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The Planckian relaxation rate $hbar/t_mathrm{P} = 2pi k_mathrm{B} T$ sets a characteristic time scale for both equilibration of quantum critical systems and maximal quantum chaos. In this note, we show that at the critical coupling between a superconducting dot and the complex Sachdev-Ye-Kitaev model, known to be maximally chaotic, the pairing gap $Delta$ behaves as $eta ,, hbar/t_mathrm{P}$ at low temperatures, where $eta$ is an order one constant. The lower critical temperature emerges with a further increase of the coupling strength so that the finite $Delta$ domain is settled between the two critical temperatures.
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A variety of strange metals exhibit resistivity that decreases linearly with temperature as $Trightarrow 0$, in contrast with conventional metals where resistivity decreases as $T^2$. This $T$-linear resistivity has been attributed to charge carriers scattering at a rate given by $hbar/tau=alpha k_{rm B} T$, where $alpha$ is a constant of order unity. This simple relationship between the scattering rate and temperature is observed across a wide variety of materials, suggesting a fundamental upper limit on scattering---the Planckian limit---but little is known about the underlying origins of this limit. Here we report a measurement of the angle-dependent magnetoresistance (ADMR) of Nd-LSCO---a hole-doped cuprate that displays $T$-linear resistivity down to the lowest measured temperatures. The ADMR unveils a well-defined Fermi surface that agrees quantitatively with angle-resolved photoemission spectroscopy (ARPES) measurements and reveals a $T$-linear scattering rate that saturates the Planckian limit, namely $alpha = 1.2 pm 0.4$. Remarkably, we find that this Planckian scattering rate is isotropic, i.e. it is independent of direction, in contrast with expectations from hot-spot models. Our findings suggest that $T$-linear resistivity in strange metals emerges from a momentum-independent inelastic scattering rate that reaches the Planckian limit.
We present a lattice model of fermions with $N$ flavors and random interactions which describes a Planckian metal at low temperatures, $T rightarrow 0$, in the solvable limit of large $N$. We begin with quasiparticles around a Fermi surface with effective mass $m^ast$, and then include random interactions which lead to fermion spectral functions with frequency scaling with $k_B T/hbar$. The resistivity, $rho$, obeys the Drude formula $rho = m^ast/(n e^2 tau_{textrm{tr}})$, where $n$ is the density of fermions, and the transport scattering rate is $1/tau_{textrm{tr}} = f , k_B T/hbar$; we find $f$ of order unity, and essentially independent of the strength and form of the interactions. The random interactions are a generalization of the Sachdev-Ye-Kitaev models; it is assumed that processes non-resonant in the bare quasiparticle energies only renormalize $m^ast$, while resonant processes are shown to produce the Planckian behavior.
We present the electron tunneling transport and its magnetic field modulation of a superconducting (SC) Josephson junction with a barrier of single ferromagnetic (FM) Kitaev layer. We find that at H = 0, the Josephson current IS displays two peaks at K/{Delta} = 3.4 and 10, which stem from the resonant tunnelings between the SC gap boundaries and the spinon flat bands and between the SC gap edges and the spinon dispersive bands, respectively. With the increasing magnetic field, IS gradually decreases and abruptly drops to a platform at the critical magnetic field hc = g{mu}BHc/{Delta} = 0.03K/{Delta}, since the applied field suppresses the spinon density of states (DOS) once upon the Kitaev layer enters the polarized FM phase. These results pave a new way to measure the spinon or Majorana fermion DOS of the Kitaev and other spin liquid materials.
The field-reentrant (field-reinforced) superconductivity on ferromagnetic superconductors is one of the most interesting topics in unconventional superconductivity. The enhancement of effective mass and the induced ferromagnetic fluctuations play key roles for reentrant superconductivity. However, the associated change of the Fermi surface, which is often observed at (pseudo-) metamagnetic transition, can also be a key ingredient. In order to study the Fermi surface instability, we performed Hall effect measurements in the ferromagnetic superconductor URhGe. The Hall effect of URhGe is well explained by two contributions, namely by the normal Hall effect and by the large anomalous Hall effect due to skew scattering. The large change in the Hall coefficient is observed at low fields between the paramagnetic and ferromagnetic states for H // c-axis (easy-magnetization axis) in the orthorhombic structure, indicating that the Fermi surface is reconstructed in the ferromagnetic state below the Curie temperature (T_Curie=9.5K). At low temperatures (T << T_Curie), when the field is applied along the b-axis, the reentrant superconductivity was observed in both the Hall resistivity and the magnetoresistance below 0.4K. Above 0.4K, a large jump with the first-order nature was detected in the Hall resistivity at a spin-reorientation field H_R ~ 12.5T, demonstrating that the marked change of the Fermi surface occurs between the ferromagnetic state and the polarized state above H_R. The results can be understood by the Lifshitz-type transition, induced by the magnetic field or by the change of the effective magnetic field.
Inelastic neutron scattering was used to study the low energy magnetic excitations of the ferromagnetic superconductor UGe$_{2}$. The ferromagnetic fluctuations are of Ising nature with a non-conserved magnetization and have an intermediate behavior between localized and itinerant magnetism.
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