(90)90224-u.

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28

Bracken, Paul. "Topological invariance of the Hall conductance and quantization." Modern Physics Letters B 29, no. 24 (September 3, 2015): 1550135. http://dx.doi.org/10.1142/s0217984915501353.

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It is shown that the Kubo equation for the Hall conductance can be expressed as an integral which implies quantization of the Hall conductance. The integral can be interpreted as the first Chern class of a [Formula: see text] principal fiber bundle on a two-dimensional torus. This accounts for the conductance given as an integer multiple of [Formula: see text]. The formalism can be extended to deduce the fractional conductivity as well.
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29

Srivastav, Saurabh Kumar, Manas Ranjan Sahu, K. Watanabe, T. Taniguchi, Sumilan Banerjee, and Anindya Das. "Universal quantized thermal conductance in graphene." Science Advances 5, no. 7 (July 2019): eaaw5798. http://dx.doi.org/10.1126/sciadv.aaw5798.

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The universal quantization of thermal conductance provides information on a state's topological order. Recent measurements revealed that the observed value of thermal conductance of the 52 state is inconsistent with either Pfaffian or anti-Pfaffian model, motivating several theoretical articles. Analysis has been made complicated by the presence of counter-propagating edge channels arising from edge reconstruction, an inevitable consequence of separating the dopant layer from the GaAs quantum well and the resulting soft confining potential. Here, we measured thermal conductance in graphene with atomically sharp confining potential by using sensitive noise thermometry on hexagonal boron-nitride encapsulated graphene devices, gated by either SiO2/Si or graphite back gate. We find the quantization of thermal conductance within 5% accuracy for ν = 1;43;2 and 6 plateaus, emphasizing the universality of flow of information. These graphene quantum Hall thermal transport measurements will allow new insight into exotic systems like even-denominator quantum Hall fractions in graphene.
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30

Fadaly, Elham M. T., Hao Zhang, Sonia Conesa-Boj, Diana Car, Önder Gül, Sébastien R. Plissard, Roy L. M. Op het Veld, Sebastian Kölling, Leo P. Kouwenhoven, and Erik P. A. M. Bakkers. "Observation of Conductance Quantization in InSb Nanowire Networks." Nano Letters 17, no. 11 (July 14, 2017): 6511–15. http://dx.doi.org/10.1021/acs.nanolett.7b00797.

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31

Agraït, N., J. G. Rodrigo, and S. Vieira. "Conductance steps and quantization in atomic-size contacts." Physical Review B 47, no. 18 (May 1, 1993): 12345–48. http://dx.doi.org/10.1103/physrevb.47.12345.

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32

Alekseev, Anton Yu, and Vadim V. Cheianov. "Nonuniversal conductance quantization in high-quality quantum wires." Physical Review B 57, no. 12 (March 15, 1998): R6834—R6837. http://dx.doi.org/10.1103/physrevb.57.r6834.

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33

Elhoussine, F., S. Mátéfi-Tempfli, A. Encinas, and L. Piraux. "Conductance quantization in magnetic nanowires electrodeposited in nanopores." Applied Physics Letters 81, no. 9 (August 26, 2002): 1681–83. http://dx.doi.org/10.1063/1.1503400.

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34

Costa-Krämer, J. L., N. García, and H. Olin. "Conductance Quantization in Bismuth Nanowires at 4 K." Physical Review Letters 78, no. 26 (June 30, 1997): 4990–93. http://dx.doi.org/10.1103/physrevlett.78.4990.

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35

Yanson, A. I., and J. M. van Ruitenbeek. "Do Histograms Constitute a Proof for Conductance Quantization?" Physical Review Letters 79, no. 11 (September 15, 1997): 2157. http://dx.doi.org/10.1103/physrevlett.79.2157.

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36

Taboryski, R., A. Kristensen, C. B. So/rensen, and P. E. Lindelof. "Conductance-quantization broadening mechanisms in quantum point contacts." Physical Review B 51, no. 4 (January 15, 1995): 2282–86. http://dx.doi.org/10.1103/physrevb.51.2282.

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37

Li, C. Z., H. X. He, A. Bogozi, J. S. Bunch, and N. J. Tao. "Molecular detection based on conductance quantization of nanowires." Applied Physics Letters 76, no. 10 (March 6, 2000): 1333–35. http://dx.doi.org/10.1063/1.126025.

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38

Kiesslich, G., A. Wacker, and E. Sch�ll. "Geometry Effects at Conductance Quantization in Quantum Wires." physica status solidi (b) 216, no. 2 (December 1999): R5—R6. http://dx.doi.org/10.1002/(sici)1521-3951(199912)216:23.0.co;2-1.

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39

Oshima, Hirotaka, and Kenjiro Miyano. "Spin-dependent conductance quantization in nickel point contacts." Applied Physics Letters 73, no. 15 (October 12, 1998): 2203–5. http://dx.doi.org/10.1063/1.122423.

