Magnetic field effects on the CDW and SC states in  -(BEDT-TTF) 2 KHg(SCN) 4 Dieter Andres, Sebastian Jakob, Werner Biberacher, Karl Neumaier and Mark Kartsovnik Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Garching, Germany Ilya Sheikin Laboratoire National des Champs Magnétiques Intenses, Grenoble, France Harald Müller European Synchrotron Radiation Facility, Grenoble, France Natalia Kushch Institute of Problems of Chemical Physics, Chernogolovka, Russia

c a  -(BEDT-TTF) 2 KHg(SCN) 4 : basic features BEDT-TTF molecule: bis(ethylenedithio)-tetrathiafulvalene a b  || (300K)  10  20 m  cm   /  || ~ 10 4  10 5  a /  c  2  (300K) /  (1.4K) ~ 10 2 t || /t   670   ,coh /  ||  2.2  T. Mori et al., Bull. Chem. Soc. Jpn. 1990; R. Rousseau et al., J. Phys. I (France) 1996; P. Foury-Leylekian et al., PRB 2010

 -(BEDT-TTF) 2 KHg(SCN) 4 : basic features 2D Fermi surface  CDW formation at  8 K Nesting instability of the Fermi surface Q very low!! small  CDW  k B T CDW  high sensitivity to external conditions: pressure, magnetic field [P. Foury-Leylekian et al., PRB 2010]

Q+Q+ Q-Q- CDW in a magnetic field  Pauli paramagnetic effect: suppresses CDW [W. Dieterich & P. Fulde, 1973] 2BB/vF2BB/vF B Q - < Q + T CDW /T CDW (0), exp Phase diagram of  -(BEDT-TTF) 2 KHg(SCN) 4 P. Christ, W. Biberacher, M.K., et al., JETP Lett ~ 23 T T CDW /T CDW (0) Theory: A. Buzdin & V. Tugushev, JETP 1983 D. Zanchi et al., PRB 1996; P. Grigoriev & D. Lyubshin, PRB 2005 CDW x CDW 0 NM

CDW in a magnetic field  Orbital effect (requires an imperfectly nested FS): stimulates CDW

CDW in a magnetic field  Orbital effect (requires an imperfectly nested FS): stimulates CDW  y ~ 1/B z electrons become effectively more 1D Real space orbit:

D. Andres, M.K., et al., PRB 2001  -(BEDT-TTF) 2 KHg(SCN) 4 CDW in a magnetic field  Orbital effect (requires an imperfectly nested FS): stimulates CDW Theory: D. Zanchi et al., PRB 1996

R    (deg) CDW in a magnetic field  Orbital effect (requires an imperfectly nested FS): stimulates CDW Angle-dependent MagnetoResistance Oscillations (AMRO) in  -(BEDT-TTF) 2 KHg(SCN) 4 P > P c ambient pressure M.K. et al., SSC 1994 normal state CDW state normal state field-induced

D. Andres, M.K., et al., PRB 2001  -(BEDT-TTF) 2 KHg(SCN) 4 CDW in a magnetic field  Orbital effect (requires an imperfectly nested FS): stimulates CDW Theory: D. Zanchi et al., PRB 1996 FICDW at t  ’ > t  ’ * ??? L. Gor’kov & A. Lebed, J. Phys. Lett. (Paris) 1984

CDW in a magnetic field  Field-induced CDW (FICDW) transitions The “slow oscillations”  appear at P  P c  2.5 kbar  approximately periodic with 1/B SdHo  display a weak hysteresis P = 3 kbar Positions of the FICDW transitions can be fitted with t   0.5 meV [A. Lebed, PRL 2010]

CDW in a magnetic field  Field-induced CDW (FICDW) transitions A. Kornilov et al., PRB 2002 FICDW in  -(BEDT-TTF) 2 KHg(SCN) 4 FISDW in (TMTSF) 2 PF 6 A. Lebed, JETP Lett FICDW is weaker than FISDW due to the paramagnetic effect!

Superconductivity vs. CDW Sample #2: zero resistance but no Meissner! R  (Ohm) R  0 R = 0  Resistance at zero field See also: H. Ito et al., SSC (1993) – inhomogeneous superconductivity at P = 0

Superconductivity vs. CDW A. Kusmartseva et al., PRL 2009 Cu x TiSe 2 NbSe 3 S. Yasuzuka et al., J. Phys. Soc. Jpn R. Yomo et al., PRB 2005 ZrTe 3 (TMTSF) 2 PF 6 I. J. Lee et al., PRL 2002

Superconductivity vs. CDW  Onset of superconductivity

The SC onset temperature is 3 times higher in the SC/CDW coexistence region! The SC onset temperature is 3 times higher in the SC/CDW coexistence region! Superconductivity vs. CDW  Onset of superconductivity CDW+SC R = 0 R  0

Superconductivity in a magnetic field; P > P c  Critical field  layers at P = 3 kbar:   (0)  250 nm cf. mean free path  1  m

Superconductivity in a magnetic field; P > P c  Critical field // layers GL: H c2  (T c -T ) H p0 : Chandrasekhar-Clogston paramagnetic limit  dH c2 /dT  12 T/K   (0) = 1.0 nm  d/2;  || (0)/   (0)  250! 1.6H p0

Superconductivity in a magnetic field; P > P c T = 90 mK

Superconductivity in a magnetic field; P > P c Direct manifestation of the paramagnetic pair-breaking Direct manifestation of the paramagnetic pair-breaking!

Summary CDW state: rich phase diagram due to the interplay of Pauli paramagnetiorbital competing Pauli paramagnetic and orbital effects of magnetic field SC state: at P < P c : coexists with the CDW state; the SC onset temperature is drastically increased in the coexistence region; at P > P c : bulk SC state with a highly anisotropic H c2 near T c (0) and a clear paramagnetic pair-breaking manifestation of paramagnetic pair-breaking at H // layers.

CDW in a magnetic field  Field-induced density wave transitions, t  ’ >t  ’ *: B kFkF -k F Q x = 2k F + NG, G = ea y B z / 

CDW in a magnetic field  Field-induced CDW (FICDW) transitions 2Q P = MG N =3,43,42,32,3 1,21,2 0,10,1 0 Commensurate splitting (A. Bjelis et al., 1999; A. Lebed, 2003) “Spin-zero” 2Q P = (M + 1/2)G with M - integer

CDW in a magnetic field  Field-induced CDW (FICDW) transitions N = no Pauli effect (FISDW) Pauli effect on (FICDW) Q x = 2k F + NG Q x = 2k F  Q P + NG G = 2ea y B z /  Q P = 2  B B/  v F

CDW in a magnetic field  Field-induced CDW (FICDW) transitions 4 N = no Pauli effect (FISDW) Pauli effect on (FICDW) Q x = 2k F + NG Q x = 2k F  Q P + NG A. Lebed, JETP Lett. 78, 138 (2003) G = 2ea y B z /  Q P = 2  B B/  v F

CDW in a magnetic field  Field-induced CDW (FICDW) transitions Spin-zero condition:  v F  1.2  10 5 m/s

The SC onset temperature is 3 times higher in the SC/CDW coexistence region! The SC onset temperature is 3 times higher in the SC/CDW coexistence region! Superconductivity vs. CDW  Onset of superconductivity CDW+SC R = 0 R  0 Ginzburg-Levanyuk parameter: Gi (2) ~ Low Tc  weak fluctuations!

Superconductivity in a magnetic field; P > P c B (mT)  Critical field  layers

Superconductivity in a magnetic field; P > P c  Critical field // layers