[论文解读] Magnetotransport in a model of a disordered strange metal

Aavishkar A. Patel, John McGreevy+2 more|arXiv (Cornell University)|Dec 13, 2017

Rare-earth and actinide compounds被引用 7

一句话总结

该论文提出了一种可解的、具有大N的无序奇异金属模型，其中巡游电子与由Sachdev-Ye-Kitaev（SYK）模型描述的随机量子点耦合，重现了奇异金属中观测到的线性温度依赖电阻率和出人意料的线性磁场依赖磁阻。该模型实现了无准粒子的扩散型边缘费米液体，宏观无序导致在高场下宏观线性磁阻呈现$\rho \sim B$的标度，与近期在铜氧化物和铁基超导体中的实验结果一致。

ABSTRACT

Despite much theoretical effort, there is no complete theory of the 'strange' metal state of the high temperature superconductors, and its linear-in-temperature, $T$, resistivity. Recent experiments showing an unexpected linear-in-field, $B$, magnetoresistivity have deepened the puzzle. We propose a simple model of itinerant electrons, interacting via random couplings with electrons localized on a lattice of quantum 'dots' or 'islands'. This model is solvable in a large-$N$ limit, and can reproduce observed behavior. The key feature of our model is that the electrons in each quantum dot are described by a Sachdev-Ye-Kitaev model describing electrons without quasiparticle excitations. For a particular choice of the interaction between the itinerant and localized electrons, this model realizes a controlled description of a diffusive marginal-Fermi liquid (MFL) without momentum conservation, which has a linear-in-$T$ resistivity and a $T \ln T$ specific heat as $T ightarrow 0$. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite-$T$ crossover to a fully incoherent regime that also has a linear-in-$T$ resistivity. We show that the MFL regime has conductivities which scale as a function of $B/T$; however, its magnetoresistance saturates at large $B$. We then consider a macroscopically disordered sample with domains of MFLs with varying densities of electrons. Using an effective-medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the magnetic field $B$ applied perpendicular to the plane of the sample, at large $B$. The resistance also scales linearly in $T$ at small $B$, and as $T f(B/T)$ at intermediate $B$. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates.

研究动机与目标

• 解释高温超导体奇异金属相中观测到的线性温度依赖电阻率和出人意料的线性磁场依赖磁阻。
• 构建一个无准粒子激发的非费米液体态的受控且可解的模型。
• 通过有效介质近似，将局域电子的微观SYK模型与宏观输运行为联系起来。
• 重现奇异金属区间的实验观测结果$\rho \sim T$和$\rho \sim B$的标度行为。

提出的方法

• 该模型由巡游电子与由Sachdev-Ye-Kitaev（SYK）模型描述的随机全连接相互作用的量子点晶格耦合而成。
• SYK模型提供了一个可解的非费米液体固定点，其格林函数满足$G(\omega) \sim 1/\sqrt{\omega}$，且自能虚部满足$\mathrm{Im}\,\chi(\omega) \sim \tanh(\omega/2T)$。
• 采用大N极限使模型精确可解，从而利用Keldysh形式和梯度展开计算输运性质。
• 应用Keldysh形式计算在弱电场和磁场下传导电子格林函数及自能修正。
• 采用有效介质近似，对空间变化的电子和岛密度进行建模，从而实现宏观无序下的宏观输运行为。
• 通过求解在$\mathbf{E}$和$\mathbf{B}$存在下的线性化输运方程分析磁输运，得到电导率随$B/T$的变化关系。

实验结果

研究问题

• RQ1 可解的巡游电子与SYK量子点耦合模型能否重现奇异金属的线性温度依赖电阻率？
• RQ2 此类模型是否自然地产生线性磁场依赖磁阻，如近期在铜氧化物和铁基超导体中所观测？
• RQ3 局域SYK子系统中无准粒子的存在如何影响巡游电子的输运性质？
• RQ4 宏观无序在生成宏观线性磁阻标度$\rho \sim B$中起什么作用？
• RQ5 该模型能否描述从扩散型边缘费米液体到完全相干性丧失的线性电阻率$\rho \sim T$的转变？

主要发现

• 该模型实现了无动量守恒的扩散型边缘费米液体（MFL），表现出线性温度依赖电阻率和低温下$T\ln T$的比热。
• MFL区表现出电导率随$B/T$的变化关系，且在大磁场下磁阻趋于饱和。
• 通过调节耦合强度与能带宽度的相对大小，模型在有限温度下表现出向完全无序区的转变，其电阻率呈线性温度依赖。
• 在具有空间变化的电子和岛密度的宏观无序样品中，有效介质近似导出的宏观电阻率在高场下与$B$呈线性关系。
• 在小$B$下，电阻率也与$T$呈线性关系；在中等磁场下，电阻率随$T f(B/T)$变化，与实验趋势一致。
• 该模型在非费米液体态中提供了线性磁阻的受控实现，与近期高温超导体中的观测结果一致。