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40

Younis, Adnan, Dewei Chu, and Sean Li. "Voltage sweep modulated conductance quantization in oxide nanocomposites." J. Mater. Chem. C 2, no. 48 (October 10, 2014): 10291–97. http://dx.doi.org/10.1039/c4tc01984a.

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41

Imamura, Hiroshi, Nobuhiko Kobayashi, Saburo Takahashi, and Sadamichi Maekawa. "Conductance Quantization and Magnetoresistance in Magnetic Point Contacts." Physical Review Letters 84, no. 5 (January 31, 2000): 1003–6. http://dx.doi.org/10.1103/physrevlett.84.1003.

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42

Li, Jingze, Taisuke Kanzaki, Kei Murakoshi, and Yoshihiro Nakato. "Metal-dependent conductance quantization of nanocontacts in solution." Applied Physics Letters 81, no. 1 (July 2002): 123–25. http://dx.doi.org/10.1063/1.1491015.

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43

Xu, Ying, Xingqiang Shi, Zhi Zeng, Zhao Yang Zeng, and Baowen Li. "Conductance oscillation and quantization in monatomic Al wires." Journal of Physics: Condensed Matter 19, no. 5 (January 16, 2007): 056010. http://dx.doi.org/10.1088/0953-8984/19/5/056010.

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44

Faist, J., P. Guéret, and H. Rothuizen. "Possible observation of impurity effects on conductance quantization." Physical Review B 42, no. 5 (August 15, 1990): 3217–19. http://dx.doi.org/10.1103/physrevb.42.3217.

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45

Li, C. Z., H. Sha, and N. J. Tao. "Adsorbate effect on conductance quantization in metallic nanowires." Physical Review B 58, no. 11 (September 15, 1998): 6775–78. http://dx.doi.org/10.1103/physrevb.58.6775.

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46

Koma, Tohru, Toru Morishita, and Taro Shuya. "Quantization of Conductance in Quasi-periodic Quantum Wires." Journal of Statistical Physics 174, no. 5 (January 16, 2019): 1137–60. http://dx.doi.org/10.1007/s10955-019-02227-1.

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47

Krinner, Sebastian, Martin Lebrat, Dominik Husmann, Charles Grenier, Jean-Philippe Brantut, and Tilman Esslinger. "Mapping out spin and particle conductances in a quantum point contact." Proceedings of the National Academy of Sciences 113, no. 29 (June 29, 2016): 8144–49. http://dx.doi.org/10.1073/pnas.1601812113.

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We study particle and spin transport in a single-mode quantum point contact, using a charge neutral, quantum degenerate Fermi gas with tunable, attractive interactions. This yields the spin and particle conductance of the point contact as a function of chemical potential or confinement. The measurements cover a regime from weak attraction, where quantized conductance is observed, to the resonantly interacting superfluid. Spin conductance exhibits a broad maximum when varying the chemical potential at moderate interactions, which signals the emergence of Cooper pairing. In contrast, the particle conductance is unexpectedly enhanced even before the gas is expected to turn into a superfluid, continuously rising from the plateau at 1/h for weak interactions to plateau-like features at nonuniversal values as high as 4/h for intermediate interactions. For strong interactions, the particle conductance plateaus disappear and the spin conductance gets suppressed, confirming the spin-insulating character of a superfluid. Our observations document the breakdown of universal conductance quantization as many-body correlations appear. The observed anomalous quantization challenges a Fermi liquid description of the normal phase, shedding new light on the nature of the strongly attractive Fermi gas.
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48

LESOVICK, G. B. "THERMOPOWER IN BALLISTIC 2D MICROJUNCTION WITH QUANTIZED RESISTANCE." Modern Physics Letters B 03, no. 08 (May 20, 1989): 611–13. http://dx.doi.org/10.1142/s0217984989000960.

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It is shown that thermopower, under condition of good quantization of conductance (in units of e2/h), could be of the order of kB/e. When the temperature difference between opposite sides of a microjunction is finite, thermopower becomes nonlinear. This phenomenon is connected with energy dependence of conductance.
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49

Danneau, R., W. R. Clarke, O. Klochan, A. P. Micolich, A. R. Hamilton, M. Y. Simmons, M. Pepper, and D. A. Ritchie. "Conductance quantization and the 0.7×2e2∕h conductance anomaly in one-dimensional hole systems." Applied Physics Letters 88, no. 1 (January 2, 2006): 012107. http://dx.doi.org/10.1063/1.2161814.

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50

Simanullang, Marolop Dapot Krisman, G. Bimananda M. Wisna, Koichi Usami, and Shunri Oda. "Synthesis and characterization of Ge-core/a-Si-shell nanowires with conformal shell thickness deposited after gold removal for high-mobility p-channel field-effect transistors." Nanoscale Advances 2, no. 4 (2020): 1465–72. http://dx.doi.org/10.1039/d0na00023j.

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