Observation of Majorana fermions in superfluid 3 He.

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Brice Brooks
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1 XV-Международная Молодежная Научная Школа "Актуальные проблемы магнитного резонанса Казань Observation of Majorana fermions in superfluid 3 He. Yury Bunkov Institut Neel, Grenoble, France Kazan Federal University, Russia

2 Symmetry breaking phase transition E Suprconducters, 4 He, Magnetics, 3 He, Neutron stars A e if Universe A25 e if 4He An a i e if i A e if Paramagnetic Ferromagnetic a i e if i 3He A 9 e if

3 GUT in Standard Model SO10 SU(3) x SU L (2) x U(1) SU(3) x U Q (1)

4 Quantum field theory

5 Superfluid 3 He Quantum vacuum, characterized by Y (phase) S (magnetization) L (orbital momentum) Particles: Quasiparticles Magnons Acoustic modes Fields: Texture of orbital momentum Topological defects: Boojum Vortex Brane

6 Superfluid 3 He is the most complex system of quantum fields, experimentally accessible, for which we already have The Theory of Everything

7 Multiple Higgs bosons from superfluid 3He

10 Multiple Higgs bosons from superfluid 3He

12 - Candidate for Dark matter

15 Fermi liquid

16 Fermi Sea Superfluid D Cooper pairs Physical vacuum

17 Mass Superfluid 3 He Degenerate Vacuum States: Domain wall bound state Domain Wall

18 Andreev scattering Majorana fermions

19 Majorana heat capacity experiment. C. B. Winkelmann, J. Elbs, Yu. M. Bunkov, E. Collin, H. Godfrin and M. Krusius Bolometric calibration of a superfluid 3He detector: direct measurements of the quenching factor for neutron, electron and muonevents Nucl. Instrum. Meth. A574, (2007) J. Elbs, Yu. M. Bunkov, E. Collin, H. Godfrin, O. Suvorova Electron- nuclear recoil discrimination by pulse shape analysis. J. of Low Temp. Phys.. 150, 536, (2008) 3 He E 2mK D k B T -p F p F

20 Number of quasiparticles T 10 exp ( - D ) kt kev K cm 3 Heat capacity, ev/cm V/Ax = Majorana Temperature (µk)

21 6 mm H 4.5 mm VWR-heater VWR-C Thermal contact orifice

22 Superfluid 3 He bolometry Copper box Sintered silver 60 µm hole Detector Vibrating Wires (5 µm and 13 µm) Absolute thermal isolation due to Kapitza resistance

23 Copper box Sintered silver 60 µm hole Vibrating Wires (5 µm and 13 µm)

24 V(µV) V (V) B Self-calibration of 3 He bolometer W(T) Signal en phase I e i w t Lorentz force Induced voltage V e i w t Signal en quadrature fréquence (Hz) f (Hz) Width W(T) measures damping by quasiparticles H a 1/W

25 Current (µa) Voltage (µv) B Self-calibration of 3 He bolometer Heater Heater Thermo Time (ms) 0

26 W mes (Hz) Amplitude (a.u.) Bolometric calibration by pulsed heating Energy injection by heater-vwr U puls = linear dependence H(U puls ) Bradley et al., PRL 1995; Bäuerle et al., PRB 1998 V.Idt 6 4 heater 2 V int W heater = W heater ther W heater 0 I time (s) temps (s) 1.08 thermometer H time temps (s)

27 Bolometric calibration coefficient Specific heat of quasiparticle gas C qp = C 0 T c T 3 / 2 exp ( D/ k B T) Total enthalpy count from zero absolute Calibration coefficient = dw du = A 1 U T + Vibrating Wire damping W exp ( D /k B T)

28 Bolometric calibration by pulsed heating 1/ T

29 W ret (Hz) Response to an instantaneous heat release Thermal equilibrium time eq 1 ms Relaxation time of the bolometer b 1/ S orifice 5 s Instantaneous heat release W 0 (t) = W base Aexp(t/ b ) (t) W ret (Hz) H A Response time of the thermometer w = 1/W time temps (s) Dynamical response of the thermometer W ret (t) = W base A b exp(t / b ) exp(t / w ) b w y = m1*(m3/(m3-0.77))*... m1 m2 m3 (t) Value Error e

30 Bolometric calibration by pulsed heating VWR intrinsic Loses + Majorana heat capecity 1/ T Thermometer delay

31 W mes (Hz) Amplitude (a.u.) Bolometric calibration by pulsed heating Energy injection by heater-vwr U puls = linear dependence H(U puls ) Bradley et al., PRL 1995; Bäuerle et al., PRB 1998 V.Idt 6 4 heater 2 V W heater = W int heater W QP heater 0 I time (s) temps (s) 1.08 thermometer H time temps (s)

32 Current (µa) Voltage (µv) B Self-calibration of 3 He bolometer Heater Heater Thermo Time (ms) 0

34 Grenoble 2011 exp = C total /C bulk

35 Heat capacity, ev/cm 3 Number of quasiparticles T 10 exp ( - D ) kt kev K cm V/Ax = Majorana Temperature (µk)

Message from 3He-B to Standard Model: sum rule found by Nambu in 3He-B gives a hint for extra Higgs bosons By the considered experiment the existence of low energy gapless

The further experiments with a developed surface of the walls and with different amplitude of magnetic field are desire Acoustic investigations Review: Okuda Y and Nomura

36 Message from 3He-B to Standard Model: sum rule found by Nambu in 3He-B gives a hint for extra Higgs bosons By the considered experiment the existence of low energy gapless excitations is established and measured by its heat capacity. They are corresponds to a prediction of gapless Majorana excitations! The further experiments with a developed surface of the walls and with different amplitude of magnetic field are desire Acoustic investigations Review: Okuda Y and Nomura R, J. Phys.: Condens. Matter 24 (2012) , Electron bubble probe K. Kono, RIKEN. V. Mourik et all. "Signatures of Majorana fermions in hybrid superconductorsemiconductor nanowire devices". Science. arxiv:

First, we need a rapid look at the fundamental structure of superfluid 3 He. and then see how similar it is to the structure of the Universe.

Outline of my talk: First, we need a rapid look at the fundamental structure of superfluid 3 He and then see how similar it is to the structure of the Universe. Then we will look at our latest ideas on